Multiplying and Dividing in the Common Core (grades 3-5) Julia Doverspike, Armando Rodriguez,...

Julia Doverspike, Armando Rodriguez, Maricela Garcia

Multiplying and Dividing in the Common Core (grades 3-5)

SecondGrade• Iden'fynumbers(upto20)asOddorEven• Countby2s,5s,10s,and100supto1000• Showrepeatedaddi'onwithobjectsandnumbersupto5groupsof5

ThirdGrade• Mul'plyandDivideupto100usingpictures• Understandtherela'onshipbetweenmul'plica'onanddivision• Relateareaofashapetomul'pica'on• Knowfrommemorymul'pica'onfactsupto9X9=81

FourthGrade• Interpretamul'plica'onequa'onasacomparison• Mul'plynumberswithupto4-- digits‐bya1-- digit‐numberor2-- digit‐by2--‐digitusingdrawingsandequa'ons• Dividenumbersupto4--‐digitby1-- digit‐usingdrawingsandequa'ons

Fi1hGrade• Mul'plymul'-- digit‐wholenumbers• Dividenumbersupto4-- digit‐by2-- digit‐usingdrawingsandequa'ons• Relatevolumeofa3Dshapetomul'plica'on• UnderstandplacevalueusingPowersof10Libby Schwaegler 2015

Kristy Cortright 2015

Reasoning with numbers

Arrays


Creating Arrays

3 rows

2 columns

2 + 2 + 2 = 6


Area

How many different

rectangles can I make with an area

of 12?


Area Models

Five rows of 3

3 + 3 + 3 + 3 + 3 = 15

5 x 3 = 15


Equal Groups Model

2 groups of 4

4 + 4 = 8

2 x 4 = 8


Using Manipulatives

Modeling Division


Quotative Division

Uses repeated subtraction Provides student with a total number and the number of objects in each group

Focus on the question, “How many equal groups can you make?”


Partitive Division

Provides student with a total number and the number of groups

Focus on the question, “How many objects are in each group so that the groups are equal?”


Number Line

There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill?

12

3 6 90

- 3

- 3

- 3

- 3

12 ÷ 3 = 4


Tape Diagram

There are 12 brownies on the plate. If you are sharing the brownies equally among three bags, how many brownies will go in each bag?

? ?? = 12

44 4

12 ÷ 3 = 4


Array Model

If 15 cars are parked 3 in each row, then how many rows will they fill?

3

5


For Multiplication

Properties of Operations


Identity Property


Commutative Property

4 x 5 = 20

5 x 4 = 20


Associative Property

3 x 5 x 2 = 30

5 x 2 x 3 = 30

2 x 3 x 5 = 30


Distributive Property

Decomposing rectangles

8 x 6

= (3 x 6) + (5 x 6)


Multiplication and Division Patterns

Doubles (2)Double-Doubles(4)Double-Double-Doubles(8)HalvesBy 10s and 5s


Multiplicative Comparison


Language

18 = 6 x 3

40 is 5 times as much as 8

5 x 8 = 40

18 is 6 times as much as 3


Bar Model (Tape Diagram)

A tennis ball costs $2. A soccer ball costs six times as much as a tennis ball. How much does the soccer ball cost?

6 x 2 = n


Try These

Manny has lived in Illinois for 21 years and that is 7 times as many years as Lucas. How many years has Lucas lived in Illinois?

A tree in Ashton’s yard is 15 feet tall. Ashton is 3 feet tall. The tree is how many times as tall as Ashton?


Place Value

Each place value is ten times as much

as the previous place value

Including Prime and Composite

Factors and Multiples

Rectangles

How many different rectangles can I make with an area of 7?

How many different rectangles can I make with an area of 12?

Composite

Prime

Number Line

Show the multiples of 4

1 2 3 4 5

20

16

12

840

Factors

Multiples

Table

1 6

2 12

3 18

4 24

x 6

Multi-digit Multiplication


Digi Blocks


Base Ten Blocks (or Digi-blocks)321 x 3 =

963


Base Ten Area Model

31 x 24 X

= 744


Area Model

24 x 35

= (20 + 4) x (30 + 5)

204

30

5

20

120

100

600

= 840


Partial Products

24X 36

24

6 x 412

06 x 2 tens12

03 tens

x 4600

3 tens x 2 tens864


Column Method

Regroup

4 4

2 6

4

2

62

8 08

44

1

11


Multi-digit Division


Base Ten Blocks (or Digi-blocks)My team earned $175. There are 5 people on my team. We decided to split the money up evenly between the 5 of us. How much money will we each receive?

$35 each


Area Model

966 ÷ 7

9667

Hundreds

Tens Ones100

966- 700 266

30

266- 210 56

8

56- 56 0

= 138


Partial Quotient

3 745 20

0- 600 145

40- 120 25

8- 24 1

745 ÷ 3

248 remainder 1


Interpreting Remainders

Sam wants to hide 40 eggs for his cousins to find. How many dozen eggs must he buy?

Sam buys 2 dozen packages of chocolates for his cousins. Each package has 22 chocolates. He has 9 bowls to hold the chocolates. If he wants to have the same number of chocolates in each bowl, how many chocolates will be in each bowl?


Base Ten Area Model

231 ÷ 21

X

Divisor

Quotient

Dividend

= 11


Column Division - introduction231 ÷ 21

21

231

1

210-21

1

21-0


Column Division (long division)231 ÷ 21

21

231

1

-2121

1

- 210


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Multiplying and Dividing in the Common Core (grades 3-5) Julia Doverspike, Armando Rodriguez,...

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