Common Core State StandardsK-5 Mathematics

Presented by Kitty Rutherford and Amy Scrinzi

Normsbull Listen as an Allybull Value Differencesbull Maintain Professionalismbull Participate Actively

050323 050323 bull page 2

Our Goals for this afternoonbull Recognize what makes a good taskbull Recognize how Standards for Practice

mandate better ways of managing instructionbull Importance of the relationship between

multiplication and division

050323 bull page 3

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 4

There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics

Lappan and Briars (1995 pg 138)

050323 bull page 5

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 6

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Normsbull Listen as an Allybull Value Differencesbull Maintain Professionalismbull Participate Actively

050323 050323 bull page 2

Our Goals for this afternoonbull Recognize what makes a good taskbull Recognize how Standards for Practice

mandate better ways of managing instructionbull Importance of the relationship between

multiplication and division

050323 bull page 3

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 4

There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics

Lappan and Briars (1995 pg 138)

050323 bull page 5

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 6

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Our Goals for this afternoonbull Recognize what makes a good taskbull Recognize how Standards for Practice

mandate better ways of managing instructionbull Importance of the relationship between

multiplication and division

050323 bull page 3

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 4

There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics

Lappan and Briars (1995 pg 138)

050323 bull page 5

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 6

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 4

There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics

Lappan and Briars (1995 pg 138)

050323 bull page 5

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 6

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

There is no other decision that teachers make that has a greater impact on studentsrsquo opportunity to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics

Lappan and Briars (1995 pg 138)

050323 bull page 5

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 6

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 6

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Multiplication and Rectangles

Make as many different rectangles as you can using 12 square-inch color tiles

050323 bull page 7

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

What did you notice

bull Were the rectangles the samebull Were the rectangles differentbull How would you describe your

rectanglebull Does that description fit someone

elses rectangle

050323 bull page 8

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 9

Possible Arrays with 12 tiles

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Commutative Property of Multiplication

050323 bull page 10

2 x 4 = 8 4 x 2 = 8

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Multiplication and Rectangles

Find all the rectangles you can make with 18 tiles

Record your rectangles on grid paper

050323 bull page 11

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Multiplication and Rectangles

Nowhellip Letrsquos make a class table from

1- 25

050323 bull page 12

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 13

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 14

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

What do you notice

Which numbers have rectangles with 3 rows List them from smallest to largest

050323 bull page 15

Which numbers have rectangles with 2 rows

List them from smallest to largest

Which numbers on the chart are multiples of 4 (have rectangles with 4 rows)

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

What do you notice

How many different rectangles can you make with 5 tiles

050323 bull page 16

Which numbers on the chart are multiples of 5

How many with 7 tiles

List the prime numbers between 1 and 25Are all odd numbers prime Explain

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Letrsquos look at the number nine

What do you notice

050323 bull page 17

What other numbers have rectangles that are squares

What is the next largest square after 25

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 18

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 19

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip

How many tiles are in each row

Write a number sentence for this rectangle

050323 bull page 20

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

What standards in third and fourth would this task address

How do these standards build on what fifth grade does

050323 bull page 21

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Criteria Area in Third Grade Students use properties of operations to

calculate products of whole numbers using increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving single-digit factors By comparing a variety of solution strategies students learn the relationship between multiplication and division

050323 bull page 22

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Represent and solve problems involving multiplication and division3OA1 Interpret products of whole numbers eg interpret 5 times 7 as the total number

of objects in 5 groups of 7 objects each For example describe a context in which a total number of objects can be expressed as 5 times 7

3OA2 Interpret whole-number quotients of whole numbers eg interpret 56 divide 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each For example describe a context in which a number of shares or a number of groups can be expressed as 56 divide 8

3OA3 Use multiplication and division within 100 to solve word problems in situations involving equal groups arrays and measurement quantities eg by using drawings and equations with a symbol for the unknown number to represent the problem1

3OA4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers For example determine the unknown number that makes the equation true in each of the equations 8 times = 48 5 = 1048781 divide 3 6 times 6 =

050323 bull page 23

Operations and Algebraic Thinking 3OA

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Understand properties of multiplication and the relationship between multiplication and division

3OA5 Apply properties of operations as strategies to multiply and divide2 Examples If 6 times 4 = 24 is known then 4 times 6 = 24 is also known (Commutative property of multiplication) 3 times 5 times 2 can be found by 3 times 5 = 15 then 15 times 2 = 30 or by 5 times 2 = 10 then 3 times 10 = 30 (Associative property of multiplication) Knowing that 8 times 5 = 40 and 8 times 2 = 16 one can find 8 times 7 as 8 times (5 + 2) = (8 times 5) + (8 times 2) = 40 + 16 = 56 (Distributive property)

3OA6 Understand division as an unknown-factor problem For example find 32 divide 8 by finding the number that makes 32 when

multiplied by 8

2Students need not use formal terms for these properties

050323 bull page 24

Operations and Algebraic Thinking 3OA

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Multiply and divide within 1003OA7 Fluently multiply and divide within 100 using strategies such as therelationship between multiplication and division (eg knowing that 8 times5 = 40 one knows 40 divide 5 = 8) or properties of operations By the endof Grade 3 know from memory all products of two one-digit numbers

050323 bull page 25

Operations and Algebraic Thinking 3OA

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

x a b c d e f

a g h i j k l

b h m n o p q

c i n r s t u

d j o s w x y

e k p t x z sj

f l q u y sj yt

050323 bull page 26

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Things to Think Abouthellip What does Computational Fluency mean Developing fluency requires a balance and connection

between conceptual understanding and computational proficiency On the one hand computational methods that are over practiced without understanding are often forgotten or remembered incorrectlyhellipOn the other hand understanding without fluency can inhibit the problem-solving process (PSSM Page 35)

050323 bull page 27

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Things to Think Abouthellip How do students demonstrate Computational

Fluency Students exhibit computational fluency when they

demonstrate flexibility in the computational methods they choose understand and can explain these methods and produce accurate answers efficiently The computational methods that a student uses should be based on mathematical ideas that the student understands well including the structure of the base-ten number system properties of multiplication and division and the number relationships (PSSM page 152)

050323 bull page 28

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Things to Think Abouthellip Is there such a thing as effective drill There is little doubt that strategy development and

general number sense are the best contributors to fact mastery Drill in the absence of these factors has repeatedly been demonstrated as ineffective However the positive value of drill should not ne completely ignored Drill of nearly any mental activity strengths memory and retrieval capabilities

(Van de Walle)

050323 bull page 29

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Things to Think abouthellip What about timed test Teachers who use timed test believe that the test

help children learn basic facts This makes no instructional sense Children who perform well under time pressure display their skills Children who have difficulty with skills or who work more slowly run the risk of reinforcing wrong learning under pressure In addition children can become fearful and negative toward their math learning (Burns 2000 p157)

050323 bull page 30

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Gain familiarity with factors and multiples4OA4 Find all factor pairs for a whole number in the range 1ndash100 Recognize

that a whole number is a multiple of each of its factors Determine whether a given whole number in the range 1ndash100 is a multiple of a given one-digit number Determine whether a given whole number in the range 1ndash100 is prime or composite

050323 bull page 31

Operations and Algebraic Thinking 4OA

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

When planning ask

ldquoWhat task can I give that will build student

understandingrdquorather than

ldquoHow can I explain clearly so they will understandrdquo

Grayson Wheatley NCCTM 2002

050323 bull page 32

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Time to Reflect

050323 bull page 33

Summary

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

httpilluminationsnctmorg

050323 bull page 34

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Letrsquos Play the Factor Game

050323 bull page 35

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Math Notebook

050323 bull page 36

1 What skill did you review and practice

2 What strategies did you use while playing the game

3 If you were to play the game a second time what different strategies would you use to be more successful

4 How could you tweak or modify the game to make it more challenging

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

httpilluminationsnctmorg

050323 bull page 37

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 38

httpnlvmusueduennavvlibraryhtml

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

1 Make sense of problems and persevere in solving them

2 Reason abstractly and quantitatively3 Construct viable arguments and critique the reasoning

of others4 Model with mathematics5 Use appropriate tools strategically6 Attend to precision7 Look for and make use of structure8 Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

050323 bull page 39

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Mathematical practices describe the habits of mind of mathematically proficient studentshellip

bull Who is doing the talkingbullWhorsquos doing the thinkingbull Who is doing the math

050323 bull page 40

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Letrsquos revisit your poster

Now that you have worked through the various tasks what additional numbers pictures and words could you add to your poster to further illustrate the Mathematical Practice

050323 bull page 41

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Think of a NumberMany people have a number that they think is

interesting Choose a whole number between 1 and 25 that you think is special

bull Record your numberbull Explain why you chose that numberbull List three or four mathematical facts about your

numberbull List three or four connections you can make

between your number and your world

050323 bull page 42

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

050323 bull page 54

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

DPI Mathematics Site

httpmathncwiseowlorg

050323 bull page 55

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

wwwcorestandardsorg

050323 bull page 56

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Mathematics Wikki

050323 bull page 57

httpmaccssncdpiwikispacesnetSummer+Institute

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Time to Reflect

050323 bull page 58

Summary

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

PlusDeltabull Please include on the back of the

plusDelta handout topics that you would like to see addressed or discussed during the webinars

ndashNovember 17th

ndashJanuary 10th ndashFebruary 9th

ndashMarch 8th

050323 bull page 59

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information

Contact InformationKitty RutherfordMathematics Consultant919-807-3934kittyrutherforddpincgov

Amy ScrinziMathematics Consultant919-807-3934amyscrinzidpincgov

Barbara BissellK-12 Mathematics Section Chief919-807-3838barbarabisselldpincgov

Susan Hart Administrative Assistant919-807-3846Susanhartdpincgov

050323 bull page 60

• Common Core State Standards K-5 Mathematics
• Norms
• Our Goals for this afternoon
• Think of a Number
• Slide 5
• Slide 6
• Multiplication and Rectangles
• What did you notice
• Slide 9
• Commutative Property of Multiplication
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• What do you notice
• Slide 16
• Letrsquos look at the number nine
• Slide 18
• Slide 19
• If my rectangle has a total of 18 squares tiles and 3 rows of tileshellip
• What standards in third and fourth would this task address
• Criteria Area in Third Grade
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Things to Think Abouthellip
• Things to Think Abouthellip
• Slide 29
• Things to Think abouthellip
• Slide 31
• Slide 32
• Time to Reflect
• httpilluminationsnctmorg
• Letrsquos Play the Factor Game
• Math Notebook
• Slide 37
• Slide 38
• Slide 39
• Slide 40
• Letrsquos revisit your poster
• Slide 42
• Slide 54
• DPI Mathematics Site
• Slide 56
• Mathematics Wikki
• Slide 58
• PlusDelta
• Contact Information