Let's Do Mathematics 2 – Worktext B by Regal Education

Workt ext

for learners 7 - 8 years old

Aligned to the US Common Core State Standards

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Workt ext

for learners 7 - 8 years old

Let’s Do Mathematics

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Let’s Do Mathematics is a series covering levels K-6 and is fully aligned to the United States Common Core State Standards (USCCSS). Each level consists of two books (Book A and Book B) and combines textbook-style presentation of concepts as well as workbook practice.

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Central to the USCCSS is the promotion of problem-solving skills and reasoning. Let’s Do Mathematics achieves this by teaching and presenting concepts through a problem-solving based pedagogy and using the concrete-pictorial-abstract (CPA) approach. Learners acquire knowledge and understanding of concepts through a guided progression beginning with concrete examples and experiences which then flow into pictorial representations and finally mastery at the abstract and symbolic level. This approach ensures that learners develop a fundamental understanding of concepts rather than answering questions by learned procedures and algorithms. Key features of the series include:

Anchor Task

Numbers to 1000

Anchor Task

Open-ended activities serve as the starting point for understanding new concepts. Learners engage in activities and discussions to form concrete experiences before the concept is formalized.

141

140

Let’s Learn

Concepts are presented in a clear and colorful manner. Worked problems provide learners with guided step-by-step progression through examples. Series mascots provide guidance through helpful comments and observations when new concepts are introduced.

2-Step Word Prob lem

Let’s Learn

Blake has 12 toy cars. Dominic has 3 more How many toy cars toy cars than Blake. do they have altoge ther?

In January, Jorda n saves $36. In February, he saves $15 more than in January. How much mone y did he save in total?

First, let’s find how many cars I have.

Step 1

Step 1 Find the amount of money Jordan saves in $36

Blake’s cars

Step 2

Blake’s cars

122

February

To find the numb er of cars that Domin ic has, we add. 12 + 3 = 15 Dominic has 15 toy cars. Now we can find the total number of toy cars.

Dominic’s cars

36 + 15 = 51 Jordan saves $51

ic have 27 toy cars

6 1 5 5 1

in February.

Step 2 Add the amounts togeth $36

er to find the total. $51

January

February ?

altogether.

12 + 15 = 27 Blake and Domin

February.

$15

January

Dominic’s cars

36 + 51 = 87 Jordan saved $87 in total.

3 6 + 5 1 8 7

123

Let’s Practice

Compare the lengths Fill in the blanks.

Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment. Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.

of the objects. clarinet

of the objects Compare the lengths Fill in the blanks.

60 cm

violin 36 cm

trumpet

88 cm (a) The trumpet is (b) The trumpet is

cm.

has a length of (a) The toothpaste cm. length of (b) The comb has a cm. has a length of (c) The toothbrush toothpaste. cm shorter than the is comb The (d) the comb. than longer cm is (e) The toothbrush is the longest. (f) The is the shortest. (g) The

At Home

clarinet.

cm longer than the

violin.

clarinet. cm shorter than the

is the longest.

(d) The

is the shortest.

(e) The

from the longest to

(f) Arrange the objects

21 1

Halle asked her friend s their favorite fruit. She made a table from the data she collected. What’s your favorite fruit? Apples! Mangoes!

Make a bar graph from the table. Answer the questi ons and use the space to show Class 2A’s Favor

Water

Milk

Orange juice

Apple juice

ite Fruits

Mango

Apple

Banana

Peach

Help Halle make a

ite Drink

bar graph from the

Number of peopl e

Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.

your working.

ite Drink

Class 2A’s Favor

My Friends’ Favor

shortest.

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210

cm longer than the

table.

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My Friends’ Favor

Fruit

ite Fruits

Type of drink

Friends

296

Hands On

Play this game in groups of

Hands On

Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.

3 or 4.

The first player to pick the describes the next shape.

correct shape is the winner

and

It’s a cylinder!

Solve it!

Solve It!

Consolidated practice where learners demonstrate their understanding on a range of concepts taught within a unit.

A beetle is crawling around a garden. It starts at position A and crawls for 36 m. At which position does the beetle stop? D 9m

Activities that require learners to apply logical reasoning and problem-solving. Problems are often posed which do not have a routine strategy for solving them. Learners are encouraged to think creatively and apply a range of problem-solving heuristics.

Looking Back

297

on your table. Place different 3-D shapes by saying the number of faces, One player describes a shape edges and vertices. This 3-D shape has 2 faces.

1. 2.

The beetle stops at position 2.

Jordan is running around the soccer field. He starts at position A and runs for 400 m. At which position does he stop? D

100 m

50 m

Jordan stops at position

. 215

(b)

Looking Back Write the number in numerals and words.

(a)

Fill in the blanks. Write the number in numerals and words.

Tens

Hundreds

Ones

(b)

Fill in the blanks. +

500 +

tens

hundreds

(a)

+9=

ones

Write the number. The digit 9 is in the ones place. The digit 8 is in the hundreds place. The digit 2 is in the tens place. 243

242

iii

Contents 5 Subtraction Within 1,000

6 Word Problems

7 Shapes

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1-Step Word Problems 2-Step Word Problems

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Subtracting 100s and 10s Subtraction Without Regrouping Subtraction With Regrouping

2-Dimensional Shapes 3-Dimensional Shapes Area of Shapes Halves, Thirds and Quarters

8 Time

Telling Time to 5 Minutes Telling Time in a.m. and p.m.

9 Length

Customary Units of Length Measuring Length in Inches Measuring Length in Feet and Yards Comparing Length – Inches, Feet and Yards Metric Units of Length Measuring Length in Centimeters Measuring Length in Meters Comparing Length (Centimeters and Meters)

2 4 12 26

44 44 50 58 58 74 82 90

106 108 130 144 144 146 186 176 186 188 200 208

Coins and Notes Exchanging Money Counting Money Comparing Money Money Word Problems

11 Data and Graphs

266 268 278 288 300

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Drawing Picture Graphs Reading Picture Graphs Bar Graphs Line Plots

226 227 233 242 250 256

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10 Money

Subtraction Within 1,000

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Hundreds

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Anchor Task

Tens

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Ones

–

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–

Subtracting 100s and 10s Let’s Learn Find 500 – 200.

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5–2=3 500 – 200 = 300

Subtract the hundreds. 500 – 200 = 300

5 – 2 3

0 0 0

4 – 3 1

4 0 4

3 0 3

Find 443 – 300.

Subtract the hundreds. 443 – 300 = 143

Find 253 – 10.

Subtract the tens.

5 1 4

3 0 3

Find 553 – 30.

–

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253 – 10 = 243

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5–1=4 50 – 10 = 40

Subtract the tens. T

5 3 2

3 0 3

–

513 523 533 543 553 563 573

553 – 30 = 523 5

Let’s Practice 1. Subtract the hundreds. 6 3

0 0

8 1

0 0

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(a) (b) 4 0 0 – – 2 0 0

(e) (f) 9 0 0 0 0 – – 5

–

(i) 500 – 300 =

–

0 0

(h) 800 – 700 =

(g) 700 – 400 =

7 5

–

(j) 900 – 700 =

–

0 0

2. Subtract the tens. 7

6 5

0 0

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(a) (b) 3 2 0 1 0 – –

8 3

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(e) (f) 6 5 9 – 2 0 –

–

(i) 747 – 30 =

–

9 7

9 0

(h) 866 – 60 =

(g) 372 – 20 =

7 0

–

(j) 977 – 50 =

–

3. Fill in the missing numbers. (a)

800

–

600

–

300

400

–

200

700

(c)

100

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(b)

–

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400

(d)

4. Fill in the missing numbers. (a)

397

(c)

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(b)

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–

558

337

–

608

–

769

688

–

(d)

789

Solve It! Fill in the blanks. What is the rule?

600 The rule is

777

500

400

655

182

(b)

700

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800

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(a)

727

The rule is

605 .

541

At Home 1. Complete the equation. (b) 300 – 300 =

(d) 900 – 500 =

(e) 600 – 400 =

(f) 800 – 600 =

2. Fill in the missing numbers.

= 800 (b) 800 –

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(a) 900 –

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(a) 500 – 300 =

– 400 = 100 (d)

– 400 = 500

= 400 (f) 300 –

– 300 = 300 (h)

= 200

= 100

– 700 = 200

3. Complete the equations.

(b) 542 – 30 =

(d) 984 – 80 =

(e) 663 – 30 =

(f) 788 – 40 =

(a) 534 – 10 =

4. Fill in the missing numbers.

(a) 285 – (c) (e) 771 –

(g)

= 225 (b) 356 –

– 10 = 632 (d) = 721 (f) 465 – – 90 = 909 (h)

= 306 – 50 = 510 = 445 – 70 = 622 11

Subtraction Without Regrouping Remember This! Subtract the ones. 8 ones – 5 ones = 3 ones. Ones

Tens Ones

4 2

8 5

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Tens

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Subtract 25 from 48.

–

Subtract the tens. Tens

Ones

Tens Ones

8 5

–

4 2

4 tens – 2 tens = 2 tens. 48 – 25 = 23

Find 87 – 76. Subtract the ones. Tens Ones

–

8 7

7 6 1

87 – 76 = 11 12

Subtract the tens. Tens Ones

–

8 7

7 6

Have a Go! Fill in the blanks. (a) 19 – 11 =

–

(g) 75 – 43 =

–

(d) 87 – 35 =

–

(e) 94 – 52 =

–

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–

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(b) 28 – 22 =

(f) 63 – 33 =

–

(h) 99 – 87 =

–

Let’s Learn

Hundreds

Tens

Ones

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Mrs Jenkins baked 265 pies. She sold 42 pies. How many pies does Mrs Jenkins have left? Let’s subtract 42 from 265.

6 4

5 2

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–

Subtract the ones.

6 4

Subtract the tens.

5 2 3

6 4 2

5 2 3

6 4 2

5 2 3

–

Tens

Hundreds

265 – 42 = 223 Mrs Jenkins has 223 pies left. 14

Subtract the hundreds.

Ones

–

Subtract 265 from 597. Tens

Ones

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Hundreds

Subtract the ones.

Subtract the tens.

Subtract the hundreds.

5 – 2

9 6

7 5 2

5 – 2

9 6 3

7 5 2

5 – 2 3

9 6 3

7 5 2

Tens

Ones

Hundreds

597 – 265 = 332 15

Let’s Practice 1. Cross out and subtract. (a)

Tens

Ones

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Hundreds

5 1

6 2

–

5 1

8 5

8 4

–

3 2

9 6

7 7

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–

(b)

R 16

Tens

Hundreds

(c)

Tens

Ones

(d)

Tens

Ones

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Hundreds

4 2

5 1

–

4 3

3 3

9 2

–

6 5

8 7

4 4

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–

(e)

Tens

Hundreds

Tens

Ones

(f)

7 5

2. Subtract.

(e)

7 6

(b)

5 3

8 5

(d)

–

4 2

–

8 3

6 4

(f)

0 0

9 8

(h)

5 4

(j)

–

8 3

1 0

8 5

(l)

–

9 6

9 1

6 3

9 5

3 2

–

1 1

4 1

9 3

–

7 3

2 1

6 3

–

9 3

8 2

4 3

–

4 3

6 3

8 8

–

8 8

(k)

–

8 5

(g)

(i)

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–

4 1

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(a)

3. Subtract.

–

(b) 358 – 36 = 5 1

8 2

–

8 2

(g) 992 – 852 = 9 8

–

7 1

6 4

5 4

7 4

–

6 3

0 0

9 5

5 4

7 2

5 5

9 5

(h) 557 – 542 =

9 5

(i) 824 – 614 = 8 6

8 6

(f) 609 – 305 =

–

5 3

(d) 765 – 144 =

(e) 887 – 424 = 8 4

–

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–

4 1

3 2

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(a) 153 – 12 =

2 2

–

5 5

(j) 959 – 355 = 2 1

4 4

–

9 3

Hands On

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100

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Work in pairs. Use place value disks and base-ten blocks to help you subtract.

1. Place number disks in the chart to show 176. Tens

Ones

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Hundreds

2. Take away 2 tens and 3 ones. What remains? 3. Complete the equation 176 –

4. Now continue the process to complete the following.

(a) 125 – 5 =

(b) 166 – 14 = (d) 363 – 101 =

(e) 469 – 55 =

(f) 785 – 325 =

(g) 888 – 456 =

(h) 682 – 431 =

At Home 1. Fill in the blanks. Subtract. (b) 768 – 55 =

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(a) 432 – 11 =

–

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–

(f) 983 – 911 =

(e) 818 – 508 =

(d) 758 – 644 =

–

(g) 668 – 461 =

–

(h) 579 – 227 =

–

2. Subtract. Show your working. (b) 468 – 53 =

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(a) 133 – 22 =

–

(d) 783 – 161 =

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(f) 596 – 372 =

(e) 295 – 251 =

–

(g) 585 – 472 =

–

(h) 991 – 680 =

–

(i) 794 – 191 =

(j) 687 – 341 =

–

(l) 855 – 141 =

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(k) 977 – 474 =

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–

(m) 587 – 237 =

(n) 966 – 634 =

–

(o) 851 – 731 =

–

(p) 499 – 437 =

–

Solve It! Ethan left his Mathematics notebook outside. Rain has washed away some of the numbers. Write the missing numbers.

4 4 4 – 2 4 1 2 0 3

(c)

6 9 4 – 3 3 2 3 6 2

(d)

7 8 6 – 1 4 2 6 4 4

(e)

9 5 8 – 2 4 6 7 1 2

(f)

7 9 4 – 1 5 1 6 4 3

(g)

8 0 8 – 3 0 5 5 0 3

(h)

3 6 9 – 1 2 8 2 4 1

9 9 9 – 7 8 7 2 1 2

(j)

7 9 2 – 2 7 2 5 2 0

6 4 1 – 4 1 1 2 3 0

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R (i)

(b)

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(a)

Subtraction With Regrouping Remember This! Tens

Ones

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Subtract 25 from 52.

Tens Ones

5 2

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–

2 5

We cannot subtract 5 ones from 2 ones. Regroup 1 ten into 10 ones. Tens

Ones

Tens Ones

–

5 2

12 2

12 ones – 5 ones = 7 ones. Subtract the tens.

Tens

4 tens – 2 tens = 2 tens. 52 – 25 = 27 26

Ones

Tens Ones 4

–

5 2

12 2

Have a Go! Fill in the blanks. (a) 23 – 16 =

–

(g) 81 – 48 =

–

(d) 43 – 17 =

–

(e) 63 – 35 =

–

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–

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(b) 56 – 38 =

(f) 94 – 78 =

–

(h) 64 – 27 =

–

Let’s Learn

Hundreds

Tens

Ones

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252 children visited the zoo on Saturday. 36 fewer children visited the zoo on Sunday. How many children visited the zoo on Sunday? Let’s subtract 36 from 252. H

5 3

2 6

–

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Subtract the ones. Regroup 1 ten as 10 ones.

12 ones – 6 ones = 6 ones

Hundreds

Tens

Ones

–

5 3

O 12

2 6 6

Subtract the tens. 4 tens – 3 tens = 1 ten

Tens

2 Ones

Hundreds

252 – 36 = 216 216 children visited the zoo on Sunday. 28

–

5 3 1

O 12

2 6 6

Subtract the hundreds. 2 hundreds – 0 hundreds = 2 hundreds H

2 –

5 3 1

O 12

2 6 6

Find 328 – 284. Hundreds

Tens

Ones

3 – 2

2 8

8 4

Tens

Ones

3 – 2

2 8

8 4 4

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Hundreds

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Subtract the ones. 8 ones – 4 ones = 4 ones

Subtract the tens. Regroup 1 hundred as 10 tens. 12 tens – 8 tens = 4 tens

2 8 4

8 4 4

3 – 2

Hundreds

Tens

Ones

Subtract the hundreds. 2 hundreds – 2 hundreds = 0 hundreds 2

3 – 2

2 8 4

8 4 4

328 – 284 = 44 29

Find 432 – 269. Hundreds

Tens

Ones Subtract the ones. Regroup 1 ten as 10 ones. 12 ones – 9 ones = 3 ones 4 – 2

Tens

4 – 2

al eg

3 6

2 9 3

3 6 6

2 9 3

Ones

4 – 2 1

3 6 6

432 – 269 = 163 30

Subtract the hundreds. 3 hundreds – 2 hundreds = 1 hundred 3

Tens

O 12

Ones Subtract the tens. Regroup 1 hundred as 10 tens. 12 tens – 6 tens = 6 tens 3

Hundreds

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Hundreds

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2 9 3

Find 300 – 163. Hundreds

Tens

Ones Regroup 1 hundred as 10 tens. Then regroup 1 ten as ten ones. 2

0 6

O 10

0 3 7

Hundreds

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3 – 1

Tens

Ones Subtract the tens. 9 tens – 6 tens = 3 tens 2

0 6 3

O 10

0 3 7

3 – 1

Hundreds

300 – 163 = 137

Tens

Ones Subtract the hundreds. 2 hundreds – 1 hundred = 1 hundred 2

3 – 1 1

0 6 3

O 10

0 3 7 31

Let’s Practice 1. Cross out and subtract. (a)

Tens

Ones

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Hundreds

3 1

3 7

–

5 1

7 3

4 6

–

5 2

2 6

8 4

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–

(b)

Tens

Hundreds

Tens

Ones

(c)

(d)

Tens

Ones

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Hundreds

(e)

Tens

3 5

4 6

–

5 3

0 5

6 8

Ones

Hundreds

–

7 2

2. Subtract.

(e)

7 9

(b)

2 4

8 5

(d)

–

7 2

–

8 6

6 6

(f)

2 1

8 9

(h)

4 7

(j)

–

3 5

4 7

5 9

(l)

–

9 6

9 7

1 3

9 5

6 8

–

8 5

8 1

3 9

–

6 1

1 3

3 6

–

5 1

0 9

0 6

–

8 3

6 6

7 8

–

8 5

(k)

–

1 5

(g)

(i)

7 5

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–

4 1

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(a)

3. Subtract.

–

(b) 482 – 66 = 5 2

6 9

–

0 2

(g) 752 – 176 =

7 1

–

7 1

6 8

5 4

7 8

–

5 7

5 8

(h) 921 – 573 =

5 7

(i) 854 – 668 = 8 6

2 6

(f) 255 – 78 =

–

8 6

(d) 765 – 184 =

(e) 807 – 428 = 8 4

–

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–

4 2

3 7

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(a) 253 – 27 =

2 6

–

9 5

2 7

1 3

(j) 912 – 683 = 5 6

4 8

–

9 6

1 8

2 3

Hands On

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Work in pairs. Use place value disks and base-ten blocks to help you subtract.

100

1. Place number disks in the chart to show 224. Tens

Ones

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Hundreds

2. Take away 38 by first exchanging 1 ten for 10 ones and 1 hundred for 10 tens. 3. Complete the equation 224 –

4. Now continue the process to complete the following.

(a) 115 – 9 =

(b) 230 – 28 = (d) 427 – 208 =

(e) 581 – 126 =

(f) 723 – 346 =

(g) 834 – 745 =

(h) 921 – 545 =

At Home 1. Fill in the blanks. Subtract. (b) 663 – 136 =

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(a) 172 – 91 =

–

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–

(f) 902 – 511 =

(e) 700 – 561 =

(d) 772 – 185 =

–

(g) 653 – 578 =

–

(h) 946 – 769 =

–

2. Subtract. Show your working. (b) 166 – 79 =

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(a) 744 – 427 =

–

(d) 605 – 162 =

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(f) 936 – 376 =

(e) 864 – 271 =

–

(g) 522 – 178 =

–

(h) 574 – 288 =

–

(i) 758 – 459 =

(j) 631 – 371 =

–

(l) 588 – 399 =

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(k) 914 – 475 =

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–

(m) 722 – 174 =

(n) 906 – 638 =

–

(o) 470 – 288 =

–

(p) 817 – 549 =

–

Solve It! Ethan left his mathematics notebook outside again! Rain has washed away some of the numbers. Write the missing numbers.

7 2 1 – 2 4 1 4 8 0

(c)

4 9 4 – 1 9 5 2 9 9

(d)

7 1 1 – 1 3 6 5 7 5

(e)

9 0 8 – 7 4 9 1 5 9

(f)

3 4 – 1 5 5 1 6

8 0 0 – 6 1 9 1 8 1

(h)

9 6 3 – 1 6 6 7 9 7

4 1 5 – 2 8 7 1 2 8

(j)

7 7 4 – 2 7 9 4 9 5

(i)

6 0 4 – 1 8 2 4 2 2

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(g)

(b)

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(a)

Looking Back 1. Complete the equations. (b) 900 – 800 =

(d) 600 – 500 =

(e) 800 – 600 =

(f) 700 – 700 =

2. Complete the equations.

(b) 575 – 40 =

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(a) 114 – 10 =

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(a) 500 – 200 =

(d) 964 – 50 =

(e) 693 – 40 =

(f) 781 – 30 =

3. Subtract.

(a) (b) 7 8 8 4 6 – –

(e) 798 – 553 = –

7 5

8 2

1 1

9 3

6 5

0 0

8 6

3 3

8 3

(f) 938 – 433 = 9 5

8 3

–

9 4

(g) 786 – 276 =

(h) 994 - 403 =

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4. Subtract.

6 2

6 8

8 8

9 5

0 9

5 6

2 7

5 8

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(a) (b) 6 1 2 1 6 2 – –

(f) 525 – 178 =

(e) 858 – 519 =

–

8 5

(g) 912 – 467 =

–

5 1

8 9

–

5 1

(h) 784 – 595 =

–

Word Problems

1-Step Word Problems

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Let’s Learn

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Mr. Lee picked 268 strawberries and 126 mangoes. How many fruits did Mr. Lee pick in all?

268

126

Strawberries

Mangoes

2 1 3

6 2 9

8 6 4

268 + 126 = 394 Mr. Lee picked 394 fruits in all.

365 people attended a concert on Friday. 297 more people attended the concert on Saturday than Friday. How many people attended the concert on Saturday? 365

297

People on Friday 1

People on Saturday

365 + 297 = 662 662 people attended the concert on Saturday. 44

3 2 6

6 9 6

5 7 2

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Mrs. Jones and Mrs. Jenkins baked 612 cupcakes. Mrs. Jones baked 349 of the cupcakes. How many cupcakes did Mrs. Jenkins bake?

612

Mrs. Jenkins’ cupcakes

349

6 – 3 2

1 4 6

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Mrs. Jones’ cupcakes

2 9 3

612 – 349 = 263 Mrs. Jenkins baked 263 cupcakes.

Joe sold 982 chicken nuggets on Monday. He sold 438 fewer chicken nuggets on Tuesday. How many chicken nuggets did Joe sell on Tuesday?

982

Sold on Monday

Sold on Tuesday

9 – 4 5 438 fewer chicken nuggets

8 3 4

2 8 4

982 – 438 = 544 Joe sold 544 chicken nuggets on Tuesday. 45

Let’s Practice

Year 3 books read

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Year 2 books read

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1. For a school read-a-thon, the children in Year 2 read 291 books. The children in Year 3 read 347 books. How many books did the children in Year 2 and Year 3 read in all?

The children in Year 2 and Year 3 read

2. On Jacksonville Farm there are 437 sheep. There are 374 more cows than sheep. How many cows are on Jacksonville Farm?

Sheep

Cows

There are

cows on Jacksonville Farm.

books in all.

Dominic’s score

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Blake’s score

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3. Dominic scored 375 points in the school bowling competition. Blake scored 193 more points than Dominic. How many points did Blake score?

Blake scored

points.

4. Ethan has a collection of 439 marbles. Jordan gives him another 557 marbles. How many marbles does Ethan have now?

Ethan’s marbles

Ethan has

Marbles from Jordan

= marbles now.

At Home

Penguins on island

Swim away

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Penguins left

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1. There are 572 penguins on an island. 196 penguins swim away. How many penguins are left on the island?

There are

penguins left on the island.

2. A bakery sold 876 bread rolls on Wednesday. It sold 498 fewer bread rolls on Thursday. How many bread rolls did the bakery sell on Thursday?

Sold on Wednesday

Sold on Thursday

The bakery sold 48

bread rolls on Thursday.

Cars

Trucks

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3. A total of 951 vehicles passed through a toll booth. 712 of the vehicles were cars. The rest were trucks. How many trucks passed through the toll booth?

trucks passed through the toll booth.

4. On Friday, Farmer Joe picked 612 strawberries. He picked 365 strawberries in the morning. He picked the rest of the strawberries in the afternoon. How many strawberries did Farmer Joe pick in the afternoon?

Morning

Afternoon

Farmer Joe picked

strawberries in the afternoon.

2-Step Word Problems Let’s Learn

Step 1

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First, find how many children are in grade 2.

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In grade 2, there are 56 boys and 48 girls. In grade 3, there are 29 more children than in Year 2. How many children are in grade 2? How many children are in grade 3?

Boys in grade 2

Girls in grade 2

? 56 + 48 = 104 There are 104 children in grade 2.

5 4 0

6 8 4

0 2 3

4 9 3

Now, we can find the number of children in grade 3.

Step 2

104

Children in grade 3

104 + 29 = 133 There are 133 children in grade 3. 50

Children in grade 2

1 +

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On Healesville Farm there are 629 animals. 437 animals are cows. The rest of the animals are sheep. How many more cows than sheep are there on Healesville Farm?

Step 1

629

Cows

Sheep

437

–

6 4 1

2 3 9

9 7 2

3 9 4

7 2 5

Step 2

629 – 437 = 192 We know there are 192 sheep on Healesville Farm.

437

4 – 1 2

Cows

Sheep

192

437 – 192 = 245 There are 245 more cows than sheep on Healesville Farm.

Step 1 291

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On Saturday, 291 boys and 347 girls visited Central Park. On Sunday, 175 fewer people visited Central Park than on Saturday. How many people visited Central Park on Saturday? How many people visited Central Park on Sunday?

347

Boys on Saturday

Girls on Saturday

2 3 6

9 4 3

1 7 8

3 7 6

8 5 3

Step 2

291 + 347 = 638 638 people visited Central Park on Saturday. 638

6 – 1 4

Saturday

Sunday

175

463 people visited Central Park on Sunday. 52

Let’s Practice

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1. Ethan has 187 marbles. Blake has 203 more marbles than Ethan. How many marbles does Blake have? How many marbles do Ethan and Blake have in all?

Ethan’s marbles

Blake’s marbles

marbles.

Blake has

Blake’s marbles

Ethan’s marbles

Ethan and Blake have

marbles in all. 53

On a farm there are 896 lemon and lime trees in all. There are 358 lime trees. How many lemon trees are on the farm? How many more lemon trees than lime trees are there?

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Lime trees

Lemon trees

lemon trees on the farm.

There are

Lime trees

Lemon trees

There are

more lemon trees than lime trees.

A train with 3 carriages is carrying 544 people. There are 157 people in carriage A. There are 148 people in carriage B. How many people are in carriage A and B in all? How many people are in carriage C?

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Carriage A

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Carriage B

people in carriage A and B in all.

There are

Carriage A

Carriage B

Carriage C

There are

people in carriage C.

At Home

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Strawberries needed

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1. Mrs. Franklin needs 625 strawberries to bake some tarts. She has 217 strawberries at home. How many more strawberries does Mrs. Franklin need? If she buys 250 strawberries, how many more will she still need?

Mrs. Franklin’s strawberries

more strawberries.

Mrs. Franklin needs

Strawberries needed

Strawberries bought

Mrs. Franklin still needs

more strawberries.

Sunday

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Saturday

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2. 288 children visited the circus on Saturday. 397 children visited the circus on Sunday. Only 185 children visited the circus on Monday. How many children visited the circus on the weekend? How many fewer children visited the circus on Monday than the weekend?

children visited the circus on the weekend.

Weekend

Monday

fewer children visited the circus on Monday than the weekend.

Shapes

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Anchor Task

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2-Dimensional Shapes

Find interesting shapes in old magazines. Cut them out and paste below. Can you describe how the shapes look?

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Interesting Shapes!

Let’s Learn

rectangle

pentagon

hexagon

circle

square

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triangle

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These are two-dimensional shapes. In what ways are the shapes different?

trapezoid

parallelogram

Triangles have 3 straight sides and 3 angles.

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side

angle

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Squares, rectangles, trapezoids and parallelograms are quadrilaterals. A quadrilateral has 4 straight sides and 4 angles.

side

angle

side

angle

Circles are round in shape. They do not have sides or angles.

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Compare the pentagon and hexagon below. In what ways are they different?

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Pentagons have 5 straight sides and 5 angles.

angle

side

Hexagons have 6 straight sides and 6 angles.

side

angle

Let’s Practice 1. Trace the shapes and match.

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circle

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hexagon

square

parallelogram

trapezoid

pentagon

triangle

rectangle 63

2. Name the shape. Color the same shapes.

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(a)

(c)

(b)

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(d)

(f)

(e)

R (h)

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(g)

3. Draw each shape. Fill in the blanks.

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(a) Rectangle

sides

(b) Circle

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angles

sides

angles

sides angles

(d) Pentagon

sides angles 67

(e) Triangle

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sides angles

(f)

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Hexagon

sides

angles

(g) Parallelogram

angles

sides

(h) Square

sides angles

4. Fill in the blanks. (a)

Sides:

Angles:

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(b)

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Shape:

Shape: Sides:

Angles:

(c)

Angles:

(d)

Shape: Sides:

Angles:

(e) Shape:

(f)

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Shape:

Angles:

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Sides:

(g)

Angles:

Shape: Sides:

Angles:

(h)

Shape: Sides:

Angles:

Hands On

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1. Describe one of the shapes below to your partner.

This shape has 5 sides and 5 angles.

2. Have your partner draw the shape you describe.

Yes!

Is it a pentagon?

3. If your partner draws the correct shape, change roles. 71

Solve It! Make as many as you can of the shapes you have learned without crossing or breaking a toothpick.

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Take 12 toothpicks.

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We made a triangle with 6 toothpicks!

Draw them here and name them. Can you make at least 4?

At Home 1. Complete the table. Name

Number of Number of Sides Angles

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Shape

3-Dimensional Shapes These are three-dimensional shapes. How can you describe the shapes?

rectangular prism (cuboid)

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cube

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Let’s Learn

sphere

cone

cylinder

3-D shapes can be different in the number of faces, edges and vertices they have.

A face is a flat surface.

An edge is where 2 faces meet. A vertex is where 3 or more edges meet.

face edge

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vertex

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Characteristics of a cube: • 6 square faces of equal size • 12 edges • 8 vertices

Characteristics of a rectangular prism (cuboid): • 6 rectangular faces • 12 edges • 8 vertices face

edge

vertex

Characteristics of a sphere: • 1 curved surface • 0 faces • 0 edges • 0 vertices

curved surface

face edge curved surface

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vertex

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Characteristics of a cone: • 1 curved surface • 1 face • 1 edge • 1 vertex

Characteristics of a cylinder: • 1 curved surface • 2 faces • 2 edges • 0 vertices

face

curved surface

edge

Let’s Practice 1. Circle the correct shapes. (a)

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This shape has 1 curved surface and no faces.

(b)

This shape has 6 faces and 8 vertices.

(c)

This shape has 2 faces and a curved surface.

(d)

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This shape has 1 curved surface and 1 face.

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(e)

This shape has 6 faces of equal size.

(f)

Both of these shapes have 12 edges and 8 vertices.

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2. Match.

Hands On Play this game in groups of 3 or 4.

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1. Place different 3-D shapes on your table. 2. One player describes a shape by saying the number of faces, edges and vertices. This 3-D shape has 2 faces.

3. The first player to pick the correct shape is the winner and describes the next shape.

It’s a cylinder!

At Home Complete the table. C

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Number of Faces

3-D Shape

Number of Edges

Number of Vertices

A B

D E

Area of Shapes Materials Square tiles - 24 per partner

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Make arrays! You don’t have to use all the tiles. Arrange them in different ways to make different shapes.

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Anchor Task

How many tiles are in each shape? Work with your partner to find how many.

Can you use the same number of tiles each and make different shapes?

Record your shapes on this grid paper, and write how many tiles you each used.

Let’s Learn

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Ethan drew some rectangles on a piece of grid paper.

= 1 square unit

The number of square units a shape takes up is called its area.

Let’s find the area of each shape.

The area of shape A is 6 square units. The area of shape B is 8 square units. The area of shape C is 9 square units. The area of shape D is 16 square units. 83

Let’s Practice 1. Find the area of the tiles.

(a)

(b)

Area =

tiles

(c)

tiles

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Area =

tiles

Area =

(d)

Area = 84

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= 1 tile

tiles

2. Find the area of the shapes. 1

= 1 square unit

Area =

square units

(b)

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(a)

square units

Area =

square units

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Area =

(c)

Area =

square units

(d)

(e)

Area =

square units

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(f)

Area =

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(g)

square units

Area =

(h)

square units

Area = 86

square units

At Home 1. Find the area of the shapes. = 1 square unit

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Shape A

square units

Area

(a) (b) (c) (d)

Draw a shape with an area of 6 square units. Color it red. Draw a shape with an area of 9 square units. Color it blue. Draw a shape with an area of 12 square units. Color it green. Draw a shape with an area of 15 square units. Color it pink. = 1 square unit

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Solve It!

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Michelle used 6 square tiles to make the rectangle shown. Keira used 6 triangle tiles to make the rectangle shown.

Michelle thinks her rectangle has a larger area than Keira’s. Keira thinks her rectangle has the same area as Michelle’s because they both used 6 tiles.

Who is correct? Explain how you know.

Halves, Thirds and Quarters

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Anchor Task

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Let’s Learn

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We can divide shapes into equal parts. We know a shape has equal parts when each part within the shape is the same shape and size.

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These shapes have equal parts.

The shapes below have two equal parts or two halves. Each part is one half of the whole shape.

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The following shapes have three equal parts or three thirds. Each part is one third of the whole shape.

The shapes below have four equal parts or four fourths. Each part is one fourth of the whole shape. A fourth is also called a quarter.

Let’s Practice 1. Tick the shapes that are divided into equal parts. Cross the shapes that are divided into unequal parts.

(e)

(d)

(g)

(c)

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(b)

tio n

(a)

(h)

(f)

(i)

2. How is each shape divided into equal parts? Use the words ‘two halves’, ‘three thirds’ or ‘four quarters’. (b)

(c)

(d)

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(a)

(f)

(e)

(h)

(g)

(b)

(c)

(d)

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(a)

(f)

(e)

(g)

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3. Draw a line to divide each shape into halves.

(h)

(b)

(c)

(d)

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(a)

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4. Draw lines to divide each shape into thirds.

5. Draw lines to divide each shape into quarters. (b)

(a)

(d)

(c)

At Home 1. Show a different way to divide the shapes into the same number of equal parts. Complete the sentence.

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(a)

The shapes are divided into

(b)

The shapes are divided into

(c)

The shapes are divided into 98

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The shapes are divided into (e)

The shapes are divided into (f)

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(d)

The shapes are divided into

. 99

2. Draw lines to make equal parts. Color.

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(a) Divide the shapes into two halves. Color one half.

(b) Divide the shapes into three thirds. Color one third.

100

Solve It!

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1. Ethan shares a sandwich equally with his brother. (a) Draw a line to show how Ethan should cut the sandwich. (b) How much of the sandwich does Ethan’s brother get?

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2. A cake is shared equally between three friends. (a) Draw lines to show how to cut the cake.

(b) How much of the cake does each friend get?

3. Four friends share a pizza equally. (a) Draw lines to show how to cut the pizza.

(b) How much of the pizza does each friend get? 1 01

Looking Back 1. Fill in the blanks. (a)

Sides: (b)

Sides:

(c)

(d)

Angles:

Shape:

Sides:

(e)

Angles:

Shape: Sides:

Angles:

Shape: Sides:

1 02

Angles:

Shape: Sides:

(f)

Angles:

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Shape:

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Shape:

Angles:

2. Fill in the blanks. (a)

3-D Shape:

(b) 3-D Shape:

Vertices:

Edges:

Vertices:

Edges:

Vertices:

Edges:

Vertices:

Edges:

Vertices:

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Faces:

Edges:

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Faces:

(c)

3-D Shape: Faces:

(d)

3-D Shape: Faces:

(e)

3-D Shape: Faces:

103

3. Find the area of the shapes. 1

= 1 square unit

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(a) Area =

square units

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(b)

Area =

(c)

square units

Area =

square units

(d)

square units

Area =

(e)

Area = 104

square units

(b)

(c)

(d)

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(a)

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4. How is each shape divided into equal parts? Use the words ‘two halves’, ‘three thirds’ or ‘four quarters’.

(f)

(e)

(h)

(g)

105

Time

Each pair receives a clock. Set a time and show it to your partner.

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Anchor Task

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Your partner says the time and acts out an activity they do at that time.

Guess the activity. If your guess is correct, switch turns.

106

107

tio n

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Telling Time to 5 Minutes Let’s Learn

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What time is shown on the clock?

When the minute hand moves from 12 to 1, 5 minutes have passed. So the time on the clock is 5 minutes after 12 o’clock. We can write the time as 12:05. We read the time as ‘twelve o’five’.

It takes the minute hand 5 minutes to move to the next number. We can tell the time by counting on in 5s. The time is 12:25.

5, 10, 15, 20, 25

It takes the minute hand 60 minutes to move once around the clock. There are 60 minutes in 1 hour. 108

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Jordan starts eating breakfast at 7:10.

He finishes breakfast at 7:35.

Jordan walks to school at 7:50.

109

10 minutes after 8 o’clock

eight o’five 8:05

eight ten 8:10

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5 minutes after 8 o’clock

20 minutes after 8 o’clock

eight fifteen 8:15 (or quarter past eight)

eight twenty 8:20

25 minutes after 8 o’clock

30 minutes after 8 o’clock

15 minutes after 8 o’clock

eight twenty-five 8:25 110

eight thirty 8:30 (or half past eight)

40 minutes after 8 o’clock

eight thirty-five 8:35

eight forty 8:40

45 minutes after 8 o’clock

50 minutes after 8 o’clock

eight forty-five 8:45 (or quarter to nine)

eight fifty 8:50

55 minutes after 8 o’clock

60 minutes after 8 o’clock

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35 minutes after 8 o’clock

eight fifty-five 8:55

nine o’clock 9:00 111

Hands On Make a working clock!

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Materials • Cardstock blank clock face template • Paper fasteners • Cardstock arrows — one long, one shorter

112

Hands On

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I Spy Clock Times! Your teacher has placed clock faces around the room with different times on them. Write the time on each clock and fill in the blanks. Clock B

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Clock A

In 5 minutes time it will

In 35 minutes time it

will be

Clock D

Clock C

In 25 minutes time it will be

In 45 minutes time it will be

. 113

Let’s Practice

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1. Match.

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9:05

11:25

9:25

8:45

8:35

114

2. Match.

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six twenty-five

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eleven fifty-five

six ten

quarter past six

ten forty

quarter to ten

eleven o’five

115

3. Tick the clock that shows the correct time.

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(a) The train leaves the station at 9:35.

(b) It starts to rain at 11:50.

116

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(d) The boat leaves the pier at a quarter past six.

117

4. Write the times.

minutes after .

minutes after

The time is

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The time is

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(a) (b)

minutes after

The time is

minutes after

The time is

(e) (f)

minutes after

The time is 118

minutes after

The time is

(g) (h)

minutes after

The time is

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(i) (j)

minutes after

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minutes after

The time is

minutes after

The time is

(k) (l)

minutes after

The time is

minutes after

The time is

(m) (n)

minutes after

The time is

minutes after

The time is

. 119

5. Write the times on the digital clocks.

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(a) (b)

(e) (f)

120

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(g) (h)

(i) (j)

(k) (l)

121

6. Draw the times on the analog clocks.

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(a) (b)

(e) (f)

1 22

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(g) (h)

(i) (j)

(k) (l)

123

At Home 1. Tick the clock that shows the correct time.

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(a) Ethan arrives at school at 8:20.

(b) Jordan finishes his homework at 4:15.

124

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(d) Keira brushes her teeth at seven thirty-five.

125

2. Write the times.

minutes after .

minutes after

The time is

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The time is

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(a) (b)

minutes after .

The time is

minutes after

The time is

(e) (f)

minutes after

The time is 126

minutes after

The time is

3. Draw the times on the analog clocks.

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(a) (b)

(e) (f)

127

Solve It!

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2. Dominic went fishing. When he came back, he saw that the clock showed 2:35.

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1. Wyatt looked at the clock. What time did he say it was?

(a) Draw the hands on the clock to show what time it was.

(b) If it took him half an hour to unpack all his fishing supplies, what time did he finish? Write and draw the time.

1 28

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4. Halle knew her washer took 45 minutes to wash a load. If she left her washing at 9:10, what time will the machine finish?

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3. What time is three-quarters of an hour after 11:15?

5. Ethan counted 3 sets of 5 minutes after his breakfast at 8:05. What time did he stop counting?

129

Telling Time in a.m. and p.m. Anchor Task

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The pictures show Riley’s daily activities. Guess the time each photograph is taken. Which activities occur before noon? Which occur after?

130

131

tio n

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Let’s Learn 12 o’clock at night is also called midnight. 12 o’clock in the day is called midday or noon.

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We use a.m. for times between midnight and just before midday.

10:45 a.m.

7:15 a.m.

midnight

1 32

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We use p.m. for times between just after midday and just before midnight.

2:50 p.m.

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midday

7:25 p.m.

133

Let’s Practice 1. Write the time using a.m. or p.m.

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(a)

Dominic wakes up at

(b)

Dominic eats lunch with his friend at

(c)

Dominic visits the zoo at 1 34

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(d)

Michelle walks home from school at

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(e)

Michelle learns English at (f)

Michelle gazes at the stars at

. 135

Blake goes hiking at

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(h)

Jordan goes swimming at (i)

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(g)

Ethan looks at the moon at 136

2. Use ‘a.m.’ or ‘p.m.’ to fill in the blanks. (a) Sophie does her homework after dinner at 7:25

(d) School finishes at 2:45

(e) Halle eats breakfast at 7:35

. .

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(f) Jordan has lunch at 12:05

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(b) On Saturday mornings Blake goes for a jog at 9:15

(g) On Saturdays Ethan plays football at 3:20

3. Use ‘a.m.’ or ‘p.m.’ to tell the time you do each activity. (a) I wake up at

(b) I do my homework at

(d) I have lunch at

. .

(e) I leave school at

(f) I eat breakfast at

(g) I go to sleep at

. .

137

At Home 1. Write the time using a.m. or p.m.

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(a)

Sophie practices the piano at

(b)

Michelle does her homework at

(c)

Halle is asleep at 138

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(d)

Keira visits her grandmother every Sunday at

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(e)

Keira packs her lunch for school at (f)

Sophie arrives at school at

. 139

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Jordan reads with his mother at

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(g)

(h)

Blake has soccer practice at

2. Use ‘a.m.’ or ‘p.m.’ to fill in the blanks.

(a) Jordan chats with friends after school at 4:05 (b) The bakery opens at 6:30 (c) Mr. Simpson has lunch at 12:20

. .

(d) The postman delivered a letter at 11:30 140

Looking Back 1. Write the times on the digital clocks.

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(a) (b)

(e) (f)

1 41

2. Write the times.

minutes after .

minutes after

The time is

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The time is

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(a) (b)

minutes after .

The time is

minutes after

The time is

(e) (f)

minutes after

The time is 142

minutes after

The time is

minutes after

The time is

minutes after

The time is

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(i) (j)

tio n

(g) (h)

minutes after

The time is

minutes after

The time is

3. Use ‘a.m.’ or ‘p.m.’ to fill in the blanks.

(a) The pizza shop opens for dinner at 5:00 (b) The newspaper is delivered at 5:30

. .

(d) On Saturdays, Halle plays tennis at 10:15 (e) Sophie usually goes to bed at 8:45 (f) The department store closes at 6:30

. . . 143

Length

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Anchor Task

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Customary Units of Length

144

145

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Measuring Length in Inches Let’s Learn

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We can measure the length of small objects in inches. An inch is a unit of length. The paper clip below has a length of about 1 inch.

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The length of the eraser is 2 inches.

The length of the scissors is 5 inches.

We write ‘in’ for inches.

1 in

146

We can also use a measuring tape.

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We can use a ruler to measure in inches.

The height of the books is 10 inches.

The length of the shoe is 8 inches.

147

Let’s Practice

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inch

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1. Find the length of the objects in inches.

inches

1 48

inches

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inches

149

2. Estimate the lengths of the crayons in inches. Then use a ruler to find the actual lengths.

Estimate:

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(a)

inches Actual length:

Estimate:

inches Actual length:

inches

Estimate:

inches Actual length:

inches

(c)

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(b)

inches

(d)

inches Actual length:

inches

Estimate:

inches Actual length:

inches

Estimate:

(e)

150

3. Find these objects in your classroom. Estimate the lengths in inches. Then use a ruler to find the actual lengths.

notebook

textbook

scissors

Actual Length

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pencil

Estimated Length

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Object

hand span

eraser

pencil case

1 51

4. Use a ruler to draw lines.

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(a) Draw a line AB that is 4 inches in length.

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(b) Draw a line CD that is 5 inches in length.

(d) Draw a line GH that is 6 inches in length.

1 52

5. Estimate the length of the strings. Then use a piece of string and a ruler to measure the actual lengths. G

tio n

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String

Estimated Length

H Actual Length

CD EF GH IJ

J 1 53

Hands On

Object

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Use inch tiles to measure the length of these objects. Then use a ruler to measure the lengths and compare.

length of a pencil case

Length in Inch Tiles

height of a drink bottle

length of a Math book

height of a table

154

Measured Length with Ruler

Solve It! Can you work out the length of each line?

tio n

inches

Ed uc a

inches

1 55

At Home 1. Use an inch ruler to measure the objects.

The length of the candy is

in.

Ed uc a

(b)

tio n

(a)

The length of the crayon is

(c)

in.

The length of the paintbrush is

(d)

The length of the pencil is

156

in.

Ed uc a

The length of the watch is

tio n

(e)

(f)

1 57

Measuring Length in Feet and Yards Let’s Learn

tio n

We can measure the length of larger objects in feet. 1 foot is equal to 12 inches. We write ‘ft’ for feet.

* not to scale

Ed uc a

inch

1 ft

The table has a width of 1 foot.

The table has a height of 2 feet.

158

Chelsea is 3 feet tall.

We can also measure the length of larger objects in yards. 1 yard is equal to 36 inches or 3 feet. We write ‘yd’ for yards.

tio n

Ed uc a

This is a yardstick.

Your arm span is about 1 yard.

The car has a length of 4 yards.

The car has a height of 2 yards.

1 59

Let’s Practice 1. Write the length of the objects in feet.

(b)

feet long.

The shelf is about (c)

feet long.

Ed uc a

The log is about

The plant is about 160

tio n

(a)

feet tall.

Ed uc a

tio n

(d)

Ethan is about

(e)

feet tall.

The cupboard is about

feet tall and

feet wide. 161

2. Look around your classroom. (a) List 3 objects that are shorter than 1 foot.

tio n

Ed uc a

(b) List 3 objects that are longer than 1 foot.

(d) List 1 object that is about 3 feet in length.

(e) List 1 object that is longer than 3 feet.

1 62

3. Find these objects in your classroom. Estimate the lengths in feet. Then, use a ruler to find the actual lengths.

length of a desk

Ed uc a

height of a chair

Estimated Length Actual Length (feet) (feet)

tio n

Length

width of a door

width of a window

height of a friend

length of a whiteboard

height of a school bag

163

4. Write the length of the objects in yards.

The fence is about

yards wide and

Ed uc a

(b)

tio n

(a)

The length of the sofa is about

(c)

The car is about

164

yards long.

yards.

yard tall.

tio n

(d)

The park bench has a width of about

Ed uc a

(e)

yards.

The giraffe is about

yards tall.

165

Solve It! Use the numbers in the box to write the length of the objects. 3

Ed uc a

tio n

1 5 7 6

166

tio n

Ed uc a

yd yd

1 67

At Home

Length

Estimated Length Actual Length (yards) (yards)

Ed uc a

length of a bed

tio n

1. Find these objects around your home. Estimate the lengths in yards. Then use a yardstick or measuring tape to find the actual lengths.

length of a bedroom height of a door

height of a refrigerator

length of a car

height of a ceiling

width of a living room

168

2. Which is an appropriate unit of measurement? Write ‘in’ for inches, ‘ft’ for feet or ‘yd’ for yards. (a) The length of a car.

Ed uc a

(e) The width of a garden.

tio n

(b) The height of a traffic sign.

(f) The height of a banana tree. (g) The length of a banana.

(h) The height of an apartment block. (i) The length of a truck.

(j) The height of a kitten.

(k) The width of your shoe.

(l) The length of a golf club. (m) The height of a park bench.

(n) The height of a fence.

169

3. Choose an appropriate tool for measurement (ruler, yardstick or measuring tape). Estimate the length in inches, feet or yards.

height of a rubbish bin

Estimated Length

Ed uc a

height of a desk

Tool for Measurement

tio n

Length

width of a classroom

width of a whiteboard height of a teacher

length of a desk

width of a textbook

170

Hands On

String

Length (inches)

B C D

E F

Length (feet)

Ed uc a

tio n

1. Your teacher will give you some pieces of string. Use a ruler or measuring tape to find the lengths in inches and feet.

171

2. Find these objects in your classroom. Measure each object twice.

inches

Ed uc a

feet

tio n

(a) Height of a schoolbag

(b) Width of a computer

inches

feet

172

inches feet

(d) Length of a window

Ed uc a

feet

tio n

inches

(e) Height of shelves

inches

feet

(f) Height of a trash can

inches feet

173

3. Find these objects in your classroom or schoolyard. Measure each object twice.

tio n

(a) Length of a school fence

yards

Ed uc a

feet

(b) Length of a basketball court

yards

feet

174

yards feet

(d) Width of a classroom window

feet

Ed uc a

(e) Length of a whiteboard

tio n

yards

yards feet

(f) Height of play equipment

yards feet

175

Comparing Length – Inches, Feet and Yards Let’s Learn

Ed uc a

tio n

Compare the lengths of the objects.

Length of the safety pin = 1 in Length of the toothbrush = 4 in 4 in – 1 in = 3 in

The toothbrush is 3 in longer than the safety pin. The safety pin is 3 in shorter than the toothbrush.

Compare the lengths of the pencil and scissors.

Length of the scissors = 5 in Length of the pencil = 3 in 5 in – 3 in = 2 in The pencil is 2 in shorter than the scissors. The scissors are 2 in longer than the pencil.

176

Compare the lengths. Length of the branch = 4 ft Length of the fence = 7 ft 7ft – 4 ft = 3 ft

Ed uc a

tio n

4 ft

7 ft

The branch is 3 ft shorter than the fence. The fence is 3 ft longer than the branch. Compare the heights of the houses.

Height of House A = 30 yd Height of House B = 18 yd 30 yd – 18 yd = 12 yd

30 yd

18 yd

House A

House B

House A is 12 yd taller than House B. House B is 12 yd shorter than House A. 177

Let’s Practice

tio n

1. Compare the lengths of the objects. Fill in the blanks. pen

Ed uc a

marker

glue

(a) The pen has a length of

in.

(b) The marker has a length of

in. in.

in shorter than the marker.

(e) The pen is

in longer than the marker.

(d) The glue is

(f) The

is the longest.

(g) The

is the shortest.

178

Ed uc a

tio n

2. Compare the lengths of the strips of paper. Fill in the blanks.

(a) The blue strip is

(b) The orange strip is

(d) The yellow strip is (e) The blue strip is

(f) The yellow strip is

in long.

in long. in long. in long. in shorter than the green strip. in longer than the orange strip.

(g) Order the strips from the shortest to longest.

179

tio n

3. Compare the lengths of the objects. Fill in the blanks.

racquet 29 in

Ed uc a

bat

42 in

golf club

38 in

(a) The bat is

in longer than the racquet.

(b) The golf club is (c) The bat is

in longer than the golf club. is the longest.

(e) The

is the shortest.

(d) The

(f) Arrange the objects from the longest to shortest.

180

4. Compare the lengths of the shovels. Fill in the blanks.

4 ft B

Ed uc a

5 ft

tio n

2 ft

ft in length.

(b) Shovel B is

ft in length.

(a) Shovel A is

ft shorter than shovel B.

(e) Shovel A is

ft longer than shovel C.

(f) Shovel C is

ft shorter than shovel A.

(d) Shovel A is

is the shortest.

(h) Shovel

is the longest.

(g) Shovel

181

Hands On 1. Choose a pencil from your pencil case. 2. Estimate its length in inches.

Whose is longer? (guess)

Whose is longer? (measured)

Ed uc a

Name

tio n

3. Move around the classroom and compare pencils with 5 friends. Guess who has the longer pencil by looking. Then align the pencils and measure.

4. How many guesses were correct?

182

Two tortoises are crossing a bridge. The bridge is 12 ft long. Tortoise A moves 2 ft every day. Tortoise B moves 3 ft every day.

Ed uc a

tio n

Solve It!

(a) Complete the table to show how far the tortoises move. Day

2 ft

3 ft

Total distance Tortoise A Total distance Tortoise B has moved has moved

(b) Which tortoise will cross the bridge first?

days.

(d) Tortoise B will cross the bridge in

days. 183

At Home

Ed uc a

airplane: 55 yd

tio n

Compare the lengths of the vehicles. Fill in the blanks.

train: 110 yd

184

bus: 25 yd

(a) The car is

yd longer than the motorbike.

(b) The train is

yd longer than the airplane.

(e) The bus is

yd longer than the bus.

tio n

(d) The train is

yd shorter than the bus.

yd shorter than the airplane.

is 21 yd longer than the car.

(g) The

is 53 yd shorter than the airplane.

Ed uc a

(f) The

motorbike: 2 yd

car: 4 yd

185

Metric Units of Length

Ed uc a

tio n

Anchor Task

186

1 87

tio n

Ed uc a

Measuring Length in Centimeters Let’s Learn

tio n

We can measure the length of objects in centimeters. 1 centimeter is about the width of your thumbnail. We write centimeters as cm.

Ed uc a

1 cm

The length of the paper clip is 3 cm. The length of the pencil is 7 cm. The length of the pen is 12 cm. The length of the scissors is 14 cm.

188

1 cm is about the width of your finger.

Ed uc a

tio n

We can also use a measuring tape to measure length in centimeters.

The height of the lamp is 50 cm. The height of the books is 39 cm. The height of the plant is 74 cm.

The length of the badminton racquet is 65 cm. The length of the violin is 54 cm. 189

Let’s Practice

Ed uc a

tio n

1. Find the length of the objects in centimeters.

190

tio n

Ed uc a cm

191

2. Estimate the lengths of the colored pencils in centimeters. Then use a ruler to find the actual lengths.

tio n

(a) Estimate:

cm Actual length:

Estimate:

cm Actual length:

Estimate:

cm Actual length:

Estimate:

cm Actual length:

(c)

(d)

Ed uc a

(b)

(e)

cm Actual length:

Estimate:

cm Actual length:

Estimate:

(f)

192

3. Find these objects in your classroom. Estimate the lengths in centimeters. Then use a measuring tape to find the actual lengths.

length of a stapler

Ed uc a

height of a school bag

Estimated Length Actual Length (cm) (cm)

tio n

Object

width of a door

height of a chair

length of an arm span

length of a shoe

length of a pencil case

193

4. Use a ruler to draw lines.

Ed uc a

(b) Draw a line CD that is 12 cm.

tio n

(a) Draw a line AB that is 7 cm.

(d) Draw a line GH that is 15 cm.

194

5. Estimate the length of the strings. Then use a piece of string and a ruler to measure the actual lengths. B

tio n

Ed uc a

String

Estimated Length (cm)

Actual Length (cm)

CD EF

GH IJ 195

Solve It!

Ed uc a

tio n

1. Compare the lengths of the pencil colors.

(a) The blue pencil has a length of

cm.

(b) The orange pencil has a length of (c) The pink pencil has a length of

cm.

(d) The black pencil has a length of

cm.

cm shorter than the black pencil.

(f) The red pencil is

cm longer than the orange pencil.

(e) The pink pencil is

(g) The

pencil is the longest.

(h) The

pencil is the shortest.

196

2. What is the length of each child’s pencil? My pencil is 7 cm shorter than the red pencil.

Keira’s pencil is (b)

cm in length.

Ed uc a

My pencil is 4 cm longer than the blue pencil.

tio n

(a)

cm in length.

Halle’s pencil is (c)

My pencil is 5 cm shorter than the green pencil.

Sophie’s pencil is (d)

Riley’s pencil is

cm in length. My pencil is longer than the pink pencil and shorter than the red pencil. cm in length. 197

At Home Use a ruler to measure the objects.

The length of the eraser is

Ed uc a

(b)

cm.

The length of the thumb drive is

(c)

cm.

The length of the marker is

(d)

The length of the key is 1 98

tio n

(a)

cm.

The length of the pencil is

Ed uc a

(f)

cm.

tio n

(e)

cm 199

Measuring Length in Meters Let’s Learn

tio n

There are 100 cm in 1 meter.

Ed uc a

We can measure the length of larger objects in meters. To measure in meters, we can use a meter stick or a measuring tape. We write meters as m.

Let’s look at the height of the children.

Sophie

Sophie is about 1 m tall. Chelsea is shorter than 1 m. Halle is taller than 1 m. 2 00

Chelsea

Halle

tio n

Ed uc a

The length of the motorcycle is about 2 m.

The length of the car is about 4 m.

The fence is about 5 m long. 2 01

Let’s Practice 1. Write the length of the objects in meters.

Ed uc a

tio n

(a)

The wardrobe is about

(b)

m wide and

The length of the cabin is about

The height of the cabin is about

202

m tall.

Ed uc a

tio n

(c)

The van is about

The truck is about

m in length.

(d)

m in length.

The height of the tree is about

m. 203

2. Find each object in your school. Estimate the length of each object. Use a meter ruler to check your estimate.

height of a locker

Measurement (m)

Ed uc a

length of a whiteboard

Estimate (m)

tio n

Object

width of a window

width of a classroom

height of a door

length of a teacher’s desk

width of a basketball court width of a cupboard

2 04

At Home

Length

tio n

1. Find these objects around your home. Estimate the lengths in meters. Then use a meter ruler or measuring tape to find the actual lengths. Estimated Length (m)

Ed uc a

length of a kitchen

Actual Length (m)

height of a car

width of a window length of a hose

width of a bedroom

width of a television

length of a sofa

205

2. Choose an appropriate unit of measurement (cm or m). Estimate each length.

your height

Estimated Length

Ed uc a

height of a school building

Units

tio n

Length

length of a tennis racquet height of a water bottle length of a broom

length of a school bus

width of a drawer

2 06

3. Which is an appropriate unit of measurement? Write ‘cm’ or ‘m’. (a) The length of a truck.

Ed uc a

(f) The height of a bathtub.

tio n

(b) The width of a door mat.

(g) The length of a swimming pool.

(h) The length of a basketball court. (i) The height of a flag pole.

(j) The length of a computer keyboard. (k) The height of a tree.

(l) The length of your arm. (m) The width of your pillow.

(n) The length of your bed.

(o) The length of a garden hose.

207

Comparing Length (Centimeters and Meters) Let’s Learn

Ed uc a

tio n

Compare the lengths of the pencils.

Length of the blue pencil = 11 cm Length of the green pencil = 8 cm 11 cm – 8 cm = 3 cm

The blue pencil is 3 cm longer than the green pencil. The green pencil is 3 cm shorter than the blue pencil.

Compare the lengths of the pencils.

Length of the orange pencil = 5 cm Length of the pink pencil = 10 cm 10 cm – 5 cm = 5 cm The orange pencil is 5 cm shorter than the pink pencil. The pink pencil is 5 cm longer than the orange pencil.

208

Compare the lengths of the planks of wood. Plank A 10 m Length of Plank A = 10 m Length of Plank B = 6 m

tio n

Plank B 6m

10 m – 6 m = 4 m

Ed uc a

Plank A is 4 m longer than Plank B. Plank B is 4 m shorter than Plank A. Compare the heights of the trees. Height of Tree A = 12 m Height of Tree B = 22 m 22 m – 12 m = 10 m

22 m

12 m

Tree A

Tree B

Tree A is 10 m shorter than Tree B. Tree B is 10 m taller than Tree A.

209

Let’s Practice

Ed uc a

tio n

1. Compare the lengths of the objects. Fill in the blanks.

(a) The toothpaste has a length of (b) The comb has a length of

cm. cm.

(d) The comb is

(e) The toothbrush is

cm shorter than the toothpaste. cm longer than the comb.

(f) The

is the longest.

(g) The

is the shortest.

21 0

cm.

2. Compare the lengths of the objects. Fill in the blanks. clarinet

tio n

74 cm

Ed uc a

violin 63 cm

trumpet

88 cm

cm longer than the clarinet.

(b) The trumpet is

cm longer than the violin.

(a) The trumpet is

cm shorter than the clarinet. is the longest.

(e) The

is the shortest.

(d) The

(f) Arrange the objects from the longest to shortest.

211

3. Use a piece of string and a ruler to measure the strings. Fill in the blanks. A

B D

tio n

Ed uc a

cm in length.

(b) Line CD is

cm in length.

(a) Line AB is

(d) GH is

cm in length. cm in length. cm shorter than line CD.

(f) Line EF is

cm longer than GH.

(e) Line AB is

(g) Line CD is

cm shorter than EF.

(h) Arrange the strings from the shortest to longest.

212

4. Fill in the blanks.

tio n

Ed uc a

(a) The length of branch A is about

m. than 1 m.

than 1 m.

(b) The length of branch B is

is the longest.

(e) Branch

is the shortest.

(d) Branch

213

tio n

5. Compare the heights of the buildings. Fill in the blanks.

82 m

Ed uc a

58 m

40 m

Building A

Building B

Building C

(b) The height of building A is

(a) The height of building B is

m taller than building C.

(e) Building B is

m shorter than building A.

(f) Building C is

m taller than building B.

(d) Building A is

(g) Arrange the buildings from the shortest to tallest.

214

Solve It! 1. A beetle is crawling around a garden. It starts at position A and crawls for 36 m. At which position does the beetle stop? C

tio n

Ed uc a

The beetle stops at position

2. Jordan is running around the soccer field. He starts at position A and runs for 400 m. At which position does he stop? 100 m

50 m

Jordan stops at position

B . 215

At Home

Ed uc a

tio n

1. Compare the lengths of the objects. Fill in the blanks.

cm in length.

(a) The fork is

(b) The spoon is (c) The knife is

(d) The spoon is

(e) The fork is

cm in length.

cm in length. cm shorter than the knife. cm longer than the spoon.

(f) Arrange the objects from the shortest to longest.

21 6

Ed uc a

tio n

2. Compare the heights of the plants. Fill in the blanks.

98 cm

58 cm

42 cm

Plant B

Plant C

Plant A

cm taller than plant A.

(b) Plant A is

cm shorter than plant B.

cm taller than plant C.

(a) Plant C is

is the shortest.

(e) Plant

is the tallest.

(d) Plant

(f) Arrange the plants from the tallest to shortest. 217

3. Compare the lengths of the vehicles. Fill in the blanks.

tio n

train

14 m

Ed uc a

taxi

bus

m longer than the bus.

(b) The train is

m longer than the taxi.

(a) The train is

m longer than the taxi.

(d) Arrange the vehicles from the longest to shortest.

218

Looking Back 1. Use an inch ruler to measure the objects.

tio n

(a)

Ed uc a

(b)

2. Draw a line VW that is 6 inches in length.

219

3. Write the length and height of the fence.

Ed uc a

tio n

4. Write the length and height of the truck.

5. Which is an appropriate unit of measurement? Write ‘in’ for inches, ‘ft’ for feet or ‘yd’ for yards. (a) The length of a train. (b) The height of your teacher.

22 0

(f) The length of an envelope.

Ed uc a

6. Compare the lengths of the strings.

tio n

(e) The length of a pencil.

(a) The blue string is

(b) The green string is

(d) The blue string is

inches in length.

inches in length. inches longer than the blue string. inches shorter than the green string.

(e) Arrange the strings from the shortest to longest.

221

tio n

7. Compare the heights of the buildings.

Ed uc a

15 yd

4 yd

House A

House C

yd tall.

(a) House B is

House B

yd tall.

(d) House A is

yd taller than house B.

(e) House A is

yd shorter than house C.

(b) House C is

(f) Arrange the houses from the shortest to tallest.

222

21 yd

8. Use a ruler to find the lengths in centimeters. (a) cm (b)

Ed uc a

tio n

(c)

9. Draw a line XY that is 13 centimeters in length.

223

Ed uc a

tio n

10. Write the lengths in meters.

(a) The fence is about

m tall.

(b) The fence is about

m long.

m tall.

11. Which is an appropriate unit of measurement? Write ‘cm’ for centimeters or ‘m’ for meters. (a) The length of a car.

(b) The length of a necklace. (c) The height of a chair. (d) The height of a flagpole. (e) The width of a microwave oven.

224

12. Compare the lengths of the bamboo sticks. 87 cm A B

64 cm

tio n

44 cm

cm longer than bamboo C.

(b) Bamboo B is

cm shorter than bamboo A.

Ed uc a

(a) Bamboo A is

13. Compare the lengths. boat

train

51 m

truck

19 m

m longer than the truck.

(b) The boat is

m shorter than the train.

(a) The train is

Money

tio n

Anchor Task

Ed uc a

Classroom scene. Kids have opened their wallets at their desks and are looking at their money and comparing notes and coins

22 6

Coins and Notes Let’s Learn

5¢ five cents (nickel)

Ed uc a

1¢ one cent (penny)

tio n

Let’s look at our coins.

25¢ twenty-five cents (quarter)

10¢ ten cents (dime)

50¢ fifty cents (half dollar)

$1 one dollar (dollar coin)

227

pl e sa m

tio n

sa m

pl e

Let’s look at our notes.

$1 one dollar

$5 five dollars

pl e sa m

e pl

sa m

$10 ten dollars

$20 twenty dollars

$100 one hundred dollars

228

sa m

Ed uc a

$2 two dollars

$50 fifty dollars

Can you name the people on the notes?

Let’s Practice 1. Match.

tio n

1¢

Ed uc a

10¢

25¢

50¢

5¢

229

sa m

230

sa m pl e

sa m

R e

sa m

pl e

tio n

Ed uc a sa m

sa m

pl e

2. Match.

$20

$10

$100

$50

At Home

dime

Ed uc a

penny

tio n

1. Check the name of the coin.

dollar

dime

penny

dollar

nickel

quarter

nickel

dime

quarter

penny

dime

nickel

dollar

231

2. Check the name of the banknotes.

twenty dollars

tio n

sa m

one hundred dollars

twenty cents

one cent

sa m

Ed uc a

ten dollars

one dollar

sa m

one dollar ten dollars

sa m

five dollars two dollars twenty cents

pl e

one hundred dollars

sa m

pl e

five dollars fifty dollars ten dollars

232

Exchanging Money Let’s Learn

Ed uc a

tio n

Here are some ways we can exchange coins.

233

sa m

23 4

pl e

sa m

sa m e

sa m

tio n

Ed uc a

sa m

Here are some ways we can exchange our notes.

235

sa m

pl e

sa m

tio n

Ed uc a

sa m

Let’s Practice 1. Check the coins needed to exchange.

tio n

(a)

Ed uc a

(b)

(d)

(c)

(e)

236

2. Check the amounts needed to exchange.

Ed uc a

sa m

(b)

tio n

sa m

(a)

$50

$20

sa m

(c)

e pl sa m

(e)

sa m

(d)

237

Solve It!

Ed uc a

Show 3 ways to make 75¢.

tio n

Complete the tables to show different ways to make each amount of money.

Show 4 ways to make $1.40.

2 3 4

238

tio n

Show 5 ways to make $2.75.

1 2

Ed uc a

3 4

Show 5 ways to make $4.85.

3 4 5 239

At Home 1. Write the number of coins needed to exchange.

tio n

(a)

Ed uc a

(b)

(c)

(e)

(d)

(f)

240

2. Write the number of banknotes needed to exchange.

e pl e pl e pl sa m

pl e sa m

(e)

sa m

(d)

sa m

(c)

sa m

Ed uc a

sa m

(b)

tio n

sa m

(a)

e pl sa m

sa m

(f)

2 41

Counting Money Let’s Learn

I have 70¢.

Ed uc a

I have 50¢.

tio n

How much money does each child have?

I have 90¢.

I have 99¢.

2 42

How much money does each child have?

Ed uc a

tio n

I have $8.

I have $37.

I have $91.

243

Let’s Practice 1. Circle the amount of money.

tio n

(a)

(c)

20¢

4¢

13¢

8¢

20¢

60¢

21¢

30¢

35¢

31¢

15¢

75¢

30¢

61¢

36¢

56¢

(d)

(e)

10¢

Ed uc a

(b)

2¢

(f)

2 44

2. Circle the amount of money.

$68

$23

$42

$62

$80

$35

$26

$53

Ed uc a

$77

(b)

(c)

tio n

(a)

245

Hands On

Ed uc a

tio n

Work in pairs. Your teacher will show the class an amount of money. Race to show the amount with play money.

246

At Home 1. Count and write the amount of money.

tio n

(a)

Ed uc a

(b)

(c)

(e)

(d)

(f)

247

2 48

sa m

sa m pl e

pl e

sa m e

sa m

pl e

sa m

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Ed uc a e

sa m

(b)

sa m

(d)

sa m

(c)

sa m

2. Count and write the amount of money.

(a)

(e)

sa m

pl sa m

sa m

sa m sa m

sa m

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Ed uc a e

(h)

sa m

(g)

sa m

(f)

249

Comparing Money Let’s Learn

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Who has more money? I have 75¢.

I have 55¢.

Wyatt

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Ethan

75 is greater than 55. So, 75¢ is greater than 55¢. Wyatt has more money than Ethan. Who has less money?

I have 80¢.

I have 95¢.

Dominic

Jordan

80 is less than 95. So, 80¢ is less than 95¢. Dominic has less money than Jordan. 25 0

Who has more money? I have $16.

I have $11. Halle

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Sophie

16 is greater than 11. So, $16 is greater than $11. Halle has more money than Sophie. Who has less money?

I have $77.

Keira

Michelle

I have $71.

71 is less than 77. So, $71 is less than $77. Keira has less money than Michelle. 2 51

Let’s Practice 1. Find the amount of money in each set. Compare and fill in the blanks. (a)

Set B

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Set A

Set A has

¢ is greater than

So, Set (b)

¢ and Set B has ¢.

has more money than Set

Set D

Set C

¢.

Set C has

¢ is less than

So, Set 252

¢ and Set D has

¢.

has less money than Set

(c)

Set N

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Set M

Set M has $ $ So, Set (d)

is greater than $

has more money than Set

Set Q

Set P

and Set N has $

Set P has $ $ So, Set

and Set Q has $

is less than $

has less money than Set

. 253

At Home 1. Check the set with more money. (a)

Set B

(b)

Set C

(c)

Set E

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Set A

254

Set D

Set F

2. Check the set with less money.

(c)

Set B

Set C

Set D

Set F

Set E

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(b)

Set A

Ed uc a

(a)

2 55

Money Word Problems Let’s Learn

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Jordan buys a toy truck for $45. Halle buys a teddy bear for $30. How much money did Jordan and Halle spend altogether? $45

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$30

$45

$30

toy truck

teddy bear

$45 + $30 = $75 Jordan and Halle spent $75 altogether.

Ethan buys a ruler for 40¢, an eraser for 25¢ and a sharpener for 35¢. How much money does Ethan spend altogether? ¢

40¢

25¢

35¢

ruler

eraser

sharpener

40¢ + 25¢ + 35¢ = $1 Ethan spends $1 altogether. 2 56

25¢

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During recess, Sophie buys a muffin for 95¢. Riley buys an orange for 70¢. How much more money did Sophie spend than Riley?

95¢

70¢

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95¢ muffin

orange 70¢

95¢ – 70¢ = 25¢ Sophie spent 25¢ more than Riley.

Wyatt has $55. He buys a soccer ball for $20. How much money does Wyatt have left?

$55

money spent

money left

$20

$55 – $20 = $35

Wyatt has $35 left.

2 57

Let’s Practice

snacks

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movie ticket

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1. Ethan went to the cinema with his friends. He spent $8 on a movie ticket and $15 on snacks. How much money did he spend altogether?

Ethan spent $

altogether.

2. At a clothing store, a T-shirt costs $22. A pair of jeans costs $9 more than a T-shirt. What is the cost of a T-shirt and a pair of jeans?

T-shirt

jeans

A T-shirt and a pair of jeans cost $ 2 58

3. Use the space provided to solve the word problems.

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(a) Michelle took $20 to school. She bought a new pencil case for $12. How much money did she have left?

Michelle had $

left.

(b) In a craft store, colored paper is 8¢ per sheet. Glue sticks are 75¢. Find the cost of 2 pieces of colored paper and 1 glue stick.

A glue stick and 2 pieces of colored paper cost

¢.

259

At Home

Friend

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Halle

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1. At the school canteen, apples cost 32¢. Halle buys 1 apple for herself and 2 apples for her friends. How much money did Halle spend altogether?

Halle spent

¢ altogether.

2. Dominic took 90¢ to the sweet store. He bought a piece of chocolate for 25¢. How much money did Dominic have left?

Money taken to sweet store Chocolate

Money left

Dominic had 26 0

= ¢ left.

Sophie has

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3. Sophie finds 50¢ on her way home from school. She stops at the market and buys an orange for 42¢. How much money does Sophie have left?

¢ left.

4. Jim’s Beach Wear is having a sale. A pair of sunglasses costs $23, a cap costs $18 and a pair of flip flops costs $15. What is the cost of 1 pair of sunglasses and a cap?

A pair of sunglasses and a cap cost $

. 261

Hands On

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Work in pairs and make a word problem. Swap your word problems with another pair and use play money to act it out and find the answer.

2 62

Looking Back

quarter

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1¢

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1. Match.

10¢

penny

5¢

nickel

dime

25¢

1 dollar

5 dollars 263

2. Find the amount of money in each set. Compare and fill in the blanks. (a)

Set B

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Set A

Set A has

¢ is greater than

So, Set (b)

¢ and Set B has ¢.

has more money than Set

Set D

Set C

¢.

Set C has $ $ So, Set

264

and Set D has $

is greater than $

has more money than Set

Money taken to the supermarket

Money spent on groceries

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Money left

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3. Mrs. Logan took $52 to the supermarket. She bought some groceries and returned home with $13. How much money did Mrs. Logan spend on groceries?

Mrs. Logan spent $

on groceries.

4. Ethan finds 55¢ in the pocket of his pants. He finds another 35¢ in his school bag. How much money did Ethan find altogether?

Ethan found

¢ altogether. 265

Data and Graphs

Ed uc a

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Anchor Task

2 66

2 67

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Ed uc a

Drawing Picture Graphs Let’s Learn

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A tally is a quick way to record and display data. To make a tally, draw a line for the first four numbers. For the fifth number, draw a line through the last four lines as shown below.

Halle asked her friends their favorite color. She recorded the responses in a tally. Green!

Blue!

What’s your favorite color?

My Friends’ Favorite Colors

Color

26 8

Tally

Total

red

green

blue

Halle used the data from her tally to create a picture graph.

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I drew a smiley face to show 1 person.

My Friends’ Favorite Colors

red green blue

stands for 1 person.

Each

We can see from the tally that most people in her class like red.

Green is the least favorite color. 2 more people like blue than green.

10 fewer people like green than red.

269

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On his way to school, Wyatt counted the number of cars, trucks, vans and buses he spotted. He recorded the data in a tally.

Vehicles spotted

cars trucks

vans buses

At school, Wyatt used the data in his tally to make a picture graph.

270

I will use this symbol to show 1 vehicle.

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Vehicles Spotted

trucks

cars

buses

stands for 1 vehicle.

Each

vans

Wyatt spotted cars the most. He spotted 1 more bus than vans. He spotted 3 fewer trucks than vans. He spotted 25 vehicles in all. 271

Let’s Practice

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1. Count the fruits on the shelves. Complete the tally.

Number of Fruits

Fruit

Orange

Apple

Pear

27 2

Tally

Total

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2. Count the shapes. Complete the tally.

Number of Shapes

Shape

Total

Square

Tally

Circle

Rectangle

Triangle

273

Cookies Sold raisin

choc chip

oatmeal

ginger

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3. A bakery recorded the number of each cookie they sold at lunch time. Use the tally to create a picture graph.

Cookies Sold at Lunch Time

1 2 74

raisin

choc chip

stands for 1 cookie sold.

oatmeal

ginger

4. Sophie made a table of the flowers she spotted in the garden. Use the table to create a picture graph. Flowers Spotted in the Garden Daisies

Petunias

Lilies

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Roses

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Flowers Spotted in the Garden

Roses

Daisies

Petunias

Lilies

stands for 1 flower.

275

At Home 1. Ethan recorded the number of different animals he saw at the aquarium. Use the table he made to make a picture graph.

Seals

Penguins

Turtles

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Fish

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Animals at the Aquarium

Fish

Seals

Penguins

Turtles

276

stands for 1 animal.

2. Michelle asked the people in her class how they get to school. She made the table below to show her findings. Use the table to make a picture graph. I take the bus.

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I walk to school.

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How do you get to school?

How My Class Gets to School

Car 10

Walk

Bike

Bus

How My Class Gets to School

Car

Walk

Bike

Bus stands for 1 person.

277

Reading Picture Graphs Let’s Learn

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Class 2B were asked about their favorite sports. The results are shown in the picture graph.

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Favorite Sports of Class 2B

soccer

1 278

tennis

stands for 1 child.

basketball

swimming

How many more people like soccer than tennis?

12 – 9 = 3 So, 3 more people like soccer than tennis.

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12 people like soccer. 9 people like tennis. Subtract to find the difference.

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How many people like basketball and swimming in all? 5 people like basketball. 3 people like swimming. Add to find the sum 5+3=8 So, 8 people like basketball and swimming in all. How many people are in Class 2B?

2 9 5 3 9

We need to add the number of people in each sport altogether.

12 + 9 + 5 + 3 = 29 So, there are 29 people in Class 2B.

279

Chocolate Strawberry Vanilla

stands for 1 ice cream.

Mint

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Ice Creams Sold

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An ice cream shop recorded the flavors of ice creams sold in a day.

How many chocolate and strawberry ice creams were sold in total?

14 chocolate ice creams and 9 strawberry ice creams were sold. Add to find the total. 14 + 9 = 23 23 chocolate and strawberry ice creams were sold in total.

280

How many more vanilla than mint ice creams were sold?

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15 vanilla ice creams were sold. 2 mint ice creams were sold. Subtract to find the difference. 15 – 2 = 13 13 more vanilla ice creams were sold than mint ice creams.

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How many ice creams sold were not strawberry?

We need to add the number of ice creams sold for the other flavors. Add the other flavors sold together.

Chocolate: 14 Vanilla: 15 Mint: 2

14 + 15 + 2 = 31 31 ice creams sold were not strawberry flavor.

281

Let’s Practice 1. Halle counted the different animals she spotted in the garden. She made a picture graph to show her findings.

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Animals in the School Garden

bees

beetles

spiders

ants

stands for 1 animal.

(a) How many more spiders than bees did she spot?

–

She spotted 2 82

= more spiders than bees.

(b) What animal did Halle spot the most? She spotted

the most.

the least.

She spotted

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(d) How many fewer bees than ants were spotted? –

fewer bees than ants were spotted.

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(e) How many beetles and spiders were spotted?

beetles and spiders were spotted.

(f) How many animals were spotted in all?

animals were spotted in all.

283

2. Sophie asked her classmates their favorite snacks. She made a picture graph to show her findings. Answer the questions and show your working.

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Candy!

Chocolate!

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What’s your favorite snack?

Favorite Snacks

Chocolate Candy

Chips Cookies

stands for 1 person.

(a) Which snack food is the most popular?

is the most popular snack food.

(b) Which snack food is the least popular?

2 84

is the least popular snack food.

and

are equally popular.

(d) How many people like chocolate and candy?

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people like chocolate and candy.

Ed uc a

(e) How many more people like chips than cookies?

more people like chips than cookies.

(f) How many people are in Sophie’s class?

There are

people in Sophie’s class.

285

At Home

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1. Riley recorded the color of each car in the school car park. She made a picture graph of her findings. Answer the questions and show your working.

Car Colors in the School Car Park

1 286

white

blue

stands for 1 car.

black

red

(a) How many cars were black?

cars were black.

(b) What car color was spotted 4 times? cars were spotted 4 times.

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Ed uc a

black cars and red cars were spotted.

(d) How many fewer blue cars than white cars were spotted?

fewer blue cars than white cars were spotted.

(e) How many cars were spotted in all?

There were

cars spotted in all.

2 87

Bar Graphs Let’s Learn

My Friends’ Favorite Subjects Subject

Tally

Art

Total

Math

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Dominic asked his friends their favorite subjects. He used a tally to record the data he collected.

English Music

2 7

He made a bar graph to show the data.

Each stands for 1 vote.

My Friends’ Favorite Subjects

Number of Votes

10 9 8 7 6 5 4 3 2 1

Art

Math English Subject

Music

When making a bar graph, remember to include labels and a title. 288

How many more people voted for Art than English?

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Art has 5 votes and English has 2 votes. 5–2=3 So, 3 more people voted for Art than English.

How many votes did Math and Music receive?

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Math has 10 votes and Music has 7 votes. 10 + 7 = 17 Math and Music received 17 votes.

How many people voted in Dominic’s class?

Add the number of votes for each subject together. 1

5 0 2 7 4

5 + 10 + 2 + 7 = 24 24 people voted in Dominic’s class.

289

Sophie asked her class to vote for their favorite season. She made a bar graph from the data she collected. Favorite Seasons of My Class

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Autumn Winter Spring

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Season

Summer

Number of Votes

The green bar is the longest!

Longer bars show more votes!

Which season received the most votes? Spring received the most votes. 10 people voted for Spring. Which season received the fewest votes? Winter had the fewest votes. Only 4 people voted for Winter.

290

How many people voted for Spring and Summer?

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10 + 9 = 19 19 people voted for Spring and Summer. How many fewer people voted for Winter than Summer?

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9–4=5 5 fewer people voted for Winter than Summer. How many people did not vote for Summer?

We need to add the votes from the other seasons. 7 + 4 + 10 = 21 21 people did not vote for Summer. How many people voted in total?

1 3

9 7 4 0 0

9 + 7 + 4 + 10 = 30 30 people voted in total.

291

Let’s Practice

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1. A clothing store stocks T-shirts in 4 different colors. The table below shows the number of T-shirts in stock for each color. T-shirts in Clothing Store Green

White

Red

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Blue

Make a bar graph from the data. Fill in the blanks.

Number of T-shirts

T-shirts in Clothing Store

Color 2 92

2. Dominic recorded the number of animals he spotted at the zoo. The table below shows the number of each animal spotted. Animals at the Zoo Tigers

Bears

Elephants

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Lions

Make a bar graph from the data. Fill in the blanks.

Animal

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Animals at the Zoo

Number

293

3. Make a bar graph from the table. Answer the questions and show your working. Pies Sold in a Bakery Blueberry

Strawberry

Apple

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Cream

Flavor

Ed uc a

Pies Sold in a Bakery

Number

(a) Which flavors are equally popular?

2 94

and

are equally popular.

(b) How many cream pies and apple pies were sold?

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cream pies and apple pies were sold.

Ed uc a

more strawberry pie was sold than apple pies.

(d) How many pies were sold in all?

pies were sold in all.

295

Solve It! A class were asked about their favorite types of movies. Read the clues and complete the drawing of the bar graph.

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Drama and comedy received the same number of votes.

Favorite Types of Movies

Number of Votes

10 9 8 7 6 5 4 3 2 1

23 people voted in all.

Ed uc a

3 fewer people voted for horror than action.

Action

2 96

Drama Horror Type of Movie

Comedy

At Home

Apples!

Mangoes!

Ed uc a

What’s your favorite fruit?

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1. Halle asked her friends their favorite fruit. She made a table from the data she collected.

My Friends’ Favorite Fruits

Mango 8

Apple

Banana

Peach

Help Halle make a bar graph from the table.

Fruit

My Friends’ Favorite Fruits

Friends 297

2. Make a bar graph from the table. Answer the questions and use the space to show your working. Class 2A’s Favorite Drink Milk

Orange juice

Apple juice

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Water

Ed uc a

Number of people

Class 2A’s Favorite Drink

2 98

Type of drink

(a) What drink was liked by 8 people? was liked by 8 people.

(b) How many more people liked water than milk?

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more people liked water than milk.

Ed uc a

There are

people in Class 2A.

(d) How many people liked fruit juices?

people liked fruit juices.

299

Line Plots

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Anchor Task

How Many Pets

Number 0 1

300

Tally

Total

Let’s Learn Wyatt asked 12 people in his class how many siblings they have. He recorded the data in a tally. How many siblings do you have?

Number

Tally

Total 3

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I have 1 brother and 1 sister.

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My Friends’ Siblings

Wyatt made a line plot from the tally. Line plots show how often values occur in a data set.

Number of Siblings

Each represents 1 person’s response.

3 01

Ed uc a

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Ethan asked 15 friends how many times per week they exercise. He recorded the data in a tally. How often do Weekly Exercise 4 times you exercise? a week. Exercise Days Tally Total

Ethan made a line plot from the tally.

From the people he interviewed, everyone exercised at least 1 time per week. Most people exercise 1 or 2 times per week.

Weekly Exercise

302

Hands On

Ed uc a

tio n

Work in small groups to measure the lengths of different pencils in your classroom. Record your findings in the line plot below.

Pencil Lengths in my Classroom

303

Let’s Practice

How many pets do you have?

Just 1.

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1. Sophie asked her friends how many pets they have. She recorded the data on a tally.

Number of Pets

0 1

Ed uc a

2 3

Use the data in the tally to complete the line plot below. Draw a for each response.

Number of Pets

304

2. Use the data in the tally to complete the line plots. (a) Hours Exercising per Week Hours Exercising 4

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5 6 7 8

(b)

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Test Scores

5 6 7

Test Scores

8 9

305

3. Create line plots from the information. Fill in the blanks. (a) 10 people were asked how many glasses of water they drank each day.

0 1

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Daily Glasses of Water

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Daily Glasses of Water

3 4 5

(b) Michelle asked her class their spelling test scores.

Test Scores

306

At Home

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1. Halle asked her friends how many hours per day they spend watching TV. She recorded the data on a tally. Daily TV Time 5

3 4

Ed uc a

A lot of people don’t watch any television!

0 1

Use the data in the tally to complete the line plot below. for each response. Draw a

Daily TV Time

307

2. Use the data in the tally to complete the line plots. (a) Hours Listening to Music Hours Listening 0

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1 2 3 4

Ed uc a

5 0

(b)

Number of Trips

1 2 3

4 5

308

Number of Trips per Year

3. Create line plots from the information. Fill in the blanks.

Ed uc a

tio n

(a) 10 people were asked how many hats they owned. 3 people owned 1 hat. 5 people owned 2 hats. The remaining 2 people owned 3 hats.

(b) 15 people were asked how many cousins they had. Number of Cousins

0 1

3 4 5

309

Solve It! Read the clues and make the line plot.

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• A group of 20 people were asked how many televisions they had in their home.

• The same number of people had 1, 2 or 3 televisions.

Ed uc a

• 4 more people had no television than people with 4 televisions. • No one had more than 4 televisions.

Televisions at Home

31 0

Looking Back 1. Create a picture graph from the table below.

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Favorite Fruits of Class 2B Apple

Pear

Banana

Ed uc a

Mango

stands for 1 person.

Each

311

2. Michelle made a picture graph of flowers she spotted in her garden. Fill in the blanks. Flowers in Michelle’s Garden

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Rose Tulip

Ed uc a

Daisy Daffodil Each

stands for 1 flower.

(a) What flower was spotted the least?

She spotted

the least.

(b) How many fewer tulips than roses were spotted? –

fewer tulips than roses were spotted.

daisies and daffodils were spotted.

312

3. A restaurant recorded the number of each dessert they sold in a night. Create a bar graph from the data they recorded.

pudding

lava cake

cheese cake

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ice cream

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Desserts Sold

Number sold

Dessert

Desserts Sold

313

4. 20 people were asked how many pairs of shoes they own. The data was recorded in a tally. Create a line plot from the tally.

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Pairs of Shoes 0 1 2 4

Ed uc a

314

5. 20 students took a test. The data was recorded in a tally. Create a line plot from the tally. Test Scores

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5 6 7 9

Ed uc a

315

tio n Ed uc a al eg

This publication would not have been possible without the tireless effort of our production team. Special thanks to: Daniel Cole, Matthew Cole, Wang Hui Guan, Kevin Mahoney, Winston Goh, Jesse Singer, Joseph Anderson, Halle Taylor-Pritchard, Sophie Taylor-Pritchard, Tejal Thakur, Natchanuch Nakapat,Varasinun Mathanattapat, Kanungnit Pookwanmuang, Saijit Lueangsrisuk Original Illustrations: Natchanuch Nakapat, GraphicsRF, Blue Ring Media and Interact Images Royalty-free images: Shutterstock, Adobe Stock