Origo Math Practice Book 1

ORIGO Stepping Stones is an innovative online program that

• Honestly addresses both the content and the intent of the CCSS.

• Fosters students’ thinking and reasoning skills.

• Delivers multiple ways to differentiate classroom instruction.

• Provides a valuable source of professional learning for the teacher.

• Offers methods to assess deep understanding and skills.

• Is rich in online and print resources that engage all students.

It’s simply a smarter approach!

STUDENT JOURNAL

Product Code: SSJ 226 22

STUD

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ORIGO Stepping Stones is a world class core math program written and developed for elementary schools implementing the Common Core State Standards.*

This revolutionary online program integrates print and digital technology to give educators what they have been requesting for years.

THIS BOOK BELONGS TO

*or the Texas Essential Knowledge and Skills (TEKS) or the Common Core State Standards for Mathematics with California Additions.

Diana Lambdin

Frank Lester, Jr.

Kit Norris

PROGRAM CONSULTANTS

James Burnett

Calvin Irons

SENIOR AUTHORS

STUDENT JOURNAL

Peter Stowasser

Allan Turton

contributing authors

James Burnett

Beth Lewis

Donna Richards

Kevin Young

PROGRAM EDITORSSAM

PLE

ORIGO Stepping Stones 2 ORIGO Stepping Stones 2

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MODULE 1

1.1 Writing Tens and Ones, and Number Names 8

1.2 Writing Two-Digit Numbers 10

1.3 Reading and Writing Two-Digit Numbers 12

1.4 Exploring the Relative Position of Two-Digit Numbers on a Number Track

14

1.5 Exploring the Relative Position of Two-Digit Numbers on a Number Line

16

1.6 Working with Two-Digit Numbers on a Number Line

18

1.7 Comparing Two-Digit Numbers on a Number Line

20

1.8 Comparing and Ordering Two-Digit Numbers

22

1.9 Exploring the Properties of Odd and Even Numbers

24

1.10 Solving Number Puzzles on a Hundred Chart

26

1.11 Sorting Data in Different Ways 28

1.12 Interpreting and Constructing One-to-One Picture Graphs

30

MODULE 2

2.1 Working with Addition 32

2.2 Using the Commutative Property of Addition with Count-On Facts

34

2.3 Relating Addition and Subtraction Facts (Count-On Facts)

36

2.4 Working with Count-On Fact Families 38

2.5 Extending the Count-On Addition Strategy to Two-Digit Numbers

40

2.6 Using Place Value (Hundred Chart) to Add Two-Digit Numbers

42

2.7 Using Place Value (Number Line) to Add Two-Digit Numbers

44

2.8 Reading and Writing Time on the Hour and Half Past the Hour

46

2.9 Working with Duration (Hours) 48

2.10 Identifying Five-Minute Intervals 50

2.11 Working with Five-Minute Intervals 52

2.12 Working with Duration (Hours and Minutes) 54

MODULE 3

3.1 Working with Hundreds 56

3.2 Writing Three-Digit Numbers 58

3.3 Reading and Representing Three-Digit Numbers

60

3.4 Writing Three-Digit Number Names 62

3.5 Writing Three-Digit Numerals 64

3.6 Identifying Three-Digit Numbers on a Number Line

66

3.7 Measuring Length with Uniform Non-Standard Units

68

3.8 Introducing the Inch 70

3.9 Working with Inches 72

3.10 Introducing Feet 74

3.11 Working with Feet and Inches 76

3.12 Introducing Yards 78

MODULE 4

4.1 Exploring the Comparison Model of Subtraction

80

4.2 Extending the Count-Back Strategy to Two-Digit Numbers

82

4.3 Using Place Value (Hundred Chart) to Subtract Two-Digit Numbers

84

4.4 Using Place Value (Number Line) to Subtract Two-Digit Numbers

86

4.5 Working with the Doubles Addition Strategy 88

4.6 Relating Addition and Subtraction (Doubles Facts)

90

4.7 Working with Doubles Fact Families 92

4.8 Extending the Doubles Addition Strategy Beyond the Facts

94

4.9 Working with Time Quarter Past the Hour 96

4.10 Identifying and Recording Time Using a.m. and p.m.

98

4.11 Working with Timetables and Duration 100

4.12 Working with the Calendar 102

MODULE 5

5.1 Representing Three-Digit Numbers (with Zeros)

104

5.2 Representing Three-Digit Numbers (with Teens and Zeros)

106

5.3 Writing Three-Digit Numbers in Numerals and Words

108

5.4 Working with Three-Digit Numbers to One Thousand

110

5.5 Comparing Three-Digit Numbers 112

5.6 Ordering Three-Digit Numbers 114

5.7 Marking the Direction of Turn 116

5.8 Describing Amounts of Turn 118

5.9 Identifying Polygons 120

5.10 Identifying Quadrilaterals 122

5.11 Working with Polygons 124

5.12 Drawing 2D Shapes 126

MODULE 6

6.1 Using the Make-Ten Addition Strategy 128

6.2 Working with Make-Ten Fact Families 130

6.3 Extending the Make-Ten Addition Strategy Beyond the Facts

132

6.4 Analyzing Addition Patterns (with Bridging) 134

6.5 Extending the Doubles Addition Strategy 136

6.6 Using Place Value to Add Two-Digit Numbers 138

6.7 Using Place Value to Add Two-Digit Numbers (with Bridging)

140

6.8 Introducing Centimeters 142

6.9 Working with Centimeters 144

6.10 Introducing Meters 146

6.11 Working with Meters 148

6.12 Using Line Plots to Record Length 150

MODULE 7

7.1 Skip Counting by 2 or 5 152

7.2 Adding Jumps of 2 or 5 154

7.3 Describing Equal Groups 156

7.4 Adding Equal Groups 158

7.5 Describing Arrays 160

7.6 Adding Equal Rows 162

7.7 Using the Turnaround Idea with Arrays 164

7.8 Identifying and Comparing Amounts of Money

166

7.9 Relating Amounts of Money 168

7.10 Working with Cents 170

7.11 Working with Dollars 172

7.12 Working with Dollars and Cents 174

MODULE 8

8.1 Composing and Decomposing Two-Digit Numbers

176

8.2 Subtracting One-Digit Numbers from Two-Digit Numbers

178

8.3 Calculating Difference Between Two-Digit Numbers

180

8.4 Consolidating Subtraction with Two-Digit Numbers

182

8.5 Relating Addition and Subtraction Beyond the Facts

184

8.6 Using the Unknown Addend Strategy to Subtract Two-Digit Numbers

186

8.7 Using Place Value (Number Line) to Solve Subtraction Problems

188

8.8 Introducing the Pound 190

8.9 Working with Pounds 192

8.10 Introducing the Kilogram 194

8.11 Working with Kilograms 196

8.12 Comparing Customary and Metric Units 198

MODULE 9

9.1 Exploring the Relative Position of Three-Digit Numbers

200

9.2 Estimating Answers (Adding within 100) 202

9.3 Estimating Answers (Subtracting within 100)

204

9.4 Using the Associative Property of Addition with Three One- and Two-Digit Numbers

206

9.5 Using the Associative Property of Addition with Four One- and Two-Digit Numbers

208

9.6 Solving Word Problems 210

9.7 Identifying One-Half, One-Fourth, and One-Third of a Collection

212

9.8 Identifying One-Half, One-Fourth, and One-Third of a Region

214

9.9 Exploring Fractions 216

9.10 Analyzing Fractions 218

9.11 Working with Parts of a Whole (Equal Size) 220

9.12 Exploring Area 222

MODULE 10

10.1 Extending the Count-On Strategy to Three-Digit Numbers

224

10.2 Using Place Value to Add Two- and Three-Digit Numbers

226

10.3 Using Place Value to Add Three-Digit Numbers

228

10.4 Composing Three-Digit Numbers 230

10.5 Using the Make-Ten Strategy to Add One- and Three-Digit Numbers (with Bridging)

232

10.6 Using Place Value to Add Two- and Three-Digit Numbers (with Bridging)

234

10.7 Using Place Value to Add Three-Digit Numbers (with Bridging)

236

10.8 Consolidating Addition with Three-Digit Numbers

238

10.9 Identifying Polyhedrons 240

10.10 Identifying Pyramids 242

10.11 Investigating 3D Objects 244

10.12 Drawing 3D Objects 246

MODULE 11

11.1 Extending the Count-Back Strategy to Three-Digit Numbers

248

11.2 Using Place Value to Subtract Two-Digit Numbers from Three-Digit Numbers

250

11.3 Using Place Value to Subtract Three-Digit Numbers

252

11.4 Consolidating Subtraction of Two- and Three-Digit Numbers

254

11.5 Using a Place-Value Strategy to Subtract Three-Digit Numbers

256

11.6 Using a Place-Value Strategy to Solve Subtraction Problems

258

11.7 Introducing the Multiplication Symbol (×) 260

11.8 Using Multiplication (Equal Groups) 262

11.9 Using Division Language (Sharing) 264

11.10 Relating Multiplication and Division (Sharing) 266

11.11 Using Division Language (Grouping) 268

11.12 Relating Multiplication and Division (Grouping) 270

MODULE 12

12.1 Decomposing Three-Digit Numbers 272

12.2 Subtracting One-Digit Numbers from Three-Digit Numbers (with Bridging)

274

12.3 Consolidating Subtraction of One-Digit Numbers (with Bridging)

276

12.4 Using Place Value to Subtract Two-Digit Numbers from Three-Digit Numbers (with Bridging)

278

12.5 Consolidating Subtraction of Two-Digit Numbers (with Bridging)

280

12.6 Using Place Value to Subtract Three-Digit Numbers (with Bridging)

282

12.7 Consolidating Subtraction of Three-Digit Numbers (with Bridging)

284

12.8 Consolidating Subtraction of Two- and Three-Digit Numbers (with Bridging)

286

12.9 Introducing Cups, Pints, and Quarts 288

12.10 Working with Cups, Pints, and Quarts 290

12.11 Introducing Liters 292

12.12 Working with a Liter 294

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ORIGO Stepping Stones 2

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There are 15 cows on this farm. Some of the cows are in the barn.

How could you fi gure out the number of cows in the barn?

ORIGO Stepping Stones 2 • 4.6

Relating Addition and Subtraction (Doubles Facts)4.6

I could start with 15 and take away 7, or I could think 7 plus "something" is 15.

Step Up 1. Write the two parts and the total for each picture.

b.a.

One part is .

The other part is .

The total is .

One part is .

The other part is .

The total is .

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2. Figure out how many dots are covered. Then write the matching equations.


a. 9 dots in total

+ =

− =

b. 13 dots in total

+ =

− =

c. 11 dots in total

+ =

− =

d. 17 dots in total

+ =

− =

e. 14 dots in total

+ =

− =

f. 16 dots in total

+ =

− =

Step Ahead Write a number fact to match each story.

a. Tyler put 6 cookies on a plate. The plate can hold 14 cookies.How many more cookies can Tyler fi t on the plate?

b. Donna and Keisha have 12 berries together. Keisha has 5 berries. How many berries does Donna have?

c. Maria bought 16 stickers. There are 7 red stickers and the rest are blue. How many stickers are blue?

d. Luis and Tien have read 12 books in total. Tien has read 6 books. How many books has Luis read?

STEP 1Step 1 provides guided discussion of enquiry. This often sets the scene for the lesson. Teachers can project this piece of the lesson and step through each question or point one at a time.

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How could you fi gure out the number of cows in the barn?




Step Up 1. Write the two parts and the total for each picture.

b.a.

One part is .

The other part is .

The total is .

One part is .

The other part is .

The total is .

Grade Module Lesson

STEP 2Step 2 provides individual work based on the discussion above.

STEP 3Step 3 puts a little twist on each lesson to develop higher-order thinking skills.

The ORIGO Stepping Stones program has been created to provide a smarter way to teach and learn mathematics. It has been developed by a team of experts to provide a world-class math program that honestly addresses the content and intent of the Common Core State Standards.

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NSTEPPING STONES RESOURCES — PRINTRegular and meaningful practice is a hallmark of ORIGO Stepping Stones. Each module in this book has perforated pages that practice content previously learned to maintain concepts and skills, and pages that practice computation to promote fluency.

PRACTICE BOOK

STUDENT JouRNALEngaging student pages accompany each lesson within ORIGO Stepping Stones. In the Student Journals for Grades 1–5, there are two pages for each lesson. Following are the features of the Grade 2 Student Journal as a part of the whole program.

Additional Resources — Print

ORIGO Big Books build on young students’ natural love for stories to help introduce key mathematical concepts. There are 12 Big Books at this grade.

The Number Case provides teachers with ready-made resources that are designed to develop students’ understanding of number.

Each book is one component of a comprehensive teaching program. Together they are a collection of consolidation and practice pages from lessons in the ORIGO Stepping Stones program.

Class teachers will decide which pages suit individual needs. So students might not complete every page in these books. For more information about the program, visit www.origoeducation.com/steppingstones.

NOTES FOR HOME

ORIGO Stepping Stones is a world class core math program written and developed for elementary schools implementing the Common Core State Standards.*

This revolutionary online program integrates print and digital technology to give educators what they have been requesting for years.

THIS BOOK BELONGS TO2

ORIGO Stepping Stones is an innovative online program that

• Honestly addresses both the content and the intent of the CCSS.

• Fosters students’ thinking and reasoning skills.

• Delivers multiple ways to differentiate classroom instruction.

• Provides a valuable source of professional learning for the teacher.

• Offers methods to assess deep understanding and skills.

• Is rich in online and print resources that engage all students.

It’s simply a smarter approach!

PRACTICE BOOK

Product Code: SSP 332 2

*or the Texas Essential Knowledge and Skills (TEKS) or the Common Core State Standards for Mathematics with California Additions.

PR

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OO

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2

0 10 20 30 40 50 60 70 80 90 100

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

hundreds tens ones

06

Additional Resources (ONLINE CHANNELS)

These are some of the innovative teaching channels integrated into the teacher’s online program.

Interactive whiteboard tools

Interactive gamesProfessional learning sessions

ORIGO MathEd Flare Fundamentals Game Boards

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3D OBJECT

A three-dimensional (3D) object shows length, width, and height. A 3D object can be solid like a brick, hollow like a football, or skeletal like a house frame. For example:

A cone is a 3D object made with one flat surface and one curved surface.

A cylinder is a 3D object made with two flat surfaces

and one curved surface.

A cube is a box-shaped 3D object made with

six flat surfaces that are the same size.

A sphere is a ball-shaped 3D object made with one

curved surface.

ADDITION

Addition is used to find the total or sum of two or more numbers of objects. This is recorded in an addition sentence that uses words or symbols. Addition is shown by the + symbol.

For example: 2 + 3 = 5

CAPACITY

Capacity is the amount something can hold.

CENTIMETER

A centimeter is a metric unit of length that is shorter than one inch.

COMPARING

When read from left to right, the symbol > means is greater than. The symbol < means is less than.

For example: 2 < 6 means 2 is less than 6

EVEN NUMBER

An even number is any whole number that has a 0, 2, 4, 6, or 8 in the ones place.

FACT FAMILY

An addition fact family includes an addition fact, its turnaround fact and the two related subtraction facts. For example:

4 + 2 = 6 addition fact with 2 + 4 = 6 its turnaround fact

6 – 4 = 2 the two related 6 – 2 = 4 subtraction facts

FRACTION

Fractions describe parts of one whole, when those parts are of equal size. For example, when one whole is split into two groups or two parts of equal size, the fraction one-half describes one of those groups or parts. When one whole is split into four groups or four parts of equal size, the fraction one-fourth (one-quarter) describes one of those groups or parts.

KILOGRAM

A kilogram is a metric unit of weight.

Mental computation strategies

These are strategies you can use to figure out a problem in your head.

Addition• Count on

See 3 + 8 think 8 + 1 + 1 + 1 See 58 + 24 think 58 + 10 + 10 + 4

• Make ten See 9 + 4 think 9 + 1 + 3 See 38 + 14 think 38 + 2 + 12

• Use a known sum (use doubles) See 7 + 7 think double 7 See 25 + 26 think double 25 plus 1 more See 35 + 37 think double 35 plus 2 more

Subtraction• Think addition

See 17 – 9 think 9 + 8 = 17 so 17 – 9 = 8

• Count back See 9 – 2 think 9 – 1 – 1 See 26 – 20 think 26 – 10 – 10

LITER

A liter is a metric unit of capacity.

METER

A meter is a metric unit of length that is longer than one yard. One hundred centimeters is the same length as one meter.

MULTIPLICATION

Multiplication is used to find the total number of objects in an array or in a number of equal groups. This is recorded in a multiplication sentence that uses words or symbols. Multiplication is shown by the × symbol.

For example:

three rows of five is fifteen

3 × 5 = 15

array1 row

three groups of two is six

3 × 2 = 6

equal groups

NUMBER FACTS

Addition facts are all the addition sentences that show two one-digit numbers being added. Addition facts can be written with the total or sum at the start or at the end.

For example: 2 + 3 = 5 or 9 = 4 + 5

Subtraction facts are all the subtraction sentences that are related to the addition facts.

For example: 5 – 2 = 3 or 9 – 4 = 5

ODD NUMBER

An odd number is any whole number that has a 1, 3, 5, 7, or 9 in the ones place.

PINT

A pint is a unit of capacity.

POLYGON

A polygon is any closed 2D shape that has three or more straight sides. For example:

A triangle is a polygon that has three sides.

A quadrilateral is any polygon with four sides.

A pentagon is a polygon that has five sides.

A hexagon is a polygon that has six sides.

POLYHEDRON

A polyhedron is any closed 3D object that has four or more flat faces.

A pyramid is a polyhedron that has any polygon for a base. All the other faces joined to the base are triangles that meet at a point.

QUART

A quart is a unit of capacity. One quart is the same as two pints.

SUBTRACTION

Subtraction involves taking one number away from another. Subtraction may be used to find an unknown addend or to find the difference between two numbers. This is recorded in a subtraction sentence that uses words or symbols. Subtraction is shown by the – symbol.

For example: 5 – 2 = 3

TURNAROUND FACT

Each addition fact has a related turnaround fact.

For example: 4 + 2 = 6 2 + 4 = 6

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Step Up 1. Write the number of tens and ones on the expander. Then complete the number name.

b.


Writing Tens and Ones, and Number Names1.1

Look at this picture.

What number does it show?

What do you know about these numbers?

fifty-one twenty-six seventy-three

a.

How could you use tens and ones blocks to show the same number?

How would you show the number on this expander? How do you know?

How would you write the number name?

Step Ahead Two people show 17 with their hands like this.

2. Write the number of tens and ones on the expander. Then write the number name.


Loop the numbers that three people could show.

thirty-eight twenty-one fifty-three thirty

a.

b.

c.

fifty three

twenty nine

d.

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Step Up 1. Write the number of tens and ones on the expander. Then write the numeral and number name.

How could you show the number using tens and ones blocks?

How many people would be needed to show the number with their fingers? How do you know?

How would you write the numeral without using an expander?

How would you write the number name?


Writing Two-Digit Numbers1.2

Look at the number on this expander. How do you read and say the number? 5 2

a.

forty

c.

2. Complete these mix-and-match puzzles.


Step Ahead

a. Write the numeral.

b. Write the number name.

Count the number of tens and ones blocks.

b.b.a.

d.c.

b.

twenty

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What do you notice when you read and say these numbers?

Do you always say the number of tens first?

What are some other numbers where you say the number of ones first?

What are some other numbers where you say the number of tens first?

Reading and Writing Two-Digit Numbers1.3

How would you show the numbers on these expanders?

Look at these number names.

fifty-two fifteen fifty

Step Up 1. Read the number name. Write the numeral with and without the expander.

d.fifty-six

f.thirty-two

e.twenty-eight

a. sixty-three c. ninety-twob. eighty-four


2. Write the numeral with and without the expander.

d. forty-one f. fourteene. forty

g. sixteen i. sixty-sevenh. sixty

a. seventy-one c. seventy-fourb. seventeen

Step Ahead Read the clues. Write the numeral on the expander to match.

a.I am greater than sixty and less than seventy. The digit in my tens place is less than the digit in my ones place.

b.I am less than forty and greater than thirty. The digit in my ones place is less than the digit in my tens place.

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Step Up 1. Draw a line to show where each numeral and number name is located on the track.


Look at this piece of number track.

What numeral would you write in the position shown by the red arrow? How do you know?

How can you figure out where each of these is located on the number track?

Exploring the Relative Position of Two-Digit Numbers on a Number Track1.4

fourteen

thirty-two

forty-seven

twenty-one

thirty-nine

forty-four

30 40

2. Write the numerals that should be shown in these positions.

a.

b.

c.


Step Ahead Look at this piece of number track.

Loop the numerals that you could show on this piece of number track.

4440 5242 55 49

38 40 50

30 40

80 90

50 60

42 37 29

12

23

29

18

31

46

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Look at the number track.

What numeral would you write in the position that is yellow? How do you know?

Look at this number line above. How is it the same as the number track? How is it different? What numeral should we write at the start of the number line?

What do you notice about the marks along the number line?What do the marks of different length show? How do you know?

Which mark on the number line shows the same number that is shaded on the number track? How do you know?


Exploring the Relative Position of Two-Digit Numbers on a Number Line1.5

20

1 20

2. Draw a line from each numeral to its position on the number line.


Step Ahead Draw arrows from each numeral to its position on the number line. Think carefully before you draw.

20 40

30 25 35

40 50 60 70

42 51 58 64

47 53 55 69

a.

70 80 90 100

74 79 85 93

71 82 89 96

b.

Step Up 1. Draw a line from each numeral to its position on the number line.

11 15 22 27

9 12 19 28

0 10 20 30

What is a quick way to find 17 on the number line?

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Step Up 1. Write the numeral that should be in each box. Think carefully before you write.

Look at this number line.

What other numerals are you able to find on this number line?

How do you know?

Mark 15 and 25 on the number line. How could you find 19? What numeral would it be near?

How could you find 12?

What numerals are closer to 10 than 20? How do you know?


Working with Two-Digit Numbers on a Number Line1.6

15 is halfway between 10 and 20.

a.

0 4020

b.

0 8040

c.

0 10050

0 10 20 30

2. Write the numerals that should be in the boxes above each number line. Then draw a line from each box below the number lines to show that numeral’s position.


Step Ahead Divide the number line into smaller parts that are the same length. Then find and mark 16 and 47.

10 5030

a.

10 5030

3515 45

b.

20 6040

3525 55

c.

10 9050

6025 75

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Step Up 1. Draw a line to join each numeral to its position on the number line. Then write < or > in each circle to describe each pair of numerals.

Look at the this number line.

What numeral should be marked at the position of each arrow? How do you know?

Which numeral is the greater distance from zero? Which numeral is greater?

What numerals are greater than 13 but less than 17? How do you know?

Which symbols do we write for greater than and less than? How do you know?


Comparing Two-Digit Numbers on a Number Line1.7

a.

30 5040

33 36 38 42 49 47

b.

50 7060

51 54 62 58 69 66

0 15105 20

2. Write the numeral that you think should be in each position.


3. Write < or > to complete these. Use the number line from Question 2 to help.

88 81a.

92 95c.

82 90b.

80 90d.

87 95f.

93 84e.

89 96g.

88 98i.

99 83h.

Step Ahead Write two-digit numerals and < or > to complete true comparison sentences.

26a.

70b.

54d.

91c.

f.e.

80 10090

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Step Up1. This table shows amounts raised by Grades 1 and 2 for a school

fundraiser. For each week, color the box that shows the greater amount raised.

Did you compare the digits in the tens place or the ones place first? Why?

Which of these amounts are greater than $26 but less than $51?

Look at all the purses above.

How would you figure out the order from least to greatest amount?


Comparing and Ordering Two-Digit Numbers1.8

Look at the amounts in these purses.

Which purse has more money? How do you know?

2. Loop the week in which less money was raised.

GradeWeek

One Two Three Four Five

1 $64 $48 $39 $55 $61

2 $57 $62 $50 $58 $35

a. Grade 1 Week 1 or Grade 1 Week 5

b. Grade 2 Week 1 or Grade 2 Week 4

c. Grade 1 Week 3 or Grade 2 Week 5

This table shows amounts raised by Grades 3 and 4. Use the table to answer Questions 3 and 4.

3. a. Write the amounts that are less than $50.

b. Write the amounts raised by Grade 3 in order from greatest to least.

c. Write the amounts raised by Grade 4 in order from least to greatest.

4. Complete these sentences.

a. Grade raised more in Week 3 than Grade .

b. Grade 4 raised less than Grade 3 in Week and Week .


GradeWeek

One Two Three Four Five

3 $63 $58 $39 $45 $53

4 $59 $65 $40 $57 $38

Step Ahead Look at the tables on page 22 and at the top of this page.

a. Use a calculator to figure out how much money each grade raised in total.

b. Which grade raised the greatest amount of money?

Total Money RaisedGrade 1 Grade 2 Grade 3 Grade 4

$51 $26

$44 $14 $34$41

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These number mats have been sorted into two groups.

How would you describe the sorting?

What types of numbers are in each group?

What are some other numbers you could show in each group? How do you know?


Exploring Properties of Odd and Even Numbers1.9 2. Look at this chart.

a. Color the odd numbers blue.

b. Write about a pattern you see.

3. Write all the even numbers between 21 and 40.

4. Write all the odd numbers between 28 and 45.

5. Write the next two even numbers. 6. Write the next two odd numbers.

a. 10 , , a. 7 , ,

b. 18 , , b. 25 , ,

c. 44 , , c. 33 , ,

d. 50 , , d. 49 , ,


1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

21 22 23 24 25

26 27 28 29 30

Step Ahead Write the numbers that you say when you start at 5 and count in steps of 5. Then color the numbers that are even.

5 10 15

Even numbers can be shown with a groups of two arrangement where every part has a partner. For odd numbers, there is always one left over.

Step Up 1. a. Look at the chart below. Color the even numbers red. Look at the number mats above to help.

1 2 3 4 5 6

7 8 9 10 11 12

13 14 15 16 17 18

19 20 21 22 23 24

25 26 27 28 29 30

b. Write about a pattern you see.SAM

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Solving Number Puzzles on a Hundred Chart1.10

Find 28 on this hundred chart.

What does the 2 tell you?

What does the 8 tell you?

What are some things you know about this two-digit number?

Read this number puzzle.

Color the hundred chart to show all the possible answers. What do you notice?

What is the greatest possible number? How do you know?

What is the least possible number?

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

Where do you see or hear two-digit numbers?

I am a two-digit number.

When you add my tens and

ones digits, the total is 7.

What numbers could I be?

Step Up Figure out these number puzzles.

a.I am between 30 and 40. I am greater than 35, but less than 39. I am an odd number.

b.I am between 60 and 70. The difference between my digits is 2. I am greater than 65.


c.I am an even number. I am between 60 and 80. I am less than 64.

g.I am between 40 and 60. When you add my digits, the total is 11. I am an odd number.

d.I am between 80 and 100. The difference between my digits is 9. I am an even number.

e.I am between 30 and 60. The difference between my digits is 0. I am an even number.

f.I am an odd number. When you add my 2 digits, the total is 6. I am less than 20.

h.I am greater than 60 and less than 90. The difference between my digits is 3. I am an even number.

Step Ahead For each flower, write what you notice about the digits in each petal.

62 8

5344

b.

31

20 c.

97

53

The total of the tens digit and the ones digit is always

The total of the tens digit and the ones digit is always

The difference between the tens digit and the ones digit is always

63

81

45

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How could you sort these bow ties and neckties?

How could you show your sorting?

What type of graph would you use? Why?


Sorting Data in Different Ways1.11

Step Up 1. a. Your teacher will give you a sheet of pictures. Sort the hats then complete this graph to show your sort.

Clown Hat Graph

0 1 2 3 4 5 6 7 8 9 10Number of hats

Type

of h

at

b. Write about your sorting above.

3. Describe another way you could sort the hats.


Step Ahead Look at your graph in Question 2. Complete these sentences to describe the data.

a. There are more hats than hats.

b. There are less hats than hats.

2. a. Sort the same hats another way. Then complete this graph to show your sort.

Clown Hat Graph

0 1 2 3 4 5 6 7 8 9 10Number of hats

Type

of h

at

b. Write about your sorting on page 28.

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30 ORIGO Stepping Stones 2 • 1.12

Interpreting and Constructing One-to-One Picture Graphs1.12

Lily asked some students to vote for their favorite type of movie. She showed the results with this picture graph.

How many students voted for each type of movie? How do you know?

What types of movies are more popular than Scary?

How many more students voted for Action than Cartoon?

How many students voted in total? How do you know?

Step Up 1. Ask each student in your class to vote for their favorite type of movie. Record the results in this tally chart.

Type of movie Tally Total

Comedy

Cartoon

Action

Scary


2. a. Draw to create a picture graph that shows your results.

b. What is the most popular type of movie?

c. What is the least popular type of movie?

d. students in total voted for Comedy and Scary.

e. What is the difference in the number of votes for Action and Cartoon?

Step Ahead a. Complete this bar graph to show the data from your tally chart.

Comedy

Cartoon

Action

Scary

Favorite Movies

0 1 2 3 4 5 6 7 8 9 10 11 12 13Number of votes

Type

of m

ovie

means 1 voteFavorite Movies

Number of votes

Type

of m

ovie

b. Which type of graph do you like best? Explain your thinking.

means 1 vote

Type

of m

ovie

Number of votes

Comedy

Cartoon

Action

Scary

Favorite Movies

Comedy

Cartoon

Action

Scary

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2. Add the groups. Then write an addition fact to match.

Step Up 1. Write numbers to match each picture. Then write the addition fact.

What addition story could you say about this picture?

Which number is the total in your story? How do you know?

Which numbers are parts of the total? How do you know?

What equation could you write to match your story?

ORIGO Stepping Stones 2 • 2.1ORIGO Stepping Stones 2 • 2.1

Working with Addition2.1

a.

There are eggs in the basket.

There are eggs out of the basket.

There are eggs in total.

+ =

a.

c.

b.

b.

There are green apples.

There are red apples.

There are apples in total.

+ =

d.

3. Read the story. Then write an addition fact to match.

a. Kimie has 6 raspberries and 2 strawberries. How many berries does she have in total?

b. Mano has eaten 7 olives and has 2 more to eat. How many olives did he have in total?

Step Ahead Write numerals to complete different number facts. Make each total less than 10.

+ 3

= = 3

+ + 3

=

= 3

+ + 3

= = 3

+

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Look at these pictures. What do you notice?

What addition facts could you write to match the pictures?

What do you call a pair of facts like this?


Using the Commutative Property of Addition with Count-On Facts2.2

These are called turnaround facts. Turnaround facts have the same parts and the same total.

Step Up 1. Write two addition facts to match each picture.

Step Ahead Write the turnaround sentences to match.

a. 14 + 2 = 16

+ =

b. 3 + 12 = 15

+ =

c. 17 + 0 = 17

+ =

2. Draw lines to join matching turnaround facts. Cross out the facts that do not have a match.

3. Write true or false.

a. b.

c. d.

8 + 3 = 11

2 + 7 = 9

0 + 8 = 8

1 + 6 = 7

2 + 3 = 5

8 + 1 = 9

3 + 2 = 5

7 + 2 = 9

4 + 1 = 5

3 + 8 = 11

1 + 8 = 9

8 + 0 = 8

a. 5 + 0 = 5is the turnaround for

0 + 5 = 5

c. 6 + 2 = 8is the turnaround for

4 + 4 = 8

b. 3 + 9 = 12is the turnaround for

12 + 9 = 3

e. 2 + 8 = 10is the turnaround for

4 + 6 = 10

d. 4 + 1 = 5is the turnaround for

1 + 4 = 5

f. 0 + 3 = 3is the turnaround for

3 + 3 = 04

+ 2 =

2 + 4 =

+ =

+ =

+ =

+ =

+ =

+ =

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2. Look at each sheet of stickers. Complete the sentences to match.

Kristina bought a sheet of 12 stickers. She put 3 stickers on a card she was making.

What subtraction story could you say about what happened?

Which number is the total in your story? Which numbers are parts of the total?

What addition story could you say about the 12 stickers?

Which number is the total in your story? Which numbers are parts of the total?

What do you notice about the parts and total in the addition and subtraction stories?


Relating Addition and Subtraction (Count-On Facts)2.3

Step Up 1. Write the number of stickers on each card and the total.

a.

One part is .

The other part is .

The total is .

b.

b.

+ 9 = 12

12 − = 9

a.

4 + = 6

6 − = 4

Step Ahead Write numerals to make each sentence true.

3. Figure out how many dots are covered. Then write the matching number sentences.

a. 11 dots in total

+

=

−

=

b. 7 dots in total c. 9 dots in total

+

=

−

=

+

=

−

=

One part is .

The other part is .

The total is .

d.

+ 8 = 9

9 − = 8

c.8 + = 10

10 − = 8

a. 5 + =

b.

− 5 =

c. 5 = +

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2. For each number fact, color the total red. Then color the two parts blue.

Step Up 1. Write two addition facts to match each picture. Then write two subtraction facts to match.

What two addition facts could you write to match?

What two subtraction facts could you write to match?


Working with Count-On Fact Families2.4

Look at this picture. What addition story could you say?

What are the parts and total for your story?

What are these four facts called?

What other fact families do you know?

These two addition facts and two subtraction facts make a fact family.

a.

+ =

+ =

− =

− =

b. c.

Step Ahead Write the other number sentences that complete these families.

a. 1 1 + 2 = 13

+ =

− =

− =

b. 3 + 15 = 18

+ =

− =

− =

c. 14 + 1 = 15

+ =

− =

− =

a.

2 + 3 = 5b.

8 = 7 + 1c.

10 − 1 = 9

d.

7 − 3 = 4e.

6 = 0 + 6f.

7 + 3 = 10

3. Use the same color to show the number facts that belong in the same fact family. The first one has been done for you.

2 + 1 = 3 8 + 3 = 11 1 + 3 = 4 11 − 3 = 8

4 − 1 = 3 7 − 6 = 1 11 − 2 = 9 6 + 1 = 7

11 − 8 = 3 9 − 6 = 3 2 + 9 = 11 3 − 1 = 2

3 + 1 = 4 1 + 2 = 3 9 − 3 = 6 4 − 3 = 1

3 + 8 = 11 7 − 1 = 6 9 + 2 = 11 6 + 3 = 9

3 – 2 = 1 3 + 6 = 9 1 + 6 = 7 11 – 9 = 2

99

+ =

+ =

− =

− =

+ =

+ =

− =

− =

99

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3. Count on 10 or 20 and write the total. You can use the chart to help.

Look at this chart. Loop a number between 13 and 18.

Think about the number of tens and ones in your number.

What happens to the tens when you move right on the chart? What happens to the ones?

What happens to the tens and ones when you move down on the chart?


Extending the Count-On Strategy to Two-Digit Numbers2.5

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

Step Ahead Use the chart above to help you.

Anna has 4 dimes and 6 pennies. Noah has 23 pennies and 2 dimes. Amos has 1 dime and 38 pennies.

Who has the most money?

4. Count on to figure out the total. Then write the turnaround.

a. b. c.46 + 30 =

+ =

20 + 59 =

+ =

82 + 10 =

+ =

Step Up 1. Count on 1, 2, or 3 and write the total. You can use the chart above to help.

2. Write the total. Then write the turnaround.

a.14 + 3 =

+ =

c.38 + 1 =

+ =

2 + 26 =

+ =

b.

d. f.29 + 1 =

+ =

e.3 + 24 =

+ =

3 + 33 =

+ =

5. Count on to figure out these totals. Use turnarounds to help you.

a. 11 + 2 = b. 3 + 16 = c. 18 + 2 =

d. 23 + 1 = e. 2 + 27 = f. 25 + 3 =

g. 3 + 32 = h. 34 + 3 = i. 1 + 33 =

a. 43 + 10 = b. 57 + 20 = c. 53 + 20 =

d. 10 + 67 = e. 68 + 20 = f. 10 + 74 =

a. 30 + 45 = b. 2 + 86 = c. 3 + 17 =

d. 20 + 33 = e. 1 + 97 = f. 30 + 68 =

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

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11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

2. Start with the greater number. Write addition sentences to show how you add the tens, then the ones. Then write the total.

a.

62 + 34 =

62 + 30 = 9292 + 4 =

b.

74 + 15 =

+ =

+ =

c. 16 + 83 =

+ =

+ =

d. 46 + 32 =

+ =

+ =

3. Start with the greater number. Write addition sentences to show how you add the ones, then the tens. Then write the total.

a. 56 + 21 =

56 + 1 = 5757 + 20 =

b. 66 + 13 =

+ =

+ =

c. 16 + 72 =

+ =

+ =

d. 35 + 54 =

+ =

+ =

Step Up 1. Draw arrows on the chart above to show how you add each of these. Then write the totals.

What is the total cost of these clothes? How did you figure it out?

How could you use a hundred chart to show how you add the two numbers?

Which method do you like best? Why?


Using Place Value (Hundred Chart) to Add Two-Digit Numbers2.6

I would start with 48 and add the tens first. 48 plus 20 is 68. Then 1 more is 69.

I would start with 48 and work with the ones first. 48 plus 1 is 49. 49 plus 20 is 69.

$48

Step Ahead Write the missing numbers along this trail.

+13 +11+21 +2215

$21

a. 15 + 12 = b. 43 + 23 = c. 49 + 11 =

d. 28 + 12 = e. 35 + 21 = f. 41 + 21 =

g. 13 + 11 = h. 37 + 31 = i. 21 + 13 =

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Step Up 1. a. Draw jumps on this number line to show how you would add 56 and 13.


How can you figure out the total cost of the guitar and book?

How could you use this number line to show how you added?

Using Place Value (Number Line) to Add Two-Digit Numbers2.7

$73 $14

b. Draw jumps on this number line to show another way you could add 56 and 13.

50 60 70

50 60 70

70 80 90

+10 +4

70 80 9073 83 87

Step Ahead Write the missing numbers on this trail.

+21 +14+40 +1113

a.

46 + 12 =

40 50 60 70

c.

62 + 27 =

60 70 80 90

b.

35 + 21 =

30 40 50 60

d.

55 + 24 =

50 60 70 80

e.

33 + 16 =

30 40 50 60

I started at 73 and added the tens then the ones of 14. I can draw jumps like this to show how I added.

2. Draw jumps to show how you could count on to figure out each of these. Then write the totals.

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2. Write each time in words.

Step Up 1. Loop in red the clocks that show a time on the hour. Loop in blue the clocks that show a time half past the hour.

How many minutes are in one hour?How many minutes are in half an hour? How do you know?

Look at these two clocks.

What times are they showing? How do you know?


Reading and Writing Time on the Hour and Half Past the Hour2.8

Look at this analog clock.What does the long hand tell you?What does the short hand tell you?What time is shown on the clock?

Look at this digital clock.What do the numbers on the left side of the colon tell you?What do the numbers on the right side of the colon tell you?What time is shown on the clock?

Step Ahead Loop the clocks that show a time after 11 o’clock in the morning and before half past 4 in the afternoon.

7:308:031:303:00 1:00

12:005:30

1 1:30

2:00

4:30

a. b.

f.4:00

e.6:30

i.h.

12:00

g.

d.12:30

c.

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3. Write the hours that have passed.

What time is shown on this clock? How do you know?

Where will the clock hands be pointing one hour later? How do you know? What time is one hour later than 8 o’clock?

Look at these two clocks.

Imagine the clock on the left shows the start time for a movie and the clock on the right shows the finish time.

How long is the movie? How do you know?

How will the clock hands move during that time? How do you know?


Working with Duration (Hours)2.9

The minute hand will make 2 full turns around the clock and at the same time the hour hand will move forward 2 numbers to show 2 hours.

Step Up 1. Write the time that is 2 hours later than the time on each clock.

2. Write the times that are 3 hours later.

4. Read each time. Then write the time that was 2 hours before.

a.

o’clock

b.half past

c.

o’clock

Step Ahead

Draw the missing clock hands to show a start and finish time for an activity that lasts 5 hours.

start finish

a. start finish

hours

b. start finish

hours

c.

hour

start

4:00

finish

5:00

d.

hours

start

9:30

finish

1 1:30

d. half past 9

:

e. 1 o’clock

:

f. half past 12

:

b. 1 1 o’clock

:

c. half past 5

:

a. 8 o’clock

:

a.

9:00

:

b.

12:30

:

c.

3:00

:

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Step Ahead Count in steps of five to figure out how many minutes have passed.

2. Write numbers to show each time.


Identifying Five-Minute Intervals2.10

How many minutes past the hour is this clock showing?

Which hour is it? What time is the clock showing?

What is another way you could read this time?

Step Up 1. Write each time.

a.

minutes past 8

b.

minutes past 9

c.

minutes past 4

b.

minutes

start finish

What time is showing on this clock? How do you know?

Count in steps of five around this clock. Write the numbers you say.

What happens when you reach 12 on the clock?

How many minutes past the hour is a half-past time? How do you know?

a.

minutes

start finish

5

finish

minutes past

a.

minutes past

b.

minutes past

c.

minutes past

d.

minutes past

e.

minutes past

f.

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2. Draw lines to connect clocks to times. Cross out the two clocks that do not have a match.

Working with Five-Minute Intervals2.11


How would you show the same time on an analog clock? How do you know?

Look at this clock. Why is there a zero just before the five? 9:05

What different ways could you say the time shown on this clock? 9:20

What time is showing on this digital clock?

How would you show the same time on an analog clock? How do you know?

9:35

Step Up 1. Draw lines to connect the matching times.

2:35 3:45 7:20 10: 15 7: 10

twenty-five past twelve

ten past six

fifteen past five

one forty

five past eleven

two forty-five

three thirty

twenty past eight

3:30

6:20

12:25 1:00

2:45

5: 15

Twenty past nine.

Nine twenty.

Step Ahead In each pattern, the next clock shows five minutes more. Complete the missing times.

a.

b.3:05 3: 10: : :

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3. Write how many minutes have passed.

Step Up 1. Write the times that are 5 minutes later.


Working with Duration (Hours and Minutes)2.12

2. Write the times that are 15 minutes later.

a.

minutes past

b.

minutes past

c.

minutes past

a.

minutes

start finish b.

minutes

start finishWhat time is shown on this clock? How do you know?

Where will the clock hands be pointing one hour later? How do you know?

Where will the clock hands be pointing five minutes later? Where will the clock hands be pointing ten minutes later?

What time is showing on this clock? How could you figure out the time that is 15 minutes later?

What time is five minutes later than 2:55? How do you know?

I would count on 15 minutes in steps of five Ð 3:15, 3:20, 3:25, 3:30.

3: 15

c.

minutes

start finish

1: 10 1:40

d.

minutes

start finish

4:20 4:55

4. Read the story. Then write the times.

Juan and Sam started making a cake at 9:10. It took 5 minutes to find all the things they needed. It took another 10 minutes to prepare and mix all the ingredients. Then the mixture was placed in the oven and cooked for an hour. When the cake was cooked, they let it cool for 5 minutes before taking the cake out of the baking pan.

a. At what time did the mixture go into the oven?

b. At what time did the cake come out of the baking pan?

a.

8: 10

:

: :

Step Ahead Read the story. Then answer the questions.

b. Donna left her friend’s house at 2:50. She arrived home at 3:15. How long did it take to get home?

minutes

a. Daniel started reading at 4:40. He read for half an hour. When did he finish reading?

:

c.

1:40

:

b.

1 1:20

:

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b.

hundreds tens ones

c.

hundreds tens ones

d.

hundreds tens ones

a.

hundreds tens ones


2. Loop groups of 10 tens blocks to make one hundred. Then write the number of hundreds, tens, and ones.

Step Up1. Loop groups of 10 tens blocks to make one hundred.

Write the number of hundreds. Then write the number of tens and ones left over.

Where have you seen or heard one hundred?

What are some different ways you could show one hundred?

How could you show one hundred using blocks like these? How many tens blocks would you need? How many ones blocks would you need? What other block could you use?

What different ways could you show 125 using blocks?

Working with Hundreds3.1

My great-grandmother is 100 years old.

There are 100 cents in one dollar.

a.

1 hundred 3 tens 5 ones

b.

hundred tens ones

Step Ahead Write the missing numbers.

is the same as1 hundred 4 tens 7 ones tens onesa.

is the same as3 hundreds 4 tens 5 onesb.

is the same as3 hundreds 4 tens 0 onesc.

1 hundreds block, 2 tens, and 5 ones, or

12 tens and 5 ones, or 125 ones.

tens ones

tens ones

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2. Write the matching number on the expanders.


Writing Three-Digit Numbers3.2

What number is shown by these blocks?

How do you know?

How could you show the same number on these expanders?

How do you know where to write the digits?

Look at the picture of blocks above. Look at these expanders.

What blocks must be added to those above to create this number?

Step Up 1. Look at the blocks. Write the matching number on the expander.

a.

b.

c.

Step Ahead Color blocks to show a number that uses more tens blocks than ones blocks. Then write the number on the expanders.

52 7

2 5 7

a.

b.

c.

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How could you show the same number on this expander?

How do you read the number? What parts of the number do you say together?

How would you read and say these numbers?

What number is shown by these blocks?

How do you know?


Reading and Representing Three-Digit Numbers3.3

Step Ahead Color more blocks to match the number on the expander.

4 2 5

6 3 6

5 4 9

2 5 4

7 8 1

2. Color blocks to show the number on the expander.

b.

a.

c.

d.

e.


a.

b.

c.

4 7 7 5 8 4

6 5 2

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Writing Three-Digit Number Names3.4

How do you read the number? What do you notice?

Which of these number words would you use to complete the number name to match?

a.

b.Step Ahead Look at these two pictures of blocks. Figure out the total

of the two numbers they show. Then write the total in words.

hundred

What number is shown on this expander? How do you know?

2. Look at the blocks. Write the number on the expander. Then complete the number name.

hundred

hundred

hundred

hundred

b.

c.

d.

a.

c.

ten twenty thirty

forty fifty sixty

seventy eighty ninety

one two three

four five six

seven eight nine

hundred

1 6 3

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2. Write the matching number on the expander, then write the numeral.

How could you show the same number on these expanders?

How would you write the numeral without an expander?

Look at the picture of blocks above. How many of each type of block must be added to create this number? How do you know?

Step Up 1. Look at the blocks. Write the matching number on the expanders.

Howcouldyoufigureoutthenumber shown in this picture of blocks?


Writing Three-Digit Numerals3.5

I add the places in my head like this: 400 + 20 + 5 = 425

b.

Step Ahead Look at these pictures of blocks. Figure out and write the total of the two numbers they show.

7 4 6

a.

a.

d.

b.

c.

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Step Ahead Natalie has made some mistakes on her number line. Find each mistake and write the correct numeral.

Write the numeral for each arrow. Think carefully before you write.

Look at this number line. What do you notice?

Could you draw more marks to find the number 1? Explain your thinking.


Identifying Three-Digit Numbers on a Number Line3.6

What numeral would you write in the position shown by the arrow? How do you know?

What other numerals could you label on the number line?

How could you draw marks to show steps of 50 from 0? What numerals would you label at these marks?

Where would you draw more marks to find 10?

You could split the part between 0 and 100 into 10 smaller parts that are the same length. The first part would be 10.

Step Up Write the numeral that should be in the position shown by each arrow.

600 800700

a. 620 b. 660 c. 720 d. 790

g. 730e. 630 f. 670 h. 760

0 400

100 700500300

1.

200 800600400

2.

a. b. d. e.c.

a. b. d. e.c.

5.

100 200

a. b. c. d.

e. f. g. h.

4.

700 900

a. b. c. d.

e. g.f. h.800

3.

300 500400

a. b. d.

e. f. g. h.

c.

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2. Measure the length of each worm using cubes.

Step Ahead Use cubes to help you draw a worm that is between 5 and 7 cubes in length.

Jess found this worm in her garden. She used cubes to measure its length.

Is the worm longer or shorter than 5 cubes? How do you know?


Measuring Length with Uniform Non-Standard Units3.7

Is her measurement accurate? How do you know? How would you use the cubes to measure the worm?

I would join the cubes together so that there were no gaps and no overlaps.

Step Up 1. Makeacubetrainwithfivecubes.Colortheworms that are close to the length of your train.

cubes

cubes

cubes

cubes

cubes

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This pattern block is one inch long and one inch wide.

Use a pattern block to find some things that measure one inch in the classroom.

Step Ahead Nails come in many shapes and sizes. Draw a nail that is between 3 and 4 inches long.

Step Up 1. Use your inch ruler to measure the length of each picture.

What do you know about one inch?


Introducing the Inch3.8

My dad said his shoe is about 10 inches long.

The store sells 6-inch subs.

2. Use your inch ruler to measure the length of each tool picture.

inches

inches

inches

inches

inches

inches

Some books are about one inch thick.

What are some things that you think measure one inch?

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The inch is a length measurement that was once used to describe the width of a man’s thumb at the base of the nail.

In some countries, the word for inch is the same as the word for thumb.

Look at your thumb.

How does your inch compare to that of other students?

Today, the inch is standard and is still used as a length measurement. The inch is also used to describe the lengths seen in different objects such as the width of a frying pan, the length of a nail, or the height of a door.

Measurements for televisions and whiteboards are taken from opposite corners like this.

This is a picture of a 86-inch whiteboard.

2. This table shows the measurement of other televisions. Complete each sentence.

a. has the largest television.

b. has the smallest television.

c. Kaitlyn’s television is inches smaller than Elijah’s.

d. Morgan’s television is inches smaller than Stevie’s.

e. ’s television is 20 inches larger than ’s .

f. ThedifferencebetweenthesizeofMorgan’s television and the size of Kaitlyn’s television is inches.

g. ’s television is 6 inches larger than Elijah’s television.

3. Look at the table of television sizes from Question 1 and Question 2. Write the measurements in order from least to greatest.

, , , , , , ,


Working with Inches3.9

Step Up 1. This table shows the measurement of some students’ televisions.

a. Sumi or Sean

b. Carson or Cole

c. Cole or Sumi

d. Carson or Sean

Student Television Size (inches)

Sumi 37

Cole 42

Sean 32

Carson 50

Student Television Size (inches)

Elijah 46

Kaitlyn 40

Stevie 60

Morgan 52

Step Ahead Work with a teacher to measure the size of a school whiteboard. Write the size below.

inch

What measuring tool would you use to measure a whiteboard?

86 inches

In each pair, loop the student who has the larger television.

inches

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What do you know about the measure called a foot?

How long do you think it is?

The foot was once used to describe the length of a man’s foot.

Imagine you measured the length of the classroom using your feet.

Would you get the same answer as your teacher? Explain your thinking.

Use orange pattern blocks to measure the length of your ruler.

What do you notice?

What could you write to describe one foot?

What are some things at home that measure about one foot long, one foot wide, or one foot thick?


Introducing Feet3.10 2. Find and write objects in the classroom to match each length.

Less than 2 feet About 2 feet More than 2 feet

3. Your teacher will give you some grid paper and explain how to make a tape measure. Use the tape to measure the width of each object.

about feet

Deska.

about feet

Whiteboardb.

about feet

Doorc.

Step Up 1. Look around the classroom. Then write some objects that you would measure in feet.

One foot is the same as 12 inches.

A wooden spoon is about 1 foot long.

A big book could be 1 foot wide.

Some mattresses are about 1 foot thick.

Step Ahead Complete the table. Then write how you found the missing numbers.

Feet Inches

1 12

2 24

3 36

4

5

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2. Color the bar graph to show the height of each plant in Question 1.

How many inches equal one foot?

How many inches equal two feet? How do you know?

What is the height of this plant? How could you say the height a different way?

How much taller than one foot is the plant?

What are some other lengths that are between one foot and two feet long?

Working with Feet and Inches3.11

15 inches

Step Up 1. This table show the height of four plants.

Complete these sentences.

a. Thedaffodilis foot and inches high.

b. The daisy is foot and inches high.

c. The marigold is foot and inches more.

d. The violet is inches less than one foot.

Plant Height

Daffodil 17 inches

Violet 8 inches

Daisy 15 inches

Marigold 19 inches

Step Ahead Write these lengths another way.

3. Writethedifferences in height between these plants.

a. The marigold and the violet

inches

b. Thedaffodiland the marigold

inches

c. The violet and the daisy

inches

d. The marigold and the daisy

inchesDaffodil Violet Daisy Marigold

Plant Heights

Typeofflower

Hei

ght i

n in

ches

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

less

than

1 fo

otm

ore

than

1 fo

ot

a. 12 inches is the same as .

b. 16 inches is the same as foot and inches.

c. 1 foot and 4 inches is the same as inches.

d. 1 foot and 7 inches is the same as inches.

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78 ORIGO Stepping Stones 2 • 3.12 ORIGO Stepping Stones 2 • 3.12

2. Write one object that you think could match each length.

a. 2 yards

b. 5 yards

c. 10 yards

d. 50 yards

Step Up 1. Write inches, feet, or yards to show how you would measure each of these.

a. television b. sport’s track

c. whiteboard d. cell phone

e. building f. adult’s height

g. library book h. handspan

How could you measure things like a sports track or a building?

Look at the classroom yardstick. What do you notice?

How long is one yard?

How many feet equal one yard? How can you figure out the number of inches that equal one yard?

What are some things that are about one yard long, one yard wide, or one yard thick?

Introducing Yards3.12

1020

30

30

40

40

50

1020

TOUCHDOWN

TOUCHDOWN

1020

30

30

40

40

50

1020

Step Ahead

3. Use your tape measure to measure each length.

The library is about

yards long.

c. The library is about

yards wide.

d.

The classroom is about

yards long.

a. The classroom is about

yards wide.

b.

A baseball bat is nearly 1 yard long.

A door is about 1 yard wide.

A big tree could be 1 yard thick.

Complete the table. Then write how you found the missing numbers.

Yards Feet1 3

2 6

3 9

4

5

10

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Exploring the Comparison Model of Subtraction4.1

How could you show your thinking on a number track?

Look at these cubes. How many green cubes are there? How many orange cubes are there?

How many more orange cubes are there than green cubes? How could you figure it out?

I can count on or count back. The difference between the numbers is always three jumps. 1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8

2. Drawjumpstofigureoutthedifferenceforeachpairofshadednumbers. Thencompletethesentences.

c.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Thedifferenceis so

− =

d.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Thedifferenceis so

− =

e.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Thedifferenceis so

− =

a.

1 2 3 4 5 6 7

b.

1 2 3 4 5 6 7 8

Step Up 1. Figureoutthedifferencebetweeneachpairofcubetrains. Thencompletethesentence.

a.

Thedifferenceis

so7−5=

b.

c.

Thedifferenceis

so16−9=

Thedifferenceis

so9−6=

Thedifferenceis

− =

Thedifferenceis

− =

soso

Step Ahead Alishafoundawormthatwas16incheslong. Miguelfoundawormthatwas11incheslong, andAlexafoundawormthatwas4incheslong.

Loop thetwostudentswhofoundwormsthathadthegreatestdifferenceinlength.

Alisha Miguel Alexa

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Step Ahead Writethemissingnumbersalongthistrail.

2. Writethedifferences.Youcanusethecharttohelp.


Extending the Count-Back Strategy to Two-Digit Numbers4.2

What will be the next three numbers in this number pattern? How do you know?

What do you think these patterns would look like on a hundred chart?

58 56 54 52

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

80 − 1 =

a.

90 − 20 =

b.

3. Figureoutandwritethedifferences.

Dana has saved $9. If she buys this ball, how much money will she have left?

Draw jumps on the number track to show your thinking.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

$2

What is another way you could figure out the difference?

Step Up 1. Writethedifferences.Youcanusethenumbertrack abovetohelpyou.

−2 −3−30 −2089

What will be the next three numbers in this number pattern? How do you know?

86 76 66 56

63 − 10 =

c.

62 − 10 =

h.

60 − 2 =

f.

75 − 3 =

d.

79 − 20 =

e.

96 − 20 =

g.

53 − 10 =

a.

42 −01 =

f.

36 − 1 =

d.

68 − 30 =

b.

47 − 2 =

c.

25 − 10 =

e.

d. 14− 2 =

g. 10 − 1 =

a. 5− 2 =

e. 10 − 0 =

h. 8 − 3 =

b. 9− 3 =

f. 15− 3 =

i . 7 − 2 =

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How much money will be left in the wallet after buying the ball?

How did you figure it out?

How could you use this chart to show how to subtract the price?

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70


Using Place Value (Hundred Chart) to Subtract Two-Digit Numbers4.3

Step Up 1. Drawarrowsonthechartabovetoshowhowyoufigureouteachofthese.Thenwritethedifferences.

I would subtract the ones then the tens of the price. 67 take away 1 is 66. Then 66 take away 20 is 46.

$67

I would start with 67 and subtract the tens and the ones of the price. 67 take away 20 is 47. Then 1 less is 46.

2. Writesubtractionsentencestoshowhowyoucountbackthetens, then the ones.Thenwritethedifference.

a.

75−22=

75 − 20 = 5555 − 2 =

b.

82−21=

− =

− =

c. 89−32=

− =

− =

d. 96− 13 =

− =

− =

3. Writesubtractionsentencestoshowhowyoucountbackthe ones, then the tens.Thenwritethedifference.

a.

78−23=

78 − 3 = 7575 − 20 =

b.

92−31=

− =

− =

c. 76−21=

− =

− =

d. 87−22=

− =

− =

Step Ahead Writethemissingnumbersalongthistrail.

–12 –23–21 –1198

$21

d. 48− 13 =

g. 65− 11 =

a. 32 − 21 =

e. 27 − 11 =

h. 60 − 21 =

b. 53− 12 =

f. 45− 32 =

i. 69− 12 =

c. 29− 11 = SAM

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2. Writethedifference.Thendrawjumpsonthenumberlinetoshowyourthinking.

Step Ahead Drawanumberlinetohelpyoufigureoutthemissingnumber.

How much will be left in the wallet after buying the cap?

How do you know?

How could you use this number line to show how you figured it out?


Using Place Value (Number Line) to Subtract Two-Digit Numbers4.4

52+ =79

Draw jumps on this number line to show how you would figure out 68 – 12.

Draw jumps on this number line to show another way you could figure out 68 − 12.

40 50 60

50 60 70

50 60 70

−3 −10

40 50 6044 5747

I started at 57 and counted back the tens then the ones of the price. I can draw jumps like this to show how I subtracted.

Step Up 1. a. Drawjumpsonthisnumberlinetoshowhowyouwould figureout68−12.

b. Drawjumpstoshowanother wayyoucouldfigureout68−12.

50 60 70

50 60 70

a.66−13=

c.85−21=

b.57−15=

d.67−23=

e.88−26=

50 70 80 90

30 40 50 7060

50 60 70 80 90

30 40 50 60

40 50 60 70

$57 $13

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2. Writethedoublesfactthathelps.Thencompleteeachdouble-plus-2fact.

Step Up 1. Writethedoublesfactyouwouldusetofigureouteach double-plus-1fact.Thencompletethefact.

What doubles fact does this domino show?

What number sentence can you write to show this double?

How can you use that doubles fact to figure out the total number of dots on this domino?

What number sentence can you write to match?

What doubles fact would you use to figure out each of these?


Working with the Doubles Addition Strategy4.5

6 + 7 = 8 + 6 =

a.

Icanusedouble . 3+4=

b.

Icanusedouble . 7 + 8 =

c.


c.


b.


a.


Step Ahead a. Writeadoublesequationthat hasasumgreaterthan20.

b. Thenusethisknownsumtowritefournear-doublesequations.

+ =

+ =

+ =

+ =

3. Writethetotal.Thenwritetheturnaround.

a.4+5=

+ =

b.4+ 6 =

+ =

c.6 +5=

+ =

d.8 + 7 =

+ =

e.8 + 10 =

+ =

f.10 +9=

+ =

+ = SAM

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2. Figureouthowmanydotsarecovered.Thenwritethematchingequations.


How could you figure out the number of cows in the barn?




a. 9dotsintotal

+ =

− =

b. 13dotsintotal

+ =

− =

c. 11dotsintotal

+ =

− =

d. 17dotsintotal

+ =

− =

e. 14dotsintotal

+ =

− =

f. 16dotsintotal

+ =

− =

Step Ahead Writeanumberfacttomatcheachstory.

a. Tylerput6cookiesonaplate.Theplatecanhold14cookies.HowmanymorecookiescanTylerfitontheplate?

b. DonnaandKeishahave12berriestogether.Keishahas5berries.Howmanyberriesdoes Donnahave?

c. Mariabought16stickers. Thereare7redstickersandtherestareblue.Howmanystickersareblue?

d. LuisandTienhaveread 12booksintotal.Tienhas read6books.Howmanybooks hasLuisread?

Step Up 1. Writethetwopartsandthetotalforeachpicture.

b.a.

Onepartis .

Theotherpartis .

Thetotalis .

Onepartis .

Theotherpartis .

Thetotalis .

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2. Thecircleshowsthetotal.Thesquaresshowtheparts. Writethemissingnumbers,thencompletethefactfamily.

Step Up 1. Writethefactfamilyforeachdomino.

Look at these facts.

Use red to loop each total. Use blue to loop the parts in each fact.

What do you notice about the parts and total in the facts?

What do you call these four related facts?

What is the fact family for each of these dominos?

What do you notice?


Working with Doubles Fact Families4.7

4 + 6 = 10 10 − 4 = 6 6 + 4 = 10 10 − 6 = 4

a.

+ =

+ =

− =

− =

c.

+ =

+ =

− =

− =

b.

+ =

+ =

− =

− =

Step Ahead Writenumberstocompletethesedoublesandnear-doublesfacts.

a.

+ = 8b.

11 = +

c.

− = 8d.

19 = +

e.

− = 7f.

14 = +

a.

+ =

+ =

− =

− =

9

17c.

8

15

+ =

+ =

− =

− =

b.

+ =

+ =

− =

− =

76

3. Usethesamecolortoshowthefactsthatbelonginthesamefactfamily.

3+4=7

14−6=8

4+5=9

11=6+5

5+6=11

9−5=4

7−3=4

14=8+6

7−4=3

6+8=14

11−6=5

7=4+3

11−5=6

5+4=9

9−4=5

14–8=6SAM

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2. Doublethetens,thendoubletheones.Writethetotal.

3. Writethetotals.

Look at this shirt. What will be the total cost of two shirts?

How could you figure it out?


Extending the Doubles Addition Strategy Beyond the Facts4.8

$20

How could you figure out the total cost of two pairs of shorts?

20 is the same as 2 tens. Double 2 is 4 so double 2 tens is 4 tens. The total is 40.

I could double the tens first. Double 20 is 40. Then I would double the ones. Double 3 is 6. So 40 plus 6 is 46.

a. 12 + 12

Double 10 is 20 Double 2 is 4

20 + 4 =

b. 31 + 31

Double 30 is

Double is

+ =

c. 24+24

Double is

Double is

+ =

d. 45+45

Double is

Double is

+ =

Step Ahead ChooseoneoftheequationsfromQuestion3. Writeadoublesstorytomatch.

$23

Step Up 1. Writethemissingnumbers.

80 + 80

tens+ tens

is the same as

a. 70 + 70

tens+ tens

is the same as

b. 90 + 90

tens+ tens

is the same as

c.

2. Writethetotals.

b. 30 + 30 = c. 50+50= a. 40+40=

a. 14+14=

d. 35+35=

b. 21 + 21 =

e. 43+43=

c. 44+44=

f . 13 + 13 =

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2. Drawhandsontheanalogclocktoshowthematchingtime.

3. Writeeachtimetwodifferentways.

Step Up 1. Writethematchingtimeonthedigitalclock.

Look at this analog clock.

Where will the hands be pointing when the time is 11 o’clock? How do you know?

Where will the hands be pointing when the time is half past 11? How do you know?

How many minutes has the minute hand moved past the hour on this clock?

What are the different ways you could read or say the time shown on the clock?


Working with Time Quarter Past the Hour4.9

Fifteen minutes past nine, a quarter past nine.nine fifteen, or

a.

quarterpast

minutespast

c.

quarterpast

minutespast

b.

halfpast

minutespast

d.

halfpast

minutespast

Step Ahead

a.

Completetheclockstokeepeachpatterngoing.

How could you show the same time on this digital clock?

How do you know?

a.

2: 15

b.

9: 15

c.

8: 15

d.

7:30

b.

:

10:30 1 1:30 12:30 ::

d.

:

b.

:

c.

:

a.

:

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2. Writeeachoftheseasdigitaltimes. Loop a.m. or p.m.

Step Up 1. Writethedigitaltimeforeachevent. Thenwritea.m. or p.m.tomatchtheevent.

At what time does a day begin? What time does it end? How do you know?

What time is exactly in the middle of the day?

What do you know about this time of the day?

How could you show the difference between 6 o’clock in the morning and 6 o’clock in the afternoon?

We write a.m. to describe times between midnight and noon.

We write p.m. to describe times between noon and midnight.

Identifying and Recording Time Using a.m. and p.m.4.10


a.m. is short for ante meridiem which means before midday. p.m. is short for post meridiem which means after midday.

a. eatbreakfast

:

b. walkhome fromschool

:

c. preparefordinner

:

d. packlunch

:

Step Ahead

a. Whosefamilywillreachthecampsitefirst?

b. Atwhattimeofdaywilltheyarrive?

ChangandEmmaliveindifferenttowns. Theirfamiliesaredrivingtothesamecampsiteforavacation.

Chang’sfamilywillleaveat9p.m.onFriday.Theirjourneywilltake10hours.Emma’sfamilywillleaveat3a.m.onSaturday.Theirjourneywilltake5hours.

e. quarterpasteleven inthemorning

a.m. p.m.:

f. fourfifty intheafternoon

a.m. p.m.:

a. twenty-fiveminutespastteninthemorning

a.m. p.m.:

b. sevenforty-five atnight

a.m. p.m.:c. fifteenminutespastthree

intheafternoon

a.m. p.m.:

d. tenminutespasteleven atnight

a.m. p.m.:

g. tenthirty atnight

a.m. p.m.:

h. eightfifteen atnight

a.m. p.m.:

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Step Ahead Makeatimetabletoshowfiveeventsthathappentoday.

a. Whicheventcanyouwatchat11:30a.m.?

b. Howlongdothefireworkslast?

c. Whicheventtakesexactly2hours?

d. Howmanyeventstakeexactlyonehour?

e. Howmanyeventstakeexactlyhalfanhour?

f. Ifyouarriveat2:30p.m.,howlong willyouwaittoseetheDemolitionDerby?

g. Ifyouarriveat3:00p.m.,howmanyevents canyouseebeforethefaircloses?

h. Whicheventtakesthemosttime?

i. Whicheventisrepeated?

Step Up Usethisshowprogramtoanswerquestionsonpage101.

What do you think happens at 9 o’clock?

Which activity is before the morning recess?How long is the morning recess?

What time does lunch start? What time does it finish?

What time does math start?

How long is it from the start of school to the end of the first recess?Which activities last for more than one hour?Which activities are exactly half an hour long? How do you know?Which activity lasts the longest time?


Working with Timetables and Duration4.11

This timetable shows what I do on Wednesday at my school.

Our school day

9 : 1 0 a.m. reading10 : 4 5 a.m. recess1 1 : 00 a.m. math12 : 1 5 p.m. lunch12 : 4 5 p.m. writing1 : 1 5 p.m. science1 : 4 5 p.m. socialstudies2 : 1 5 p.m. recess2 : 2 5 p.m. music3 : 00 p.m. schoolends

8 : 00 a.m. Motocross1 1 : 3 0 a.m. MarchingBand12 : 3 0 p.m. DogShow1 : 00 p.m. SkydivingMarvels1 : 3 0 p.m. FashionParade2 : 3 0 p.m. HotDogEatingContest3 : 00 p.m. FolkDancing3 : 3 0 p.m. CommunityBand

Gates open 5 : 3 0 p.m. DemolitianDerbyat 7:30 a.m. 7 : 00 p.m. SkydivingMarvels

7 : 3 0 p.m. GoldenGuitarBand8 : 00 p.m. Fireworks8 : 3 0 p.m. Close

Time ActivitySAM

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102

Step Up Usethecalendaronpage102tocompletethesequestions.

Look at this calendar. What year is it for?

What do the red letters mean? Write the names of the months that are missing.

Which day of the week has been circled?

A date tells you the number of the month and the day. What date has been circled?

Some celebrations happen on the same date each year. Imagine today was “Hooray for Math Day”.

Write today’s date.

Which day of the week is it this year? Which day of the week will it be in 2021?

Some celebrations happen on a certain day of the week during the month. Mother’s Day is celebrated on the second Sunday in May. What will that date be in 2021?


Working with the Calendar4.12

JANUARY

S M T W T F S1 2

3 4 5 6 7 8 910 11 12 13 14 15 1617 18 19 20 21 22 2324 25 26 27 28 29 3031

MARCH

S M T W T F S1 2 3 4 5 6

7 8 9 10 11 12 1314 15 16 17 18 19 2021 22 23 24 25 26 2728 29 30 31

APRIL

S M T W T F S1 2 3

4 5 6 7 8 9 1011 12 13 14 15 16 1718 19 20 21 22 23 2425 26 27 28 29 30

FEBRUARY

S M T W T F S1 2 3 4 5 6

7 8 9 10 11 12 1314 15 16 17 18 19 2021 22 23 24 25 26 2728

JUNE

S M T W T F S1 2 3 4 5

6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30

S M T W T F S1 2 3

4 5 6 7 8 9 1011 12 13 14 15 16 1718 19 20 21 22 23 2425 26 27 28 29 30 31

S M T W T F S1

2 3 4 5 6 7 89 10 11 12 13 14 1516 17 18 19 20 21 2223 24 25 26 27 28 2930 31

AUGUST

S M T W T F S1 2 3 4 5 6 78 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30 31

SEPTEMBER

S M T W T F S1 2 3 4

5 6 7 8 9 10 1112 13 14 15 16 17 1819 20 21 22 23 24 2526 27 28 29 30

S M T W T F S1 2

3 4 5 6 7 8 910 11 12 13 14 15 1617 18 19 20 21 22 2324 25 26 27 28 29 3031

DECEMBER

S M T W T F S1 2 3 4

5 6 7 8 9 10 1112 13 14 15 16 17 1819 20 21 22 23 24 2526 27 28 29 30 31

NOVEMBER

S M T W T F S1 2 3 4 5 6

7 8 9 10 11 12 1314 15 16 17 18 19 2021 22 23 24 25 26 2728 29 30

2021

2. Loopthesespecialdatesonthecalendar.Thenwritethedayforeachcelebration.

a. MemorialDay–May31

b. IndependenceDay–July4

c. VeteransDay–November11

3. Writethedatesforthesecelebrations.

a. MartinLutherKingDay 3rdMondayinJanuary

b. Washington’sBirthday 3rdMondayinFebruary

c. ThanksgivingDay 4thThursdayinNovember

1. a. Howmanymonthshaveexactly30days?

b. Howmanymonthshaveexactly31days?

c. HowmanymonthsstartonaWednesday?

d. Whichmonthsstartonaweekend day?

Step Ahead Thinkabouttwoothercelebrationsthatarespecialinyourschool,home,orcommunity.Writewhentheyhappenintheyear.

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Origo Math Practice Book 1

Documents

Transcript of Origo Math Practice Book 1