Let's Do Mathematics 4 – Worktext A by Regal_Education

n ca t Wo r k t e xt x

for le arne arners 9 - 10 year s o l d

2 km 25 min hike

Re ga le du ca tio n

This book or parts thereof may not be reproduced in any form, stored in any retrieval ieval system, or transmitted in any form by any means – electronic, mechanical, photocopy, recording, cording, g, or otherwise otherwis – without prior written permission of the copyright owner. First edition 2021 This edition is published by Regal Education Inc. ISBN 978-1-953591-08-1

Regal Education Inc. 10 Pienza, Irvine, CA 92606, United States www.regaleducation.org

Let’s Do Mathematics

Re ga le du ca tio n

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

Central to the USCCSS is the promotion of problem-solving skills ls and reasoning. Let’s Do Mathematics achieves this by teaching and presenting ng g concepts through throu a problem-solving based pedagogy and using the concrete-pictorial-abstract pictorial-abstract torial-abstract ((CPA) approach. Learners acquire knowledge and understanding a ng off concepts through thr th guided progression beginning with concrete examples and experiences which then w flow into pictorial representations and finally mastery at the and symbolic level. e abstract an a This approach ensures that learners develop a fundamental understanding of concepts damental ental understa underst rather than answering questions by learned procedures edures es and algorithms. algorit

Key features of the series include:

Anchor Task

Graphs Line Plots and Line G

Length of Pencils Total Tally

Length

Anchor Task

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

20 209

0 208

Let’s Learn n

Concepts are presented sented in a clear and a colorful manner.. Worked rked problems problem provide learners step-by-step ers with ith guided step-by ste progression through Series gh examples. Ser mascots provide rovide de guidance through throug throu helpful comments observations omments ments and observa when new concepts oncepts are introduced. intro

Numbers to Let’s Learn

Count on in

+1,000

5,000

1,000,000

thousands

6,000

Find the num ber represen ted in the plac e value cha

from 5,000.

+1,000

(a)

+1,000

7,000

Ten Thousands Thousand s

+1,000

8,000

1,000 more than 9,000 is 10,0 We read 10,0 00 as ten thou 00. sand. ten thousand s from 50,0 00.

We say: We write:

10,000

(b)

Count on in

+10,000

50,000

+10,000

60,000

+10,000

70,000

+10,000

80,000

500,000

+100,000

600,000

+100,000

700,000

800,000

100,000 mor e than 900 ,000 We read 1,00 0,000 as one is 1,000,000. million.

Ones

Hundreds

Tens

Ones

+10,000

We say:

90,000

+100,000

Tens

Twenty-five thousand, one 25,170. hundred seve nty.

Hundred Ten Thousands Thousands Thousand s

10,000 mor e than 90,0 00 is 100,000 We read 100, . 000 as one hundred thou sand. Count on in one hundred thousands from 500,000 . +100,000

rt.

Hundreds

+1,000

9,000

100,000

We write:

Three hundred hundred thirt forty-two thousand, eight y-three. 342,833.

(c)

Hundred Ten Thousands Thousands Thousand s

We say: We write:

+100,000

900,000

1,000,000

(d)

Hundred Ten Thousands Thousands Thousand s

We say: We write:

Hundreds

Tens

Ones

Five hundred one thousand 501,062. , sixty-two.

Hundreds

Tens

Nine hundred thirty thousand 930,107. , one hundred

Ones

seven.

iii

Let’s Practice

Let’s Practice 1.

Write

time using a.m. and

p.m.

(b)

(a)

(b)

(a)

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.

Write the times in 12-hour

time. the times in 24-hour

5 115 1:15

0 3:30

(d))

(c)

Morning:

Re ga le du ca tio n

Morning:

(f)

(e)

Afternoon:

(d)

(c)

:5 1:1:5 11:50 111:5

: 9:25 9

t the table. ete Comple

t International Airpor Flight Departures JFK Departure Departure (24-hour time) (12-hour)

Morning:

City

Night:

1:45 a.m.

less Los Angele

(f)

(e)

07 35

Miamii

0 9:05 9

5 45 4 :4 :45 77:45

3:40 p.m.

Dallas

g: Morning Morn

i g: Mornin

0 20 20

g gton Wa Washin Was

Night:

(b) Home At

Write the equivalent

fractions.

Use multiplication

(a)

At Home

to find equivalent

4 7

1 2

(b) (b

(b)

2 9

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.

2 9

1 3

Use division to find

(a) (a

3 4

(b)

3 6

÷6

18 42

÷3

18 = 42

152

÷3

18 42

÷4

12 = 20

(d)

equivalent fractio ns.

12 20

÷2

12 20

2 9

2 = 9

(c)

4 = 7

fractions.

4 7

÷6

153

Hands On

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

he dice. on the n on hown Hands On err sh ber mbe umb u num ke . ket kets h n e the Mov Move dii e. Mo shown in brac g a dice ng ing r llin i ro nt to the unit ent u ns in eme ake ttur a Take measurem cm ic met metrric e me rt the ert ve vert nve Con

36 cm (mm)

22,000 g (kg)

start. es back to the e rules: S Som rrectly,, go 3 spaces. a wer inco leap forward • If you ans a honey pot, 3 spaces. k ou land on • If you a bee, fly bac you land on • Iff y winner! hive is the h bee e the to er The first play

11 km (m)

182 dm (cm)

S RT STA

c 0 cm 110 dm)) ((dm (d

7 kg (g)

4,000 m (km (km)

00 ml 000 00 ,000 6,00 6 (l)

14 kg (g)

Solve It!

5l (ml)

Solve It!

What is Sophie’s favorite fruit? Match the mixed numbe rs and improper fractions to find out.

10 km (m)

0 80

Activities that require learners earners ers to apply logical reasoning problem-solving. Problems ng and nd problem-solvin problem-s hich do o not have a rou are often posed which routine strategy rners are encouraged encourag enc for solving them. Learners to think creatively and apply problem-solving y a range of probl p heuristics.

Looking Back

Consolidated solidated practice where whe learners demonstrate on a emonstrate their understanding under u range ange of concepts taught taug within a unit.

1 = 8

(e)

3 = 7

22 3

(f)

2 = 9

(d)

12 = 16

(e)

18 = 36

(f)

15 = 45

9 8

(d)

5 2

12 5

Write the improper fraction represented of the shapes.

by the colored parts

Write the mixed number represented the shapes in its simplest form.

by the colored parts of

(a)

(b)

on 6. Draw a point to show the fraction

the number line.

(a) 2 3

by writing = or ≠. 3. Tell whether the fractions are equivalent (b) 12 2 (a) 6

3 4

4 3

(b)

(c)

7 4

2 = 5

5 = 20

220

(a)

(d)

(c)

4 3

166

form. 2. Find the equivalent fraction in its simplest (b) 9 (a) 2 = =

1 3

4. 4

1. Find the first 2 equivalent fractions. (b) 3 (a) 1 = = =

(c)

Looking Back

FINISH

11 33

1 3

(b) 6

221

Contents 2 4 14 24 40 48

Re ga le du ca tio n 1

Whole Numbers Numbers to 1,000,000 Place Value Comparing and Ordering Numbers Rounding and Estimation Factors and Multiples

2 Operations on Whole Numberss n Addition and Subtraction Numbe Multiplying by a 1-digit Number Multiplying by a 2-digit git Number mber Dividing by a 1-digitt Number Word Problems

3 Fractions ractio Equivalent Fraction Fractions mbers bers and Improper Im Mixed Numbers Fractions Comparing ring and Ordering Or Orderi Fractions ng g and Subtracting Subtracti Subtr Adding Fractions tiplying ying Fractions Frac Fraction Multiplying ord Problems Word 4 Decimals Tenths enths Hundredths Hundre Hundredth Com Compar Comparing Decimals 6

66 66 66 79 92 107 122

140 140 155 170 185 203 212 146 226 226 248 269 v

Whole Numbers

Re ga

Anchor Task

City ty

Population

Numbers to 1,000,000

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Let’s Learn

Count on in thousands from 5,000. +1,000

5,000

+1,000

6,000

+1,000

7,000

+1,000 0

8,000

+1,000

9,000

10,000

1,000 more than 9,000 is 10,000. We read 10,000 as ten thousand.

00. Count on in ten thousands from 50,000. +10,000

50,000

+10,000

60,000

10,000 +10,000

70,000

+10 +10,000

80,000 80,

+10,000

90,000

100,000

0,0 iss 100,000. 100,00 10,000 more than 90,000 re thousand. We read 100,000 ass one hundred

e hundred undred thousands thousa tho Count on in one from 500,000. 000 0 +100,000

500,000

+100,000 +100,00

600,000

+100,000

700,000 7

+100,000

800,000

0,000 more than th 900,000 is 1,000,000. 100,000 1,000,00 as one million. 1,000 We read 1,000,000

+100,000

900,000 1,000,000

Find the number represented in the place value chart. Ten Thousands Thousands

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(a)

We say: We write:

(b)

We write:

(d)

Hundreds reds

Tens Te

Ones

Hundreds

Tens

Ones

Five one thousand, sixty-two. Fiive hundr hundred o 501,062. 50 062.

Hundred Ten Te Thousands Thousands sands Thousands Thousand

We say: w We write:

Ones

Three hundred eight ed d forty-two thousand, th hundred thirty-three. irty-three. -three. 342,833.

Hundred Ten Thousands Thousand Thousands Thousands

We say: We write: te:

Tens

Twenty-five thousand, one hundred undred seventy. seven seve 25,170.

Hundred Ten Thousands Thousands Thousands

We say:

(c)

Hundreds

Tens

Ones

Nine hundred thirty thousand, one hundred seven. 930,107.

Count on in tens. +10

+10

Re ga le du ca tio n

(a) 42,088

42,098

42,108

+10

(b)

206,974

42,118

+10

206,984

42,128

+10

206,994

+10

207,004 04

207,014 207,

Count on in hundreds. +100

(a)

97,563

+100

97,663

+100

(b)

115,850

+100 00

97,763 7,763

+100 00

115,950

+100

97,863 97

+100 00

116,050

97,963

+100

116,150

116,250

Count on in thousands. sands. nds. (a)

+1,000 1,000

66,400

(b)

67,400 ,400

+1,000

397,800 97,800

+1,000 1,0

68,400

+1,000

398,800

+1,000

69,400

+1,000

399,800

+1,000

70,400

+1,000

400,800

401,800

Count on in ten thousands. (a)

+10,000

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+10,000

530

10,530

+10,000

(b)

180,020

20,530

+10,000

190,020

30,530

+10,000

200,020

40,530 0,530

+10,000 10,000 0,000

210,020 20

220,020 220,

Count on in hundred thousands. (a)

+100,000

72,400

543,210

+100,000 0,000

301,064 064

+100,000 +100,

401,064 01 06

501,064

943,210

+100,000

300,022

+100,000

472,400

+100,000

843,210

+100,000

200,022

+100,000 +1

372,400 372

+100,0 +100,000

743,210 743,21

+100,000 +100 +100,0

100,022 00,022

+100,000 0,000

272,400 ,400

+100,000 0,000

643,210

+100,000 00

(c)

(d)

172,400

+100,000

(b)

+100,000

400,022

+100,000

601,064

701,064

Let’s Practice Write as numerals and words.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

Ten Thousands Hundreds Thousands

Tens

Ones es

Ten Thousands Hundreds Thousands

Tens Te

Ones

Hundred Ten Thousands Hundreds Thousan Thousands Thousands

Tens

Ones

Hundred red Ten Te Thousands Hundreds Thousands nds Thousands housa

Tens

Ones

Write the numbers.

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(a) Ten thousand, five hundred six.

(b) Seventeen thousand, six hundred ninety.

(d) Seven hundred twelve thousand, nd, one hundr hundred eighteen.

(e) Thirteen thousand, four hundred ed forty-nine. fortyforty

(f) One hundred six thousand, ousand, and, two hundred h eighty-one.

Write in words.

(a) 16,933

(b) 104,338 4,338 8

(d) 711,652

Count on in 100s.

1,860, 368, 34,705, 9,820,

Re ga le du ca tio n

(a) (b) (c)

(d)

(b) (c)

(d)

(b) (c)

(d)

51,200, 16,152, 7,251, 167,680,

270, 93,150, 87,000, 331,705 05 5,

Count on n in n 100,000s.

(a)

(b) (c)

(d))

Count on in 10,000s.

(a)

Count on in 1,000s. (a)

1,899 9, 153,151 53,151, 360, 600, 600,000 ,

Hands On

ca tio n

Form circles of 4 to 6 students. Each group receives a bean bag or ball. rd and say a Your teacher will write a number on the whiteboard count-on number.

om m the number numbe numb on the The student with the bean bag counts on from he next person in the whiteboard and throws the bean bag to the group. Continue passing the bean bag and nd counting on o until the teacher says 'Stop!'

Count on in 10,000s!

32,500!

At Home Match.

Re ga le du ca tio n

six hundred eighty thousand, twenty-seven

68,020 6

sixty-eight thousand, two hundred seventy

6,827

six hundred eight thousand, d, two hundred hu seven

680,027

sixty-eight th thousand, twenty

608,207

six thousand, eight hundred twenty seven

68,270

Write as numerals and words. Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones nes

Hundred Ten Thousands Hundreds eds Thousands Thousands

Tens Ten

Ones

Re ga le du ca tio n

(a)

(b)

Count on in 10,000s.

(a) (b) (c)

(d)

85,010, 107,290, 9,600, 272,000 000 0,

Count on in n 100,000s. 100,000s (a)

(b)) (c)

(d)

11,100 00, 480,350, 400, 599,500, 599 599,50

Place Value

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Let’s Learn

Find the value of each digit in the numbers shown. n. (a)

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones One

ds place is 2. The digit in the hundred thousands It represents 200,000. ce is 5. It represents r The digit in the ten thousandss place 50,000. rep The digit in the thousands place is 1. It represents 1,000. The digit in the hundreds place 600. ace is 6. It represents re The digit in the tens place 90. ce iss 9. It represents repre repr The digit in the ones place 3. e is 3. It represents re rep 200,000 + 50,000 + 1,000 ,000 00 + 600 + 90 + 3 = 251,693

The number can be found by adding the values of each digit.

Re ga le du ca tio n

(b)

HTh TTh

The digit in the hundred thousands sands ds place is 6. It represents 600,000. The digit in the ten thousands 8. It represents 80,000. ands nds place is 8 The digit in the thousands ds place is 9. 9 It represents 9,000. The digit in the hundreds eds place ace is 4. ItI represents 400. The digit in the tens place 20. ce is 2. It represents re The digit in the oness place ace is 5. It represents 5.

600,000 + 80,000 000 00 + 9,000 9 9,0 + 400 4 + 20 + 5 = 689,425

What is the value of the digit in the thousands place?

Let's find the value of each digit in the number. 5

Re ga le du ca tio n

(a)

9 0 0

0 0 0

5 0 0 0 0

The value of the digit 5 is 50,000. The value of the digit 6 is 6,000. The value of the digit 9 is 900. The value of the digit 8 is 80. The value of the digit 3 is 3. 50,000 + 6,000 + 900 + 80 0 + 3 = 56,983 56,983

(b)

9 0 0

5 0 0 0

0 0 0 0

0 0 0 0 0

The e value alue of the digit dig 4 is 400,000. The value 6 is 60,000. he v alue of the digit d The value value of the digit 5 is 5,000. value of the The v alue lue o th digit 9 is 900. The value value of the digit 2 is 20. value The v alue of o the digit 7 is 7. 400,000 00,0 + 60,000 + 5,000 + 900 + 20 + 7 = 465,927 00,000

Let’s Practice Write the numbers shown in the place value abacus. cus.

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(b))

(a)

HTh

TTh

HTh HT Th

TTh TTh TT Th

Th Th

HTh TTh

(d))

(c)

HTh TTh

(e)

(f)

HTh HT Th TTh TT TT Th h

Th Th

Write the number represented by the place value disks. 100,000

10,000

1,000

100

100,000

10,000

1,000

100

100,000

10,000

1,000

100

100,000

10,000

1,000

100

100,000

10,000

100

100,000

10,000

100

100,000

10,000

100 00 0

Re ga le du ca tio n

10,000 10,000

Write the value ue off the digit. dig d

(a)

(b)

(c)

(d)

Write the value of each digit. Then add the values. 4

Re ga le du ca tio n

(a)

(b)

(c)

Solve It!

Re ga le du

ion

Read the clues to find the combination to the safe!

• • • • • •

The code has 6 digits. The code is greater than an 220,000 but bu less than 420,000. The code is an odd number umber ber that is not divisible by 5. The sum of the digits in the tens and ones place is 10. he hundreds, hund The digit in the hundreds undr ndred place ace is 4. All digits are lesss than an 6 and a no 2 digits are the same.

Safe combination bin

At Home Match the numbers in two ways.

Re ga le du ca tio n

two hundred red d eighty-five eighty-fiv thousand, nd, sixty

258,602

20,000 0,000 00 + 5,000 + 600 + 20

twenty-five thousand, six twentytwenty-fi hundred hundre twenty

25,620

0 285,060

200,000 + 50,000 + 8,000 20 + 600 + 2

two hundred sixty thousand, two-hundred eighty five

two hundred fifty-eight thousand, six hundred two

60,285 0,285 260,285

200,000 + 60,000 + 200 + 80 + 5

200,000 + 80,000 + 5,000 + 60

Write the numbers shown in the place value abacus. (b))

Re ga le du ca tio n

(a)

HTh TTh

HTh TT TT TTh Th h

Th Th

Write the numbers represented by y the e place value valu va disks. (a)

100,000 100,000 10,000 10,000

1,000 000 1,000 1,000 100 1,00 0

100

100,000 100,000 10,000 10,000

11,000 ,000

1100

100

100,000 100,000 10,000 10,000 00 00

11,000 ,000

100

100,000

10,000

1,000 1,000 1,00

100

100,000

10,000 0

11,000 ,00 00

100

100,000 00 0 0

100 11,000 ,000 1,000 1,000 10

100

100,000 00,00 00 0

11,000 ,000 ,0

100

1100,000 0 00,0 0,00 00 0

1,000 11,00 ,000

100

1100,000 00,00 00 0

11,000 ,000 ,0

100

1100,000 00,00 00 00 00 0

11,000 ,0

100

(b)

Write the value of each digit. Then add the values. 1

Re ga le du ca tio n

(a)

(b)

Add the place ce values.

(a) 400,000 00,000 00 + 10,000 10,00 + 600 + 80 + 2 = (b) 200,000 00,000 + 20,000 20,00 + 2,000 = (c) c) 100,000 + 50,000 50,0 + 5 =

(d) ( 300,000 300,00 + 2,000 + 800 = (e) 700,000 + 7,000 + 70 =

(f ) 600,000 60 600,0 + 90,000 + 10 + 6 =

Comparing and Ordering Numbers ers

Re ga le du ca tio n

Let’s Learn

Let's compare the numbers.

(a) Compare the numbers 352,189 and 351,667. 7. Which number is greater? Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones

First, compare the values in the hundred thousands t place. pla are the same. p The values in the hundred thousands place he next place – ten thousands. Compare the values in the housands ands place plac are the same. The values in the ten thousands Compare the values in the thousands thousan place. 2 thousands is greater ter than 1 thousand. tho th So, 352,189 is greater reater eater than th 351,667. 35

(b) Compare the and 522,775. he numbers 522,165 522, 5 Hundred Te Ten Thousands Hundreds T Thousands Thousand Thousands

Tens

Ones

The values values in the th hundred thousands, ten thousands and place are the same. Compare the values in the thousands pla place. 1 hundred is smaller than 7 hundreds. hundreds p hund 522,165 < 522,775

522,775 > 522,165

Re ga le du ca tio n

(c) Compare the numbers in the place value chart. st. Order the numbers from the greatest to the smallest. Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones nes

First, compare the values in the hundred ndred d thousands thousan place. 85,580 does not have any digits in n the e hundred thousands place. So, it is the smallest number. ber. The remaining numbers both have ve 2 hundred hundre thousands. Compare the values in the ten en thousands thousand place. 5 ten thousands is greaterr than 4 ten thousands. tho th So, it is the greatest number. mber.r. 256,027

greatest

245,831

85,580

smallest

Always start by comparing the digits in the highest place value.

Let’s Practice Write the number represented by the place value disks. ks. Check the smaller number.

Re ga le du ca tio n

(a)

11,000

100,000 100,000 10,000 10,000

100,000 1100,000 00,00 00 00 0 10,00 110,000 00 0

1,000 100

1,000 000 11,000 ,000 1,0 11,000 ,00 1,000

100

100 1

100 00 0

100 0

100

(b)

100,000 100,000 100,000 1100,000 00,00 00 0

100,000 10,000 10,000 00 00

11,000 ,000

100,000 100,000 100,000 100,000

100,000 10,000 10,000

1,000

1,000 1,000 0 11,000 ,00 1,000 ,0 00

1,000 1,000 1,000 1,000

1,000 1,000 ,000 100 0

1,000 1,000 100

100 100

100 0

100 100

100 0

100 10

100

100 10

Write the numbers in the place value chart and compare. p

Re ga le du ca tio n

(a) Compare 704,561 and 703,761. Hundred Ten Thousands Hundreds Thousands Thousands

Tenss

Ones One

Tens

Ones

(b) Compare 185,119 and 185,102.

Hundred Ten Thousands ds Hundreds undre Thousands Thousands

mbols ols >, < and = to fill in the blanks. Use the symbols 5 (a) 11,055

11,505

(b) 135,509

135,509

80, 80,219

(d) 959,934

959,349

(e) 746,450 6,450

74 746,399

(f) 478,012

478,120

(g) 347,822

743,822

(h) 870,338

870,338

Check the smaller number. (a)

16,033

(b)

512,533

510,838

(c)

770,809

770,688 88 8

Re ga le du ca tio n

12,993

Check the greatest number.

(a)

31,533

7,543 43

4,573

(b)

192,606

193,00 193,000

192,506

(c)

742,167

742,176 742 742,1

742,168

Arrange the numbers ers from the greatest g to the smallest. (a) 109,558

105,558 105,5 105

(b) 753,186 6

119,060

93,002 93,0

29,158 (d) 29 2 9,158 158

119,414

110,598, 110 ,

401,306 ,

930,001 ,

9,455 ,

At Home Write the number represented by the place value disks. ks. Check the greater number.

Re ga le du ca tio n

(a)

HTh TTh

HTh HT Th TTh TT T T Th h

Th Th

HTh TTh

(b)

Compare re 104,070 04,070 and 10 104,101.

Hundred Ten n Thousands Hundreds Thousands ands Thousands

Tens

Ones

Check the numbers greater than 234,567.

35,675

234,560

243,650 3,650

335,707

48,589

500,367

234,558

243,006

234,580 234 234,

Re ga le du ca tio n

Use the words is greater than, is smaller maller er than and a is equal to to fill in the blanks. (a) 103,520

103,920

(b) 18,544

18,655

202,113 202 202,

(d) 999,478

999,666 9

(e) 234,980

234,980

(f) 567,010

576,010

bers fro ffrom the greatest to the smallest. Arrange the numbers

(a) 6,488

65,489

(b) 18,227 8,227

420,501

698,114

8,048

412,504 4

(d) 698,123 6 8,123 69

80,228 80,2

64,000

697,199

Number Patterns

Re ga le du ca tio n

Let’s Learn

What is the next number in the pattern? (a)

65,400

65,900

In each step, the numbers increase by 500.

66,400

66,900 0

66,900 + 500 6 = 67,400

+500 0

67,400 6 7,40 00

The next number in i the th pattern attern tt ttern t is i 67,400. 67,400

(b)

131,570

128,570

125,570

122,570

In each step, the numbers decrease by 3,000.

122,570 – 3,000 = 119,570

-3,000 -3,0

119,570

The next number in the th pattern is 119,570. Can you see a pattern with the he digits iin the thousands place?

1, 8, 5, 2, 9... They alternate between odd and even numbers!

284,900

304,900

ga le du ca tio n

244,900

The numbers increase by 20,000 in each step. 304,900 + 20,000 = 324,900 The next number in the pattern is 324,900. (d)

582,090

577,090

572,090

567,090 090

The numbers decrease by 5,000 0 in each step. 567,090 – 5,000 = 562,090 ern is 562,090. The next number in the pattern (e)

782

50,782

100,782 ,78

1150,782

The numbers increase ase by 50,000 50,0 in each step. 150,782 + 50,000 = 200,782 ,782 782 The next number ber er in the th pattern tte is 200,782. (f)

910,400

907,900

905,400

902,900

The numbers numb bers decrease decreas by 2,500 in each step. decre 2,900 00 – 2,500 = 900,400 90 902,900 he ne ext number num i the pattern is 900,400. The next in

What is the missing number? ?

, 20,558, 20,553

ed uc ati on

(a) 20,578, 20,573, 20,568,

The numbers decrease by 5 in each step. 20,568 – 5 = 20,563 The missing number is 20,563. ?

(b)

, 98,700, 94,700, 90,700, 86,700, 00, 82,700

The numbers decrease by 4,000 in n each ach step. 98,700 + 4,000 = 102,700 The missing number is 102,700. 0. What are the missing numbers? s? ?

, 608,351,

, 622,351, 22,351,1, 629,351, 629,351 636,351, 643,351

In each step, the numbers increase by 7,000.

Subtract 7,000 from 608,351 and add 7,000 to 608,351.

608,351 8,351 ,351 – 7,000 = 601,351 601 608,351 615,351 08,351 + 7,000 = 61 The missing are 601,351 and 615,351. missin numbers nu

Let’s Practice Fill in the blanks.

Re ga le du ca tio n

(a)

Hundred Ten Thousands Hundreds Thousands Thousands

5,000 less

Tens ns

Ones On

5,000 more

558,340 40

(b)

Hundred Ten Thousands Hundreds Thousands Thousands

40,000 less

(c)

(d))

Tens

Ones

30,000 more

Hundred Ten Thousands Hundreds Thousands housands Thousands

25,000 less

Ones

40,000 more

Hundred Ten Thousands Hundreds Thousands Thousands ousa

30,000 30,00 less le

Tens

25,000 more

Ones

Fill in the blanks. (a)

5,000 less

5,000 more

Re ga le du ca tio n

60,510

(b)

20,000 less

(c)

4,000 less

(d)

2,000 less

(e)

250,000 less

(f)

7,500 less

20,000 more ore

135,180

447,990

625,250 250

4,000 000 more

2,000 mo more

250,000 0,0 more

385,100 85,100 100

335,707

77,500 more

Find the number that comes mes next in i the pattern.

(a)

1,050

3,050

5,050 5,0

7,050

(b)

20,500

15,500

10,500

5,500

(c)

0 237,490

217,49 217,490

197,490

177,490

(d)

04,800 404,800

354, 354,800

304,800

254,800

(e)

12,536

25,036

37,536

(f)

908,223

708,223

508,223

308,223

Write the rule for the number pattern. The first one has been done for you.

Re ga le du ca tio n

(a)

+5,000

+5,000 0

9,311,

14,311,

19,311,

216,678,

191,678,

166,678, 6,678,

24,311

(b)

141,678

(c)

70,

60,070, 70,

120 120,0 120,070,

180,070

920, 920 920,800, 0

890,800,

860,800

(d)

950,800,

Find the missing issing ng numbers number in the number pattern. (a)

, 173,120 173,120, 19 198,120, 223,120, 248,120,

(b) 940,375, 40,375, 75,

, 640,375, 490,375, 340,375,

(d)

(e) 40,910, (f)

, 365,090,

,4 468,096, 476,096, 484,096, ,

, 16,910, 8,910, 910

, 664,944, 656,944, 648,944, 640,944,

, 500,096

Hands On Work in pairs. Write a 6-digit number in your notebook.

Re ga le du ca tio n

Flick the paper clip to spin it.

Have your friend add or subtract to find ind the next nex number.

Write the number in your notebook steps 2 to 4 ebook ok and repeat rep with a new 6-digit number.

+800 +10,0 00 –1 00

Place a paper clip on the center of the circle and hold it in place with a pencil as shown.

0 +7,50 –10 0 , 0 00

0 00 0, +2 00 –10,0 – +500 4 0 , 0 0 0

0 0 0 , +5 –1,00 0

At Home Fill in the blanks.

Re ga le du ca tio n

(a)

Hundred Ten Thousands Hundreds Thousands Thousands

5,000 less

(b)

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

50,000 more

Fill in the blanks. (a)

600 le less

(b)

8,000 less

(c)

12,0 12,000 less

(d) (d

100,000 less

(e)

30,000 less

Ones On

5,000 more

50,000 0 less

Tens ns

17,507

114,950 320,146

888,225 700,900

600 more

8,000 more

12,000 more

100,000 more

30,000 more

Ones

Fill in the missing numbers. .

Re ga le du ca tio n

(a) 10 more than 13,590 is (b) 200 less than 100,700 is

(e) 100 more than 153,100 is

(f) 1,500 less than 43,400 is

(g) 1,500 more than 161,980 is

(h) 2,500 less than 76,800 is

(i)

2,500 more than 19,300 iss

(j)

200,000 more than 51,200 ,200 200 is

Find the missing numbers number pattern. mbers rs in the nu

(a) 12,700,

, 11,650, 11,300, 10,950

(b) 205,448, 206,198, 6,198 206,948, 6,198, 948 (c)

(d) 38,500, 0,

, 208,448,

, 446,197, 452 452,197, 4 458,197, 464,197, , 30,5 30,500, 26,500, 22,500,

(e)

, 50,123 50,123, 10 100,123, 150,123,

(f)

, 189,2 189,210, 188,410, 187,610, 186,810, 189,210

, 250,123

Rounding and Estimation

Re ga le du ca tio n

Let’s Learn

Round off 105,998 to the nearest ten.

roun When rounding, remember 5 or more – ro round up!

When rounding, remember 4 or less – round down!

105,998 105,9 05,9

105,995

105,990

106,000

When rounding to the nearest arest rest ten, we look at the digit in the ones place. The digit in the ones nes place is 8, so we round up. 105,998 rounded ten is 106,000. d offf to the nearest neare ne Round 26,575 5 to o the nearest neare hundred. h

26,575

26,500

26,550

26,600

When roundin rounding to the nearest hundred, we look at the digitt in the tens place. The digit the tens place is 7, so we round up. it in th 26,575 rounded off to the nearest hundred is 26,600.

Round 162,450 to the nearest thousand.

Re ga le du ca tio n

162,450

162,000

162,500

163,000

When rounding to the nearest thousand, we look ook at the digit in the hundreds place. The digit in the hundreds place is 4, so we e round und down. down dow ousand sand is 162,000. 162,0 162,450 rounded off to the nearest thousand We write: We read:

162,450 ≈ 162,000 162,450 is approximately mately equal to 162,000

The population of San Francisco cisco o is 883,305. 883,3 883,305. unded to the th Find the population when rounded nearest thousand. ace is 3. 3 The digit in the hundreds place So we round down. thou th Rounded off to the nearest thousand, the population of San Francisco is 883,000. 8 83,000 00 883,305 ≈ 883,000 Find the he tion rounded population to the nearest he neare 100,000. 00,000.

We need to look at the digit in the 10,000s place.

Re ga le du ca tio n

A new sports car costs $274,800. Round the cost of the sports car to the nearest ten thousand usand nd dollars. d

In 274,800 the digit in the thousands place ace is 4. 4 So, we round down.

274,800 ≈ 270,000 Rounded to the nearest ten thousand ousand dollars, dollars the sports car costs $270,000.

The distance from Earth to o the moon is 384,400 km. Find the distance to the nearest thousand kilometers. arest hundred hund

384,400 km 384

The digit in the ten thousands tho place is 8. o, we round the hu So, hundred thousands up.

4,800 ≈ 400,0 400,000 384,800 Rounded ed to t the th nearest hundred thousand kilometers, the distance a from the Earth to the moon is 400,000 km.

Let’s Practice Fill in the missing numbers.

Re ga le du ca tio n

(a)

14,356

14,355

14,350

14,360 14,3 14,36

rounded off to the nearest arest st ten is

≈

(b)

231,910

231,950

231,900

232,000

rounded ded off to the nearest

hundred is

≈

470,800

(c)

470,500

470,000 000

471,000

rounded off to the nearest rou

thousan is thousand

≈

84,960

Re ga le du ca tio n

(d)

85,000

80,000

90,000 0,000

rounded off to the nearest

ten thousand is

≈

962,111 2,111

(e)

0,000 950,000

900,000

1,000,000

rounded offf to the nearest near

hundred thousand is

≈

A factory produces uces ces 23,875 2 5 paper pa clips per day. Round the number of paper aper clips to t the nearest ten thousand.

≈

The factory about tory produces abo

wimming ng pool pool contains con co A swimming 660,430 gallons of water. und d the volume to t the nearest thousand gallons. Round

≈

There about The ere are abo

pool.

paper clips per day.

gallons

gallons of water in the swimming

A house is for sale for $543,000. Round the price to the nearest one hundred thousand dollars.

eg al ed uc ati on

≈

The price of the house is about $

Round the numbers to the nearest hundred. red. d (a) 5,649 ≈

(b) 60,153 0,153 3≈

(d) 95,045 045 ≈

Round the numbers to the nearest arest st thousand. thousan (a) 12,466 ≈

(b) 701,709 701,7 70 1,7 ≈

(d) 33 3 33,187 ≈

Round the numbers to the nearest ten thousand. neare nea (a) 8,335 ≈

(b) 54,750 ≈

(d) 865,630 ≈

Round the numbers to t the th nearest hundred thousand. (a) 91,700 ≈

(b) 222,550 ≈

(d) 763,016 ≈

At Home Fill in the missing numbers.

Re ga le du ca tio n

(a)

83,395

83,500

83,000

84,000 84,0 84,00

rounded off to the nearest arest st

thousand is

≈

660,200 0,200

(b)

50,000 650,000

600,000

700,000

rounded ded d off to the nearest

hundred thousand d

≈

Round the numbers mbers to different differ di place values. (a)

≈

when rounded to the nearest hundred.

324,617 24,61

≈

when rounded to the nearest ten thousand.

≈

when rounded to the nearest thousand.

(b)

≈

Re ga le du ca tio n

when rounded d to the nearest hundred thousand. housan san

675,390

≈

when n rounded ounded to usand. the nearest ten thousand.

≈

when round rounded roun to st thousand. housand. the nearest

Round the numbers to the nearest arest st hundred. hundred

(a) 1,840 ≈

(b) 45,454 5,45 ≈

(d) 263,977 263 ≈

Round the numberss to the nearest thousand. neare nea

(a) 3,560 ≈

(b) 45,800 ≈

(d) 599,429 ≈

Round the he numbers to the th nearest ten thousand. (a) 14,630 4,630 ≈

(b) 225,000 ≈

(c)) 46,090 6,090 ≈

(d) 805,200 ≈

Round ound the numbers nu to the nearest hundred thousand. (a) a) 287,444 28 ≈

(b) 56,399 ≈

(d) 748,522 ≈ 47

Anchor Task

Factors and Multiples

Let’s Learn

Re ga le du ca tio n

Multiples erries. s Look at the products of 3 we can make with the cherries. 3x1=3

3x2=6

3x3=9

3 x 4 = 12

d any number num nu The product of 3 and is called a multiple of 3. o 3. 3 3, 6, 9 and 12 are multiples of Can you find d tthe tiple of 3? 6th multiple

6 x 3 = 18 The 6th multiple of 3 is 18!

Let's look at the first 10 multiples of 3 and 4. 3 4

6 8

9 12

12 16

15 20

18 24

21 28

24 32

27 30 6 40 4 36

Re ga le du ca tio n

Multiples of 3 Multiples of 4

Notice that 12 and 24 are multiples of both 3 and 4. Multiples of 3 Multiples of 4

3 4

6 8

9 12

12 16

15 20

18 24

211 28

24 32

27 30 36 40

We say 12 and 24 are common multiples es off 3 and 4. As 12 is the first common multiple of 3 and d 4, we say 12 is the lowest common multiple of 3 and 4. Let's find the lowest common multiple ultiple of 2 and 3. Multiples of 2: 2, 4, 6, 8, 10, 12, 2, 14, 4, 16, 18 18, 20, 20 22, 24 Multiples of 3: 3, 6, 9, 12, 15,, 18, 21, 21 24 24, 4, 27 27, 30

6, 12, 18 and 24 are common mon n multiples multip of 2 and 3. 6 is the lowest common multiple ultiple of 2 and 3.

Factors How many wayss can an we arrange arra arrang 12 cubes into equal rows?

1 x 12

2x6

3x4

The numbers that we multiply to make 12 are called factors.

Re ga le du ca tio n

12 = 1 x 12 12 = 2 x 6 12 = 3 x 4 1, 2, 3, 4, 6 and 12 are all of the factors of 12. Let's find the factors of 20.

1 x 20

2 x 10

4x5

The factors of 20 are 1, 2,, 4,, 5, 10 and an 20. We can use division on to fin find factors. Is 5 a factor of 15? 5? Let's et's divide. divide 15 ÷ 5 = 3 5 divides 15 with no remainde remainder. remai So, 5 is a factor actor or of 15. Is 4 a factor actor or of 15? 15 ÷ 4 = 3 R 3 There ere is a remainder remainde of 3. remain So, o, 4 is not a fa factor of 15.

The factors of 20 are 1, 2, 4, 5, 10 and 20.

le du ca tio n

Let's compare the factors of 12 and 20. Factors of 12: 1, 2, 3, 4, 6 and 12. Factors of 20: 1, 2, 4, 5, 10 and 20.

Both 12 and 20 share the factors 1, 2 and 4. We say 1, 2 and 4 are common factors of 12 and 20.

0 is 4. The greatest factor shared by 12 and 20 We say 4 is the greatest common factor actor or of 12 and 20. Look at the numbers and their factors table. ctorss in the ta Number 18 30 45 56 60

Factors

1, 2, 3, 6, 9, 18 1, 2, 3, 5, 6, 10, 15, 30 1, 3, 5, 9, 15, 45 1, 2, 4, 7, 8, 14, 28, 56 1, 2, 3, 4, 5,, 6, 6 10, 12, 15, 15 20, 20 30, 60

(a) Let's list the common factors of 18 and 45. ommon mon fact fa 1, 3 and 9.

(b) What iss the common factor of 30 and 56? e greatest greatest c com The common of 30 and 56 are 1 and 2. ommon mon factors factor o So, 2 is the greatest c common factor. (c) What are factors of 30 and 60? are the common com 1, 2, 3, 5, 6, 110, 15 and 30. (d) What is the greatest common factor of 30 and 60? From m (c), we w can see the greatest common factor is 30. 52

Re ga le du ca tio n

Prime and Composite Numbers Let's find the factors of 7. I can only make 1 row of 7 dots!

7 can only be arranged in 1 row of 7. The only factors of 7 are 1 and 7.

A number that is greater than 1 and of nd only nly has factors fa 1 and itself is called a prime number. mber. mber

Numbers that have more than an 2 factors factor are a called composite numbers. We can identify the numbers mbers ers 2 to 12 1 as prime or composite in the table. ble. Number 2 3 4 5 6 7 8 9 10 11 12

Factors tors

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

Prime or Composite

Prime Prime Composite Prime Composite Prime Composite Composite Composite Prime Composite

Let’s Practice (a) Color the multiples of 3 and 5 in the 100-square. re.

Re ga le du ca tio n

39 9

58 8

60 6

69 6

76 6

88 8

99 100

(b) What is the lowest common lowes lo w mm multiple of 3 and 5?

Complete the he following.

(a) List the of 8. he first six multiples multiple mu ,

(b) Listt the first four multiples of 12. ,

(d) List Lis the th third multiple of 9.

Complete the following.

Re ga le du ca tio n

(a) Find two common multiples of 3 and 7. and

(b) What is the lowest common multiple of 4 and d 6? 6

Fill in the blanks.

(a) Multiples of 6.

, 18, 24,

, 42

(b) Multiples of 7.

7, 14, 21,

, 49,

, 16,

, 32,

, 48,

, 64

(d) Multiples of 9.

, 36, 36 45, 4

, 63,

Find out if 4 is a factor factor of o 18. 18

cle to make groups group gr (a) Circle of 4 boats.

(b) b) Are Ar there the any boats remaining? (c) Is 4 a factor of 18?

Is 3 a factor of 20? Show your working.

Re ga le du ca tio n

Is 6 a factor of 42? Show your working.

List the factors of each number.

(a) 12: (b) 18:

(f) 100:

Find the common ommon mon factors. factor Show Sh your working. mmon on factors of 24 2 and 42: (a) Common

(b) ( C Common ommon ffactors of 60 and 15: omm

Re ga le du ca tio n

10. Find the greatest common factor. Show your our working.

11.

(a) The greatest common factor of 20 and 50 is

(b) The greatest common factor of 54 a an and 24 is

Circle e the he prime numbers. num

Solve It!

Re ga le du ca tio n

Michelle is looking for prime numbers between 2 and 100.. She knows 2 is a prime number. She colors it green and then crosses out all of the multiples of 2.

40 0

50 0

58 8

59 5

60 0

68 68

70 7

78 8

87 7

88 88

96 96

99 100

Multiple of prime Multiples numbe cannot numbers be prime prim numbers themselves! t

(a)

ue the he process proces to find the prime numbers between 2 Continue and 100. List them here. her

(b)

792 is a composite compos om number. Look Lo ook at the th digit di in the ones place and explain how you know 79 792 is not a prime number.

At Home The table shows the first 20 multiples of 3, 4, 5 and d 6.

Re ga le du ca tio n

Multiples of 3

Multiples of 4

Multiples of 5

Multiples of o 6

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

4 8 12 16 20 24 28 32 36 40 44 48 2 52 56 0 60 64 68 7 72 76 80

5 10 15 20 5 25 0 30 35 4 40 45 50 55 60 65 70 75 80 85 90 95 100

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120

(a) Find nd two two common comm multiples of 3 and 4.

(b) Find two two common com multiples of 4 and 5.

Find two tw common c multiples of 5 and 6.

(d) What is the first common multiple of 3 and 5?

Complete the following.

Re ga le du ca tio n

(a) Find two common multiples of 2 and 8. and

(b) What is the lowest common multiple off 3 and 12?

Fill in the blanks.

(a) Multiples of 4.

, 16,, 20,

, 28,

(b) Multiples of 10.

, 30, 0, 40,

, 70

, 24,

, 48,

Find out if 13 iss a factor factor of o 39.

(a) Circle to make ake groups grou of o 13 dots.

(b) b) Are Ar there the any dots remaining? (c) Is 13 3 a factor of 39?

, 72,

, 96

Complete the sentences with the word factor or multiple. (a) 12 is a

Re ga le du ca tio n

of 4.

(b) 36 is a

of 9.

of 60.

(d) 7 is a

of 49.

List the factors of each number.

(a) 21:

(b) 47:

(d) 80:

Find the four prime numbers umbers rs between betwe 100 and 110. Show your working.

, 61

Looking Back Write the numbers.

Re ga le du ca tio n

(a) Fifty-eight thousand, two hundred forty-one. ne.

(b) Six hundred thirty-four thousand, nine e hundred seven. seve sev

Write in words.

(a) 256,915

(b) 42,003

Count on in 1,000s.

(a) 8,710,

(b) 496,800,

(d) 695,500, 5,500,

Count Count unt on in 100,000s. 100, (a) 600, 6

(b) 125,780, 125,780 125

Count on n in 10,000s. (a) 1,121, 21,

Write the value of each digit. Then add the values. 7

Re ga le du ca tio n

(a)

(b)

Use the symbols mbols ls >>,, < and = to fill in the blanks. (a) 30,765 65

31,700 31,70

945,608 9 945,6

(b) 125,844

125,844

(d) 733,012

733,021

Arrange numbers from the greatest to the smallest. rrange ge the numb

(a) 79 779,754 9,754 754

779,761

(b)) 205,126 20

205,121

70,988 ,

205,120 ,

Fill in the blanks. (a)

2,000 more

20,830

al ed uc ati on

(b)

2,000 less

50,000 less

100,000 less

10,000 less

50,000 more ore

251,200 103,660

100,000 0,000 ,000 more

10,000 mo more

307,500 00

10. Find the missing numbers in the e number mber pattern. patt pa (a)

(b) 254,500,

, 3,600, 4,600, 5,600,, 6,600, 6,60

, 234,500, 34,500, 224,500, 224,50 224,5 214,500,

11.

, 410,355,

, 80,250, 50, 130,250, 180,250, 18

, 280,250

Round the numbers ten thousand. mbers bers to the nearest ne (a) 8,335 ≈

(b) 54,750 ≈

(d) 865,630 ≈

12. Round nd the numbers tto the nearest hundred thousand.

(a) 99,700 a) 99 9,700 ≈

(b) 222,550 ≈

(d) 763,016 ≈

13. Complete the sentences with the word factor or multiple. (a) 14 is a

Re ga le du ca tio n

of 7.

(b) 3 is a

of 18.

of 24.

(d) 42 is a

of 6.

14. Fill in the blanks.

(a) Multiples of 5. 5, 10,

, 30, 35, 5,

(b) Multiples of 8. 8,

, 40,

,5 56

h number. mber. 15. List the factors of each (a) 21:

(b) 47:

16. Find the two o prime numbers numbe between 20 and 30. nu Show yourr working.

, 65

Addition and Subtraction Anchor Task

ion

Operations on Whole Numbers

Let’s Learn

25,650

Keira scored 25,650 points in a computer game. Sophie hie scored cored hie score? 5,380 more points than Keira. How many points did Sophie 5,380

Keira

Re ga le du ca

Sophie ?

To find Sophie's score, we add. Step 1

Step 2

Add the ones.

Add the tens.

2 5 16 5 0

2 5 6 5 0

5 3 8 0

5 3 8 0 3 0

We can regroup 13 tens into 1 hundred and 3 tens.

Ten Thousands housands

Thousands Tho

Hundreds

Tens

Ones

Step 3

Re ga le du ca tio n

Add the hundreds. 2 15 16 5 0

We can regroup roup 10 hundreds eds into 1 thousan thousand.

5 3 8 0 0 3 0

Ten Thousands

Thousands

Hundreds

Tens ns

Ones

Step 4

Add the thousands. 1

Regroup 11 thousands into 1 ten thousand and 1 thousand.

2 15 1 6 5 0 5 3 8 0

1 0 3 0

Ten Thousands

Thousands

Hundreds

Tens

Ones

Step 5 1

2 15 16 5 0

5 3 8 0 3 1 0 3 0

25,650 + 5,380 = 31,030. Sophie scored 31,030 points.

uc ati on

Add the ten thousands.

Re ga le

Mr. Begg bought a boat and a trailerr for a total pri price of $52,350. p The trailer cost $4,750. Find the cost st off the boat.

$52,350

$4,750 $4,7

To find the cost st of the boat, bo we subtract. Step 1

Step 2

Subtract ract the one ones.

Subtract the tens.

5 2 3 5 0

–

4 7 5 0 0

–

4 7 5 0 0 0 69

Step 3

Re ga le du ca tio n

Subtract the hundreds. 5 1 2 133 5 0

–

Regroup 1 thousand into 10 re hundreds.

4 7 5 0

6 0 0

Ten Thousands

Thousands

Hundreds

Tens ns

Ones

Step 4

s.. Subtract the thousands.

Regroup 1 ten tthousand into 10 thousands.

5 11 2 133 5 0

–

4 7 5 0 7 6 0 0

Ten Thousands

Thousands Thousand

Hundreds

Tens

Ones

Step 5

Re ga le du ca tio n

Subtract the ten thousands. 4

5 11 2 133 5 0

–

4 7 5 0

4 7 6 0 0

52,350 – 4,750 = 47,600. Mr. Begg’s boat cost $47,600.

Find the sum and difference of 73,892 3,892 2 and 14,266. 14,26

To find the sum of 2 numbers, we add them together. 7

The sum of 73,892 2 and nd 14,266 14,26 is 88,158.

To find the difference 2 numbers, we subtract the smaller fference nce between betw number from m the greater number. nu 6

–

The difference between 73,892 and 14,266 is 59,626. differ

Let’s Practice Add.

Re ga le du ca tio n

(a)

(c)

(e)

(g)

(b)

(d)

(f) (f

(h)

Subtract. (a)

(b)

Re ga le du ca tio n

5 –

(c)

–

(e)

–

(g)

–

(i)

–

(d)

–

(f)

–

(h)

–

(j)

–

Use the column method to add or subtract. (b) 14,603 – 10,735 35 =

Re ga le du ca tio n

(a) 63,210 + 18,824 =

(d) 70,656 – 8,779 =

(e) 43,855 55 + 7,054 =

(f) 64,003 – 8,325 =

Solve It!

Re ga le du ca tio n

It’s Blake’s birthday! What flavor is his cake? Match the letters to the correct answers to find out! R

–

70,208

87,070 87

70,802

87,070

17,820

82,017

82,710 75

(b) Home At Add.

Re ga le du ca tio n

(a)

(c)

(e)

(g) 3,679 9 + 27,052 =

(b)

(d)

(f)

(h) 44,080 + 9,326 =

Subtract. (a)

(b)

Re ga le du ca tio n

6 –

(c)

–

(e)

–

(g) 23,207 – 9,416 9 416 =

–

(d)

–

(f)

–

(h) 70,925 – 38,716 =

Find the sum and difference of each pair of numbers.

Re ga le du ca tio n

(a) 3,827 and 7,294

sum =

difference ifference =

(b) 56,845 and 12,033

sum =

difference =

0 and 36,109 (c) 21,040

su = sum

difference =

Multiplying by a 1-digit Number

Re ga le du ca tio n

Anchor Task

Hundreds

Tens

Ones

Let’s Learn

Re ga le du ca tio n

The Paradise Hotel has rooms for $132 per night. How much ch does it cost to stay at the hotel for 3 nights? se a place value valu va We need to multiply $132 by 3 to find out. Let’s use chart to help find the answer. Hundreds

Tens

Each row r represent the cost represents of 1 n night’s stay.

Ones

$132

3x2=6

Step 1

Multiply the ones. 1 3 2

Hundreds

Tens

Ones

3 6

3 x 30 = 90

Step 2

Multiply tiply the tens. tens 1 3 2

9 6

Hundreds

Tens

Ones

Step 3

3 x 100 = 300

Re ga le du ca tio n

Multiply the hundreds. 1 3 2

Hundreds

Tens

Ones

3 9 6

132 x 3 = 396 So, 3 nights at the Paradise Hotel costs $396.

hod. Find 403 x 2 using the column method. 4 0 3

4 0 3

0 6

8 0 6

403 x 2 = 806

Find 2,130 x 3 using method. g the column colu co 2 1 3 0

2 1 3 0

9 0

2 1 3 0

3 9 0

2 1 3 0

6 3 9 0

2,130 x 3 = 6,390

Re ga le du ca

A new car has a mass of 1,275 kg. 3 identical cars are loaded onto a truck to be transported to a dealership. Find the total mass of ss o the 3 cars.

1,275 kg

We need to multiply 1,275 kg g by 3 to find the th total mass of the cars. Let’s use a place value chart art to help find the answer. 5 x 3 = 15. Regroup 15 into 1 ten and 5 ones.

Step 1

Multiply the ones. nes. 1

Thousands

Hundreds

Tens

2 17 5

3 5

5 x 3 = 15 Regroup 110 o ones into 1 ten and write 5 in the ones column.

Ones

Step 2 Thousands

Hundreds

Tens

Ones

Re ga le du ca tio n

Multiply the tens. 1

2 7 5

2 5

7 tens x 3 = 21 tens. 21 tens + 1 ten = 22 tens. Regroup 20 tens into 2 hundreds and write column. e 2 in the tens te t Step 3

Multiply the hundreds. 2

Thousands sands

Hundreds Hundred

Tens

Ones

Tens

Ones

1 2 7 5

8 2 5

2 hundreds x 3 = 6 hundreds. un und 6 hundreds + 2 hundreds ndreds eds = 8 hundreds. Step 4

Multiply the thousands. housands. 1 22 1 7 5

Thousands

Hundreds

3 8 2 5

1 thousand housand x 3 = 3 thousands. housa 1,275 x 3 = 3,825 3,82 al mass of the 3 cars is 3,825 kg. So, the total

Find 48 x 6 using the column method. 4

4 8

Re ga le du ca tio n

4 8

2 8 8

48 x 6 = 288

Find 577 x 4 using the column method. 5 27 7

5 27 7

0 8

2 3 0 8

577 x 4 = 2,308

Find 1,392 x 5 using the column c mn method. m 1 43 1 9 2

1 3 19 2

1,392 x 5 = 6,960 960

6 0

1 43 1 9 2

9 6 0

1 43 1 9 2 5

6 9 6 0

Let’s Practice Multiply.

Re ga le du ca tio n

(a)

(b)

4 2

(c)

(g)

(f) (f

(d)

6 4

(e)

0 4

(h)

6 8

Use the column method to multiply. (b) 738 x 8 =

Re ga le du ca tio n

(a) 95 x 6 =

(d) 456 x 5 =

(e) 6,782 2x7=

(f) 9,813 x 4 =

Solve It!

Re ga le du ca tio n

The shapes represent digits.

berss they form. form for Here are some clues about the digits and the numbers •

x 12 =

•

+2=

Can you work out what numbers the shapes represent? rep

Re ga le du ca tio n

Sophie is having ice cream for dessert. What fruit does she like on her ice cream? Match the letters to the correct answers to find out! I

3 2

22,806 2,806

18,160

9,963

926

24,655

9,963

3,458

(b) Home At Multiply.

Re ga le du ca tio n

(a)

(b)

(c)

(g)

(f) (f

(d)

3 8

(e)

5 9

(h)

0 4

Multiply using the column method. (b) 837 x 4 =

Re ga le du ca tio n

(a) 173 x 6 =

(d) 5,389 x 3 =

(e) 6,841 x 8 =

(f) 9,409 x 7 =

Hands On

Re ga le du ca tio n

Ethan, Dominic and Jordan are having problems with ch child hild has h multiplication. Work in pairs to identify the errors each made. Explain the error and how they can fix it. 1

3 9 4 x 4 8 3 8

2 10 5 x 3 6 4 5

1 7 6 x 3 3 2 1 1 8

Multiplying by a 2-digit Number

Re ga le du ca tio n

Anchor Task Dice 1

x 10

Dice 2

Let’s Learn

Re ga le du ca tio n

Let’s use place value disks to help multiply numbers by y ten. n. 4 x 10 = 40 1

x 10

23 x 10 = 230 10

x 10

100

10 0 10

62 x 10 = 620 10

100 0

100 100

x 10

100 10

100

Do you see a pattern?

Re ga le du ca tio n

Let’s use place value disks to help multiply numbers by tens. We know that when we multiply a number by ten, we shift the values val va to the left one place and put a zero in the ones place. When multiplying a number by a multiple of ten, we can separate separa separ the tens and ones and multiply in 2 steps. Find 32 x 20.

Method 1 Multiply by 10 first. Then multiply by 2. 10

x 10

100

100 00 0

100 0

100 10

100 0

100

Method 2 Multiply by 2 first. Then multiply tiply by 10. 1 10

32 x 20 = 640

10 0

1 10

10 0

x 10

100

Re ga le du ca tio n

Multiply 26 and 14. We can regroup these numbers into tens and ones, then en place plac lac them in a table and multiply each column and row. x

200

Now, add uc the products er! together!

Add the products. 1

2 0 8 6 + 2 3 6

0 0 0 4 4

So, 26 multiplied by 14 is 364. 4.

Find the product of 48 and an a 17 using usin i the column method. Step 1

Multiply by the ones. nes. 5

4 8 1

7 x 8 = 56 Regroup into 5 tens and 6 ones.

3 3 6

7 x 4 tens = 28 tens 28 tens + 5 tens = 33 tens.

Step 2

Re ga le du ca tio n

Multiply by the tens. 4 8

4 8

3 3 6

8 0

4 8 0

1 ten x 8 = 8 tens ens

1 ten x 40 = 40 tens 40 tenss = 4 hundreds

Step 3

Add the products. 4 8

3 3 6

4 8 0

4 8

3 3 6

4 8 0

3 3 6

4 8 0

48 x 17 = 816

Find 56 x 27 using ng the column method. m

Multiply by 7.

Multiply by 20. M Multip

5 6

2 7

3 9 2

Add the products.

5 6 2 7

3 9 2

1 1 2 0

5 6

2 7

3 9 2

1 1 2 0

1 5 1 2

56 x 27 = 1,512 1 96

Let’s Practice Fill in the blanks.

Re ga le du ca tio n

(a)

1 1

(b)

22 x

(c)

10 0

100

(d)

100

100 100

100

Find the products. (b) 4 x 7 =

Re ga le du ca tio n

(a) 6 x 5 = 6 x 50 =

4 x 70 =

(d) 12 x 3 =

30 x 8 =

12 x 30 0=

(e) 9 x 2 =

(f) 5 x 8 =

5 x 80 =

90 x 2 =

Work out 17 x 36 by multiplying plying ying rows and an columns in a table. Then add the products. x

30 6

17 x 36 =

Multiply using the column method. 1

(b)

Re ga le du ca tio n

(a) x

(c)

(d)

(e)

(f)

Multiply using the column method. (b) 28 x 14 =

Re ga le du ca tio n

(a) 13 x 36 =

100

(d) 54 x 39 3 =

(e) 73 x 25 =

(f) 96 x 23 =

Solve It!

Re ga le du ca tio n

Can you work out what numbers the shapes represent? nt?

Try and nd solve sing Guessthis using and-Check. -Chec

1 01

At Home Fill in the blanks.

eg al ed uc ati on

(a)

(b)

0 100

100 00 0

100 0

10 0

1 10

10 0

110

100

100 0

1100 10

100

100 0

100

10 0

110

100 0

100

100 00 0

100

10 0

100 0

100

1 10 100

x 102

100 0

(c)

100

Find the products. (b) 5 x 9 =

Re ga le du ca tio n

(a) 3 x 4 = 3 x 40 =

70 x 7 =

(e) 9 x 4 =

90 x 4 =

5 x 90 =

(d) 10 x 6 =

100 x 6 =

(f) 8 x 7 =

80 x 7 =

g. Multiply. Show your working. (a) 4 x 70 =

(b) 30 x 80 =

(d) 50 x 6 =

(e) e) 40 0x4=

(f) 70 x 8 =

1 03

Work out the following by multiplying rows and columns in a table. Then add the products.

Re ga le du ca tio n

(a) 33 x 27 = x

20 7

(b) 58 x 46 = x

104

Multiply using the column method. 1

(b)

Re ga le du ca tio n

(a) x

(c)

(d)

(e)

(f)

1 05

Multiply using the column method. Show your working. g (b) 28 x 15 =

Re ga le du ca tio n

(a) 14 x 16 =

106

(d) 53 x 34 3 =

(e) 82 x 62 =

(f) 93 x 76 =

Dividing by a 1-digit Number

48 4

Anchor Task

720

840 1 07

Let’s Learn

Re ga le du ca tio n

Let’s use place value disks to divide 164 by 4.

Regroup 1 hundred ndred into 10 tens. Now we can mak make equal ual groups!

100

10 0

110 0

10 0

There are 4 equal group groups of 41. 164 ÷ 4 = 411

The division equation have special names. he parts of a divis d

164 ÷ 4 = 41

dividend 108

divisor

quotient

Let’s use place value disks to divide 368 by 3. 10

100 100

Re ga le du ca tio n

100

10 0

100 10

ups of 122 with 2 ones remaining. We can make 3 equal groups We say: We write:

22 remain rema 368 divide 3 is 122 remainder 2. 1 R2 368 ÷ 3 = 122

The quotient is 122!

The T remainder is 2!

1 09

Divide 96 by 4. Divide 9 tens by 4. 9 tens ÷ 4 = 2 tens remainder 1 ten. 9 tens – 8 tens = 1 ten.

Re ga le du ca tio n

Step 1 2

8 1

Step 2 2 4

Bring the 6 ones down. n. 1 ten and 6 ones is 16..

8 1

y 4. Divide 16 ones by s 16 ones ÷ 4 = 4 ones. 16 ones – 16 ones nes = 0.

96 ÷ 4 = 24

The quotient is 24 and theree is der no remainder!

quotient

divis d divisor

8 1

110

dividend

remainder

Find 742 ÷ 6. Divide 7 hundreds by 6. 7 hundreds ÷ 6 = 1 hundred remainder nder 1 hundred. hundre hund 7 hundreds – 6 hundreds = 1 hundred. ndred. ed.

Re ga le du ca tio n

Step 1 1

6 1

Step 2 1 2

Bring the 4 tens down. n. Now there are 14 tens. ns.

ns remainder emainder 2 tens. 14 tens ÷ 6 = 2 tens ns = 2 tens. 14 tens – 12 tens

6 1

2 2

Step 3 1 2

22 ÷ 6 = 3 R 4 22 – 18 = 4

6 1

Bring ring down d n the 2 ones. there are 22 ones. Now w the ther

T The remainder is 4!

742 ÷ 6 = 123 12 R 4

111

Find 1,813 ÷ 7. Step 1 Divide 1 thousand by 7. Regroup into 10 hundreds and add d 8 hundreds. hund hundre mainder 18 hundreds ÷ 7 = 2 hundreds remainder 4 hundreds. 18 hundreds – 14 hundreds dss = 4 hundreds. hundred

Re ga le du ca tio n 2

Step 2

Bring down the 1 ten. en. Now there are 41 tens. ns.

41 tens ÷ 7 = 5 tenss remainder remaind 6 tens. 41 tens – 35 5 tens ns = 6 tens. tens

Step 3

4 4

63 ÷ 7 = 9 63 – 6 63 = 0

1,813 ÷ 7 = 259

112

Brin down Bring Br own the th 3 ones. there are 63 ones. Now th

Let’s Practice Find the quotient and remainder.

Re ga le du ca tio n

(a) 6 ÷ 3 Quotient:

(b) 8 ÷ 2 Quotient:

Remainder:

Remainder: inder: nder:

(d) 12 ÷ 5 Quotient: tient:

Remainder:

Remainder: Remaind Remainde

(f 35 ÷ 8 (f) Quotient: Quot

(e) 21 ÷ 3 Quotient:

Remainder: R

Remainder:

Divide.

(a) 5 ÷ 2 =

(b) 9 ÷ 3 =

(d) 22 ÷ 6 =

(e) 27 ÷ 3 =

(f) 31 ÷ 3 =

(g) 28 ÷ 9 =

(h) 36 ÷ 6 =

(i))

(j)

52 2÷8=

42 ÷ 6 =

1 13

Divide. (b)

(c)

Re ga le du ca tio n

(a) 3

(d)

(e)

114

(f)

(g)

(h) 3

(i)

ed uc ati on

(j)

eg a

1 15

Complete the following. (b)

Re ga le du ca tio n

(a) 3 9 3

4 9 6

d) (d)

(c)

5 7 8

(e)

(f)

4 3 1 0 8

116

3 2 6 4

7 6 5 3 9

Hands On

tio n

Work in pairs. Take turns choosing a 3 or 4-digit number. ber. Show e you your the number using place value disks. Roll a dice and divide er to o show the number by the number on the dice. Work together ks ks. quotient and remainder with the place value disks.

1 17

At Home Write the division equation represented by the place ace value disks. dis

Re ga le du ca tio n

(a)

100

1 1

(b)

100

10 0

(c)

100 10 0

118

(d)

Re ga le du ca tio n

100 100 100

100

100 100 100

1,000

100 100 100

0 100 100 100

(e)

1,000

10 0 10

1,000 00 0

1,000 000 0

1,000 0

1 10

1 19

Divide. (b)

(c)

Re ga le du ca tio n

(a) 2

(d)

(e) e)

1 20

Complete the following. (b)

Re ga le du ca tio n

(a) 3 8 1

5 9 4

d) (d)

(c)

8 3 9 2

(e)

6 7 8 0

(f)

4 1 2 2 7

9 7 0 3 8

121

Word Problems

Re ga le

ion

Mr. Wong bought a new dining set which included a dining ining g table and 6 chairs. The table cost $488 and one chair cost $136. 6. Find the mation on to chec total cost of the dining set. Use rounding and estimation check if your answer is reasonable.

Step 1 First, let’s find the total al cost of the 6 chairs. $136

chairs

To find the he total al cost of the t 6 chairs, we multiply. 2

1 33 6 6

8 1 6

136 x 6 = 816 81 The total cost of the chairs is $816.

122

Step 2 $816

Re ga le du ca tio n

$488 table

6 chairs

To find the total cost of the dining set, we add. 1

488 + 816 = 1,304 et iss $1,304. The total cost of the dining set

Check Let’s use rounding and estimation that the answer is mation to check c reasonable. Cost of 6 chairs = $816 16 ≈ $800 800

e Cost of table

= $488 ≈ $500

00 = $1,300 $800 + $500 0 is approximately approxim 1,300 equal to 1,304. So, the answer is reasonable.

123

Re ga le du ca tio

A clothing factory makes shirts that have 8 buttons. The factory orders 715 buttons and uses them to make shirts. (a) Find the total number of shirts that can be the e made with th buttons. Check that your answer is reasonable. onable. able. Let’s use a bar model to help find the e answer. swer. 8 buttons

shirts

4 7

715 ÷ 8 = 89 R 3 The clothing lothing ng factory can ca make 89 shirts with 3 buttons left over.

Check heck k Let’s Let’s check that th the th answer is reasonable. 70 ÷ 8 ≈ 9 700 ÷ 8 ≈ 90

90 is close to 89, so our answer is reasonable. 1 24

Re ga le du ca tio n

(b) The shirts are sold for $28 each. How much money does the clothing factory receive if all of the shirts are sold? Check eck that your answer is reasonable. $28

1 shirt

89 shirts ts

To find the total amount of money, we e multiply. ultiply. 2 8

8 9

2 5 2

2 2 4 0

2 4 9 2

The clothing factory willl receive $2 $2,492.

Check Let’s use rounding to check that the answer is ding ng and an estimation m reasonable. Round 28 and 89 to the nearest 10. ne 28 ≈ 30 and d 89 ≈ 90

3 x 9 = 27 3 x 90 0 = 270 30 x 90 = 2,700 2,70

close to 2,492, so our answer is reasonable. cl 2,700 is close

125

Farmer Joe picks 1,758 apples from his orchard in the morning. He picks 4 times ass many apples in the afternoon. The apples are placed in small baskets to be sold at the market. Each basket holds 6 apples. Find the total number of baskets of apples. Check that your answer is reasonable.

Re ga le du ca t

Step 1 First, we need to find the total number of apples ples picked. picked 1,758

morning

afternoon

Multiply 1,758 by 4 to find the number of o apples picked in the afternoon. 3

1 27 35 8

7 0 3 2

7,032 appless were ere picked in the t afternoon. 1,758

7,032

morning

afternoon

1 7 15 8

+ 7 0 3 2

8 7 9 0

1 26

8,790 apples were picked in all.

Re ga le du ca tio n

Check 1,758 ≈ 1,800 7,032 ≈ 7,000 1,800 + 7,000 = 8,800 8,800 is close to 8,790, so the answer is reasonable. le. Step 2

6 apples

apples

8,790 app apples

Now we can divide. 1 6 8 6 2 2

4 6 5 7 9 0

7 4 3 9 3 6 3 0 3 0 0

A total of 1,465 are used to pack the apples. 465 baskets a

Check ck 8790 790 ≈ 9000 90 ÷ 6 = 15 900 ÷ 6 = 150 1,50 9000 ÷ 6 = 1,500 1,500 is close to 1,465, so the answer is reasonable.

127

A computer costs 3 times as much as a printer. Summer Bay Primary School bought a printer and 5 computers for the IT center. The printer cost $476, find the total cost of all the items. Check that your answer is reasonable.

Re ga le du ca

Step 1 Find the cost of a computer. $

printer

computer

A computer puter er cost $ ck Check

1 28

Let’s Practice

Re ga le du ca tio n

Step 2 Find the cost of 5 computers.

Step 3 Find the total cost of the items. $

printer

computers

The total cost of the ite ititems is $

Check

129

Halle buys gifts for the 23 pupils in her class. Each gift box is tied with a piece of ribbon that is 36 cm long. She bought ought ght 1,000 cm of ribbon. How much ribbon does she have ave left? Check that your answer is reasonable.

Re ga le du ca tio n

130

Mrs. Cooper orders 3,192 kg of soil for her new garden. She puts half of the soil on the front lawn. She puts equal ual amounts of the remaining soil into 7 big pots. Find d the e mass of o easonable. nable the soil in each pot. Check that your answer is reasonable.

Re ga le du ca tio n

1 31

At Home

ion

76 people in an office each donate $63 for a charity rity lly fundraiser. The money is collected and shared equally h charity between 4 charities. How much money does each bl ble. receive? Check that your answer is reasonable.

Re ga le du c

Step 1 Find the total amount off money oney raised. raise rais $63

76 6 peo people

A total of $ Check eck

132

was w raised.

Re ga le du ca tio n

Step 2 Find the amount of money each charity received.

charities

Each charity received $

Check

1 33

A bakery bakes 3,310 rolls. It sells 1,014 rolls in bags of 6. The remaining rolls are sold in bags of 8. Find the total number umber mber of bags to be sold. Check that your answer is reasonable. nable. e.

Re ga le du ca tio n

1 34

Looking Back Add or subtract.

Re ga le du ca tio n

(a)

(c)

(b)

–

d) (d)

–

(e) 1,068 + 7,951 =

(f) 2,106 2 – 955 =

(g) 23,840 ,840 0 + 27,291 =

(h) 46,040 – 18,565 =

1 35

Work out the following by multiplying rows and columns in a table. Then add the products.

Re ga le du ca tio n

(a) 18 x 39 = x

30 9

(b) 24 x 26 = x

20 6

Multiply using ng the column colu method.

(a)

1 36

(b)

(d) 52 x 13 =

Re ga le du ca tio n

(e) 44 x 43 =

(f) 25 x 77 =

(g) 16 x 82 =

(h) 39 x 64 =

1 37

Divide. (b)

Re ga le du ca tio n

(a) 3

(c)

(d) d)

4 7 8 3 9

1 38

8 6 2 2 4

A factory produces 1,368 tins of pears and 4 times as many tins of peaches. They are placed into 4 storage containers tainers ners in equal numbers. Find the number of tins in each h storage orage e. container. Check that your answer is reasonable.

Re ga le du ca tio n

1 39

Fractions

Equivalent Fractions Anchor Task

140

ion

Let’s Learn

Re ga le du ca tio n

Halle, Sophie and Chelsea each have a paper strip of the same size. si Halle divides her paper strip into 3 equal parts. She colors 1 part. 1 of the p paper 3 strip is co colored.

ual parts. arts. Sophie divides her paper strip into 6 equal She colors 2 parts.

2 6

of the paper strip is colored.

trip into 9 equal equa parts. Chelsea divides her paper strip She colors 3 parts.

3 9

of the paper strip is colored.

ach strip of paper. p Let’s compare each

1 3 2 6

3 9

and 39 are equal. qual fr fractions a Equal are called equivalent fractions. The he fractions

1 2 3, 6

1 2 3 = = 3 6 9

1 41

Find equivalent fractions of 1 using multiplication. 4

Re ga le du ca tio n

Multiply the numerator and denominator by the same number.

1 4

2 8

1 4

2 8

1 4

3 12

1 4

4 16

1 4

2 3 4 , , and 5 are equivalent fractions ractions tions of 1 . 8 12 16 20 4 1 4 2 8

3 12

4 16

5 20

1 = 2 = 3 = 4 = 5 4 8 12 16 20 1

142

= 20

Find the first 4 equivalent fractions of 1 . 5

Re ga le du ca tio n

1 5

2 10

1 5

3 15

1 5

= 20

1 5

= 25

2 3 4 , , and 5 are equivalent fractions of 1 . 10 15 20 25 5

1 = 2 = 3 = 4 = 5 5 10 15 20 25

Find the first 4 equivalent fractions ractions ons of 2 . 3

2 3

= 6

2 3

6 9

2 3

= 12

2 3

= 15

4 6 8 , , and 10 are re equivalent equivale ffractions of 2 . 6 9 12 15 3 5

2 = 4 = 6 = 8 = 10 3 6 9 12 15

1 43

Re ga le du ca tio n

We can find equivalent fractions by multiplying the numerator and denominator by the same number. e numerator merat We can also find equivalent fractions by dividing the and denominator by the same number.

÷3

6 = 18

÷2

2 6

÷3

2 6

1 3

÷2

6 18

We cannot divide the numerator an and denominator off 1 3 further.

2 6

1 3

When a fraction cannot be f divided further by the same number, numb we say it is in its simplest form. sim 1 is the simplest form of 6 . 3 18

m of 8 . Find the simplest form 12

The numeratorr and are both divisible by 4. d denominator denominato denomin ÷4

8 = 12

2 3

÷4

2 is the simple simplest fo form of 8 . 3 12

1 44

8 12 2 3

Let’s Practice Use the fraction chart to find equivalent fractions.

Re ga le du ca tio n

1 2

1 3

1 4

1 5

(c)

1 2

1 4

1 5

1 6

1 7

1 8

1 9

1 10

1 11

1 12

(b)

(d)

1 4

1 5

1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 1 8 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 1 10 10 10 10 10 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 1 12 12 12 12 12 12 2

(a)

1 3

1 5

1 6

1 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 12 12 12 12 12

2 3

4 5

1 45

Use multiplication to find equivalent fractions. (a)

Re ga le du ca tio n

3 4

(b)

2 5

(c)

1 4

(d)

3 7

146

1 4

2 5

3 7

1 4

3 7

Use division to find equivalent fractions. (a)

÷4

Re ga le du ca tio n

÷2

8 20

÷2

8 20

÷4

÷3

(b)

18 27

÷9

18 27

÷3

18 27

÷9

÷2

6 18

÷3

6 18

÷2

6 18

8 3 32

8 32

÷2

8 3 32

6 18

÷3

÷6

÷4

÷8

÷4

÷6

÷2

(d)

(c)

8 32

÷8

1 47

Fill in the blanks. (b)

Re ga le du ca tio n

(a)

4 5

8 10

(c)

4 12 2

2 7

110 35

7 10

42 60

3 8

12 32

12 16

3 4

(d)

9 15

3 5

(e)

(f))

12 32

3 8

(g)

(h) (

10 35

2 7

(i)

(j)

42 60

148

1 3

7 10

Find the first 2 equivalent fractions.

3 4

(b) =

1 4

1 9

7 12

1 2

2 3

8 16

12 18

Re ga le du ca tio n

(a)

(c)

(e)

2 5

5 7

(d)

(f)

Write an equivalent fraction. (a)

(c)

(e)

(g)

1 3

3 4 6 8

10 2 12

(b)

(d) (d

(f)

(h)

4 2

1 49

Check the fraction that is in its simplest form.

Re ga le du ca tio n

(a)

(b)

(c)

8. Circle the fractions ctions that tha are in their simplest form.

150

1 3

4 8

2 5

3 6

5 15

3 12

4 7

3 11

10 16

6 18

7 10

6 8

12 22

8 24

4 9

Solve It!

ed uc ati on

Ethan and Jordan bought pizza for lunch. Their pizzas were cut into 4 equal slices. They each ate 3 slices of pizza. izza left, but Ethan said that they have an equal amount of pizza Jordan disagrees. Look at their pizzas below and decide who iss correct. Explain your answer.

What about the sizee and shape of the slic slices?

Re ga

We both have 1 4 of a pizza left!

1 51

(b) Home At Write the equivalent fractions.

Re ga le du ca tio n

(a)

1 2

1 3

3 4

3 6

(b)

(c)

(d))

152

Use multiplication to find equivalent fractions. (a)

Re ga le du ca tio n

4 7

(b)

2 9

Use division to find equivalent ivalent frac fractions. (a)

÷2

12 20

÷4

12 2 20

÷2

12 0 20

÷4

÷3

(b))

18 42

÷6

18 42

÷3

18 42

÷6

153

4. Write an equivalent fraction. (b)

1 3

5 7

4 5

2 3

Re ga le du ca tio n

(a)

(c)

30 25

(d)

20 22

5. Find the first 2 equivalent fractions. (a)

(c)

2 7

1 12

(b)

(d)

5 6

4 11

6. Find the equivalent fraction form. raction tion in its simplest sim (a)

(c)

4 8

18 20

(b)

(d)

9 12

15 35

7. Tell whether are equivalent by writing = or ≠. ether the fractions fract

154

(a))

3 4

6 8

(b)

10 14

5 6

(c))

8 12 2

2 3

(d)

24 32

3 4

Mixed Numbers and Improper Fractions ct

Re ga le du ca tio n

Let’s Learn

How many pizzas are there?

1 whole

1 whole ole

1 half

d 1 half pizza. p pizz There are 2 whole pizzass and 2+ 1 =2 1 2

There are t and a half two pizzas.

There are 2 1 pizzas. zzas. zas. 2

2 1 is a mixed ed number. umber. 2

Adding a whole number and a fraction gives a mixed number.

155

Re ga le du ca tio n

How many y limes are there?

1 whole

1 quarter

There are 3 whole limes and 1 quarter of a lime. me. e 3+ 1 =3 1 4

There are 3 1 limes. 4

Write a mixed number that represents presents the colored c parts of the shapes. (a)

2+ 1 =2 1 3

(b)

2+ 3 =23 5

(c)

3+ 5 =35 8

156

Let’s look at mixed numbers on a number line.

Re ga le du ca tio n

(a) 1 3

2 3

The arrow is pointing at 1 2 . 3

(b)

1 2

The arrow is pointing at 2 1 . 2

(c)

1 4

2 4

3 4

22 23 4

The arrow is pointing nt ntin at 2 3 . 4

(d)

1 5

2 5

3 5

4 5

The e arrow arrrow is pointing at 1 3 . 5

157

Re ga le du ca tio n

Express the amount of cake in quarters.

1 whole

1 quarter

1 1 1 1 1 1 = + + + + 4 4 4 4 4 4 5 = 4 There are 5 of a cake. 4 5 is an improper fraction. 4

4 quarters

There are five quarters of cake.

When the numerator or is greater g ter than th or equal to the denominator, we get an minator, nator, w ion.. Improper fractions fra improper fraction. are ual to one. on greater than or equal Five quarterss is an improper improp fraction. f

5 4

e numerator merator is less le than the When the denominator, minator, ator, we get a proper fraction. Proper er fractions are a less le than one. One-half fraction. e-half is a proper pro

1 2

1 58

1 quarter

Write an improper fraction to represent the shapes. (a)

Re ga le du ca tio n

17 6

(b)

13 3

(c)

17 5

3 x 5 = 15

(d)

21 8

2 x 8 = 16

(e)

27 9

27 3x9=2

(f)

19 2

9 x 2 = 18

159

Let’s Practice

Re ga le du ca tio n

1. Match.

160

3 8

1 2

3 4

1 4

3 4

Write the mixed number represented by the colored parts of the shapes.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

(e)

(f)

1 61

3. Fill in the blanks. (a) 1 1 is represented by point

Re ga le du ca tio n

1 2

(b) 2 2 is represented by point

nt (c) 1 3 is represented by point

S 2

4. Draw a pointt to show the fraction fra on the number line. (a) 1 3 5

(b) 1 4 7

1 62

5 2

5 3

8 4

7 5

ed uc ati on

5. Match.

10 3

12 7

1 63

Write the improper fraction represented by the colored parts of the shapes.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

(e)

(f)

1 64

Check the improper fractions.

5 2

1 2

4 5

1 2

9 3

Re ga le du ca tio n

(a)

(b)

6 7

5 2

(c)

2 3

2 2

1 2

12 5

7 4

6 8

3 4

3 10

action. Check to name each fraction.

(a)

(b)

(c)

(d)

5 2

proper rop

improper

mixed number

1 2

proper

improper

mixed number

4 7

proper prop

improper

mixed number

7 8

proper

improper

mixed number

1 65

Solve It!

Re ga le du ca tio n

What is Sophie’s favorite fruit? Match the mixed numbers and improper fractions to find out. N

1 66

4 3

7 4

4 3

5 2

At Home Write the mixed number represented by the colored red parts of the shapes.

Re ga le du ca tio n

(a)

(b)

Write the improper fraction ction represented repres by the colored parts of the shapes. (a)

(b)

1 67

Match.

1 2

Re ga le du ca tio n

8 3

1 3

6 2

1 2

12 2 7

168

Write the mixed number shown on the number line.

Re ga le du ca tio n

(a) 0

(b)

(c)

(d)

Label each fraction io as proper, ion roper improper or mixed number. (a)

(b)

4 3

1 2

c) (c)

8 9

(d)

12 5

1 69

Comparing and Ordering Fractions ons

Re ga le du ca tio n

Let’s Learn

Ethan and Dominic each bought a pumpkin pie off the e same size. siz They compared how much pie they had left. I hav have 2 of 3

the pie left.

2 3

I have 3 of 4

3 4

the pie left.

Dominic has more pie left ft than han Ethan. Eth Etha

2 3

We say:

3 is greater th than 2 . 4 3

write We write:

3 > 2 4 3

We say:

2 is smaller than 3 . 4 3

We write:

2 < 3 3 4

170

3 4

How else can you compare these fractions?

Compare the fractions. Which is greater 1 or 3 ? 5

Re ga le du ca tio n

1 2

3 5

3 > 1 5 2

Compare the fractions. Which is smaller 3 or 3 ? 4

3 4

3 7

3 < 3 7 4

Arrange the fractions 7 , 1 and 1 in order from the smallest to 8 6 2 the greatest. 1 6

7 8

1 2

smallest est

greatest

Arrange ge the he fractions 3 , 5 and 6 in order from the greatest to 4 9 7 mallest. est. the smallest. 6 7

greatest st

3 4

5 9

smallest

1 71

Riley has 3 of an apple pie. Halle has 5 of an apple pie of 4

Re ga le du ca tio n

the same size.

Which child has the larger portion of apple pie? 3 4

5 8

Riley’s apple pie

Halle’s apple pie

Let’s find an equivalent fraction of 3 that has the same 4 denominator as 5 .

3 4

and d ar are 8 equivalent fract fractions.

6 8

3 4

5 8

6 8

Riley’s apple pie

Halle’s apple pie

When comparing omparing paring fractions fraction fractio with the same denominator, the greater the numerator, greater the fraction. merator, rator, the grea So, 6 is greater tthan 5 . 8 3 > 5. 4 8

Riley has the portion of apple pie. t larger la

172

Compare 5 and 5 . Which fraction is greater? 6

Re ga le du ca tio n

5 9 5 6

When comparing fractions with the same numerator, merator, the th smaller the denominator, the greater the fraction. n. So, 5 > 5 . 6

First, let’s find equivalent fractions with a common den denominator.

Compare 3 and 5 . 4

Which fraction is smaller? x3

3 4

9 12

5 6

10 12

3 4

9 12

5 6

10 12

9 is smaller th than 10 . 12 12 2 So, 3 < 5 . 4 6

1 73

Let’s Practice Compare the fractions.

Re ga le du ca tio n

(a)

1 4 1 5

(b)

3 5 3 7

(c)

1 6 1 8

(d)

5 9 4 7

174

Label the fractions on the number line and compare.

Re ga le du ca tio n

(a)

(b)

(c)

1 75

Write the fractions. Arrange the fractions from the smallest to the greatest. test.t.

Re ga le du ca tio n

(a)

smallest

greatest test

smallest est

greatest

(b)

176

Re ga le du ca tio n

(c)

smallest

grea greates greatest

smallest mallest

greatest

(d)

1 77

Make equivalent fractions, then compare. The first one has been done for you.

Re ga le du ca tio n

(a) Compare 1 and 3 . 2

1 2

2 4

3 4

1 2

3 4

(b) Compare 2 and 4 . 3

2 3

4 9

5 6

7 12

1 4

5 16

5 6

12 2

(d) Compare ompare 1 and 5 . 4

1 4

178

Make equivalent fractions, then compare. (a) Compare 1 and 1 . 3

Re ga le du ca tio n

1 2

1 3

2 3

5 9

(b) Compare 2 and 2 . 5

2 5

2 3

4 6

5 9

1 79

Hands On

uc ati on

Work in pairs. Take turns picking a domino from a bag. Your domino represents a proper y fraction. Compare your fractions by placing them in the boxes below.

Re ga

ur Draw and label the fractions in your notebook. Repeat the process until the bag of dominoes is empty.

180

At Home Write and compare the fractions.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

(e)

(f) (

1 81

Write the fractions. Arrange the fractions from the smallest to the greatest. test.t.

Re ga le du ca tio n

(a)

smallest

greatest test

(b)

smallest mallest

182

greatest

Arrange the fractions from the smallest to the greatest.

2 3

2 7

2 5

Re ga le du ca tio n

(a)

smallest

(b)

1 8

greatest

1 9

smallest

(c)

4 7

greatest eatest

1 3

smallest st

(d)

5 6

smalle smallest

1 3

3 4

greatest gre

1 6

5 7

greatest

1 83

Make equivalent fractions then compare. (a) Compare 2 and 5 .

2 3

5 8

ed uc ati on

5 8

5 7

1 6

(b) Compare 4 and 5 . 5

4 5

5 7

Re ga

4 5

184

3 4

1 6

Anchor Task

Adding and Subtracting Fractions

1 85

Let’s Learn

Re ga le du ca tio n

Jordan folds a piece of paper into 9 equal parts. He colors 1 of the paper blue. 9

Dominic colors 4 of the paper green. 9

Find the total fraction of paper they colored.

ollder older Jorda an Jordan

1 9

4 9

5 9

1 + 4 = 5 9 9 9

When adding ding like fractions, fractio we add the numerators and leave the denominator unchanged. ominator ator unchang unc

186

Find the sum of 5 and 3 . 12

Divide the numerator and the denominator or by 4 to simplify. ify.

Re ga le du ca tio n

Write the answer in its simplest form. 5 + 3 = 8 12 12 12 = 2 3

Halle and Riley shared an orange. Halle ate 1 of the orange.

1 4

1 2

2 Riley ate 1 of the orange. 4

How much of the orange did Halle all and Riley eat in all?

1 2

1 4

2 4

1 4

2 4

3 4

1 + 1 = 2 + 1 2 4 4 4 3 = 4

Halle and nd Riley ate 4 of the orange in all.

1 87

Find the sum of 1 and 3 . 10

Re ga le du ca tio n

1 5

3 10

2 10

3 10

2 10

1 5

Express the answer in its simplest form.

1 + 3 = 2 + 3 5 10 10 10 = 5 10 = 1 2

5 = 1 2 110 0

Find the sum of 2 and nd 2 . 3

6 9

2 3

6 9

2 9

2 + 2 = 6 + 2 3 9 9 9 = 8 9

188

5 10

1 2

Keira and Riley each have a similar shaped pancake for breakfast. 2

2 3

du ca ti

Keira eats 3 of her pancake. 4 Riley eats 9 of her pancake.

4 9

Ril Riley

Keira

How much more pancake did Keira eat than Riley? Riley? Find an equivalent 2 fraction of that has the 3 4 same denominator as . 9

2 3

and are 9 equivalent fractions.

Re ga l

2 3

6 9

6 – 9

4 = 9

2 9

2 – 4 = 6 – 4 9 9 9 3 = 2 9 Keira ate 2 more pancake than Riley. 9

1 89

Find the difference between 3 and 5 . 12

Re ga le du ca tio n

3 4

–

5 12

9 12

–

5 12 2

9 12

3 4

3 – 5 = 9 – 5 4 12 12 12 = 4 12 = 1 3

Express the answer in its simplest form.

4 = 1 12 3

Find the difference between ween n 4 and 3 . 5

8 10

4 5

8 10

3 10

4 – 3 = 8 – 3 5 10 10 10 = 5 10 = 1 2

190

4 12

1 3

Let’s Practice Add to find the fraction each shape is colored.

Re ga le du ca tio n

(a)

is green. +

is blue blue.

of the he shape is colored.

(b)

is pin pink. +

is orange.

of the shape is colored.

(c)

is yellow. +

is red.

of the shape is colored.

1 91

Use the models to help subtract the fractions. Give the answer in its simplest form.

Re ga le du ca tio n

(a)

(b)

3 – 1 = 5 5

(c)

4 – 3 = 6 6

(d)

5 – 4 = 8 8

(e)

(f)

3 – 2 = 7 7

192

6 – 1 = 10 10

3 – 2 = 4 4

Find the equivalent fraction and add. (a) 1 + 1 =

+ 1

Re ga le du ca tio n

(b) 3 + 1 = 4

+ 1

(d) 1 + 5 = 6

12 2

1 12

+ 5

12 1

(e) 4 + 2 = 5

10 0

+ 2

1 93

Find the equivalent fraction and add. Use the space to draw a model and show your working. rking. g. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 1 + 1 = 5

(b) 1 + 2 = 2

(d) 3 + 3 = 16

1 94

Find the equivalent fraction and subtract. (a) 4 – 1

– 1

Re ga le du ca tio n

(b)

9 – 1 = 9 – 12 12 4 12

(d) 1 – 3 = 2

14 4

–

(e) e) 5 – 5 =

–

3 14

5 12

1 95

Find the equivalent fraction and subtract. Use the space to draw a model and show your working. rking. g. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 5 – 3 = 6

(b) 1 – 3 = 2

(d) 1 – 7 = 4

196

28 8

Solve It!

Re ga le du ca tio

Jordan spent the weekend at his grandmother's house. In which city does she live? Add or subtract the fractions and match the letters to find out. C

3 5

7 12

3 5

1 2

1 7

1 97

At Home Color and add. Write the answer in its simplest form.

Re ga le du ca tio n

(a)

4 is green and 1 is blue bl blue.. 6 6

of the e shape hape is colored colo in total.

(b)

2 is yellow w and 3 is red. 8 8

of th the shape is colored in total.

(c)

3 is sg green and 11 is blue. 21 21

of the shape is colored in total.

(d)

1 is orange, 5 is blue and 4 is pink. 12 12 12

of the shape is colored in total.

1 98

Match. 4 – 1 9 9

Re ga le du ca tio n

7 – 2 8 8

9 – 6 12 12

3 – 2 5 5

11 – 7 14 14

6 – 1 10 10

1 3

1 5

1 2

2 7

1 4

5 8

1 99

Find the equivalent fraction and add. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 3 + 1 = 4

+ 1

(b)

2 + 3 = + 3 14 4 7 14 14

(d) 1 + 1 = 1 +

10 0

Find the equivalent fraction ion and subtract. subtra Write the answer in its simplest plest form. form (a) 5 – 3 = 5 – 6

–

(b)

20 0

3 – 1 = – 4 5 20 20

(d) 3 – 1 = 4

–

Find the equivalent fraction and add. Use the space to draw a model and show your working. rking. g. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 1 + 1 = 3

(b) 1 + 3 = 2

(d) 3 + 3 = 20 2

10 0

2 01

Find the equivalent fraction and subtract. Use the space to draw a model and show your working. rking. g. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 1 – 1 = 3

(b) 4 – 2 = 5

(d) 2 – 12 = 3

20 2

18 8

Anchor Task

Chocolate Lava Cake Recipe

Multiplying Fractions

Ingredients 1 cup unsalted uns unsa butter 2

1 teaspoon salt 3

nces of choco ch chocolate 5 3 ounces

2 large eggs

1 cup flour 4

2 large egg yolks

suga 1 1 cup sugar 3

2 03

Let’s Learn

Re ga le du ca tio n

A pizza is cut into 8 equal slices. Sophie and her 4 friends each eat a slice. What fraction of the pizza did they eat in all? 1 8

1 8

5 8

1 1 1 1 1 5 + + + + = 8 8 8 8 8 8 5 1 = 5 x 8 8 5 They ate 8 of the pizza in all.

1 5

4 5

1 5

4x 5 = 5

20 4

1 8

5 8

is the same as 5 x the unit fraction 1 . 8

Multiply 5 by 4.

1 5

1 8

Riley is making lemonade for a school fundraiser. 1 cup of fresh lemon juice per jug. ug. 3

ati on

The recipe requires a

She plans on making 5 jugs of lemonade.

Re ga le du

How much lemon juice will she need in total?

1 3

1 3 1 3 1 3

1 3

Multiply the th numerator by the whole number. umber. Then simplify. mplify.

1 3 1 3 5 2 =1 3 3

5x1

5x 3 = 3 5 2 = 3 =13

When en multiplying a ffraction by a whole number, we multiply the numerator whole number. We simplify if the product is umerator by the w to 1. greater than or o equal e 2

Riley needss 1 3 cups of lemon juice in total. 2 05

The running track at Ethan's school is

1 mile around. 4

Re ga le du ca tio n

Ethan runs 6 laps of the track. Find the total distance he ran.

Let's skip count on a number line to find the answer. we wer.

6 = 12 4 4

1 2 3 4 5 6 , , , , , 4 4 4 4 4 4

1 2

2 3 4 5 , , , 4 4 4 4

and 6

are multiples multipl of 1 . 4

Ethan ran a total distance ce of 1 Find 4 x

1 miles. 2

2 . 7

Use the number line to find the t first 4 multiples of 7 .

1 7

2 7

2 4 6 8 , , , 7 7 7 7 8 1 = 1 7 7 2 1 4x 7 =17

206

3 7

4 7

5 7

6 7

12 13 14 15 16 7

We can find the product using this method too!

2 4x2 = 7 7 8 = 7 1 =17

Let’s Practice Color the unit fractions to multiply. Write the answer in its simplest form.

Re ga le du ca tio n

(a) 3 x 1 = 4

(b) 5 x 1 = 9

(d) 5 x 1 = 2

(e) 9 x 1 = 5

(f) ( 10 x 1 = 4

2 07

Use the number line to find the product.

Re ga le du ca tio n

(a) 6 x 1 = 7

1 7

2 7

3 7

4 7

5 7

6 7

(b) 5 x 1 = 9

1 9

2 9

3 9

4 9

5 9

6 9

7 9

8 9

1 4

2 4

3 4

(d) 4 x 2 = 5

1 5

2 5

3 5

(e) (e 6 x 2 =

208

1 3

4 5

2 3

Multiply the fractions. Write the answer in its simplest form. Use the space provided to show your working.

Re ga le du ca tio n

(a) 3 x 4 =

(b) 3 x 3 =

(d) 8 x 1 =

(e) 5 x 5 =

(f) 3 x 7 =

2 09

At Home

Re ga le du ca tio n

1. Match.

5x 1

3x 1

18 x 1

15 6

7x 1

13 4

11 x 1

210

Use the number line to find the product.

Re ga le du ca tio n

(a) 7 x 1 = 2

1 2

(b) 6 x 2 = 5

1 5

2 5

3 5

4 5

12 13 14 5

2 2 1 22 23 24 5

1 4

2 4

3 4

13 4

23 4

Multiply the fractions. actions. ons. Write the answer simplest form. nswer wer in its sim simp Use the space pace provided to sshow your working.

(a) 6 x 5 = 8

(b) 10 x 4 = 5

211

Word Problems

Re ga le du ca tio n

Let’s Learn 1

Sophie spent 3 of her pocket money on a present nt for or her fathe father and 1 of her pocket money on some new pencils. 6

What fraction of her pocket money did she e spend end in total? tota

Express the answer in its simplest form.

1 2 = 3 6

1 6

1 1 2 1 + = + 3 6 6 6 3 = 6 1 = 2 1

3 6

can be

1 simplified to . 2

Sophie ie spe spent 2 of her pocket money.

212

Blake picked 48 strawberries at the farm. He ate 1 of the strawberries he picked.

Re ga le du ca tio n

How many strawberries did he eat? 48

If 6 units is 48 strawberrie strawberries, then 1 unit is 48 ÷ 6 = 8

48 x 1 = 48 x 1 6

= 48 = 8 6

strawberries! t

Blake ate 8 strawberries.

Mr. Hopkins has an empty corn and wheat. pty field for planting pla eld and wheat in 3 of the field. He plants corn in 1 off the field 2

What fraction of his field does he use in all? do d 3 8

1 2

1 = 4 8 2

dd dd. Add.

3 + 4 = 7 8 8 8

ns u Mr. Hopkins used 7 of his field in all. 8

213

Dominic bought a 3 kg pack of flour. 4

He used 1 of the pack to bake some cookies.

ca tio n

Re ga le d

How many kilograms of flour does he have left?

3 kg 4

kg of flour

pack of flour

1 3

1– 1 = 2 3

Each unit in the model is 1 kg. 4

2x 1 = 2x1 4

= 2 = 1 4

Dominic h has as 1 kg flour left. 2

21 4

The units in the model represent 1 4

kg and of 3 a pack.

Let’s Practice Halle eats 1 of a health bar.

Re ga le du ca tio n

Her sister eats 3 of the health bar. 8

tal? ttotal? What fraction of the health bar did they eatt in tot

They ate

of the health ealth bar in tot to total.

A baker bakes 28 pies. es.

She sells 2 of the he pies pie before p f fore lunch time. e. 7

How many pies remain?

7 units units = un 1 unit nit =

units = 5 x 5 units

pies

pies pie

pies

pies remain. 215

Jordan and Dominic shared a pizza. Together they ate 7 of the pizza. 8

If Jordan ate 3 of the pizza, find the 8

Re ga le du ca ti

fraction of the pizza that Dominic ate. e.

–

Dominic ate

of the pizza. pizza

iece ece of o ribbon on 4 m in length. Sophie has a piece

5 1 She uses of the ribbon to tie a bow on a gift. 2

How much ch ribbon ibbon does she sh have left?

ie h Sophie has

21 6

m of ribbon left.

Wyatt takes $42 to the mall. He spends 1 of his money on a movie ticket. 3

Re ga le du ca tio

How much money does he have left?

Wyatt has $

left.

th of rope. Halle has a 5 m length

pe to make mak a swing. She uses 2 of the rope 3

How much rope pe does she s have left?

Write your answer wer as a mixed m mixe number.

le h has Halle

m of rope left.

217

At Home Michelle read 4 of a book on Saturday and the rest res est on Sunday. Sunda S d day.

Re ga le du ca tio n

nday? y? What fraction of the book did she read on Sunday?

–

Michelle read

of the e book ook on Sunday. Sun

Ethan had 2 cakes.

He ate 2 of a cake. 5

How much cake he have left? ke does h

Write your answer mixed number. wer as a m mixe

1 cake ake

1 cake

Ethan an has

21 8

cakes left.

Mrs. Taylor uses 1 of a tank of gas to drive to the beach. ac 4

m. She then uses 2 of a tank to drive to her family's farm.

Re ga le du ca to n

What fraction of the tank did she use in all?

Mrs. Taylor used

off the tank of o gas in all.

3 of her money on a new tennis 200 0 and spent s Keira saved $200 4

racket. Find the e cost of the th racket. r

The racket ck cost $

. 219

Looking Back (a)

(c)

(e)

1 7 1 8 3 7

ed uc ati on

1. Find the first 2 equivalent fractions. (b)

(d)

(f)

3 4

2 5

2 9

2. Write the equivalent fraction on n in its simplest simple form. (a)

(c)

5 20

(b)

(d)

Re ga

(e)

2 4

18 36

(f)

9 15

112 16

15 45

3. Write ite = or o ≠≠..

22 0

(a) a)

1 3

6 9

(b)

12 14

2 7

(c)

3 4

9 8

(d)

11 33

1 3

Write the improper fraction represented by the colored parts of the shapes.

Re ga le du ca tio n

(a)

(b)

Write the mixed number represented parts of sented d by the colored c the shapes in its simplest form. m. (a)

(b)

6. Draw a point fraction on the number line. nt to show the fra (a) 2 1

((b) 9

2 221

Arrange the fractions from the smallest to the greatest.

1 3

1 7

1 2

Re ga le du ca tio n

(a)

smallest

2 3

(b)

6 10

smallest

3 4

greatest reatest atest

Find the equivalent fraction action on and add. ad fo Write the answer in its simplest form. w a model mode and show your working. Use the space to draw

(a) 3 + 3 = 5

(b) (b 6 + 1 = 16

222

greatest

Find the equivalent fraction and subtract. Write the answer in its simplest form. Use the space provided to draw a model and show ow your working. work

Re ga le du ca tio n

(a) 4 – 1 = 5

(b) 3 – 2 = 7

10. Multiply the fractions. s. Write the answerr in its simplest form. Use the space provided your working. provid to show provide sh (a) 3 x 5 = 8

(b) 7 x 3 = 5

223

11.

Sophie went to the cinema. She spent 1

Re ga le du ca tio n

of her money on the admission ticket and 1 of her money on some snacks. What 5

fraction of her money did she have left?

Sophie had

of her money ney left.

n the cinema. cine 12. There are 60 people in 1 of the people ple e are children. ch en 4

How many adults ults are in the t cinema?

adults are in the cinema. ad

224

13. Dominic has 4 m length of string. 5

Jordan gives him 3 m of string. 4

Re ga le du ca tio

What is the total length of string Dominic now? minic has now ow? Express your answer as a mixed number in its simplest form. for fo

Dominic has

mo off string.

14. Halle drank 2 of a cup up of fruit juice ju uice uice 5

fr f and Riley drank 1 of a cup of fruit 3

juice of the same me size. size

How much more re juice did Halle H

drink than n Riley? iley?

Halle drank e dran

cup more juice than Riley.

225

Decimals

Tenths Anchor Task

2 26 22

Let’s Learn

Re ga le du ca tio n

Halle counts the color of jelly beans in a packet. 3

She finds that 10 of the jelly beans are red. 3

We can write the fraction 10 as the decimal 0.3.

ght of the A decimal is a number that has digits to the right

decimal point.

3 = 0.3 0 10

Ones

Tenths

The digit to the right of the decimal p point tells us the number of tenths.

Zero point three.

decimal mal point oin

We say: We write::

zero ro point three th 0.3 3

ber line shows show tenths between 0 and 1 as The number fractions ctions and decimals. decima dec 0 0 10

1 10

2 10

3 10

4 10

5 10

6 10

7 10

8 10

9 10

10 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

227

This 1 whole is divided into ten equal parts.

Re ga le du ca tio n

1 whole

1 part of the whole is colored orange.

1 part = 1 tenth

1 whole

= 1 10 1 = 0.1

0.1

We say ‘zero point one’.

0.1

Ones 0

0.5

. Tenths .

4 parts of the whole are ar coloured. loured. oured.

4 parts = 4 tenths

le 1 whole

= 4 10 = 0.4

0.4

We say ‘zero point four’.

0.4

Ones On 0

22 8

. Tenths .

0.5

There are 10 tenths in 1 whole. 0.1

0.1

0 0.1

Re ga le du ca tio n

0.1

Write and say the decimal represented by the place valu value disks. 0.1

0.1

Ones 0

0.1

Ones One 0

Ones

0.1

0.1 0.1

0.1

0.11 0

. Tenths .

. Tenths

0.1

. Tenths enth

0.5 zero point five

0.8 zero point eight

1.3 one point three

Tens

Ones

. Tenths

0.1

12.6 twelve point six

0.1

229

Let's find the value of each digit in the number. 4.2

Re ga le du ca tio n

(a)

0.2

The value of the digit 4 is 4. The value of the digit 2 is 0.2. 4 + 0.2 = 4.2

(b)

7.3

0.3 7

The value of the digit git 1 is 10. The value of the digit git 7 is 7. e digit 3 is 0.3. The value of the 10 + 7 + 0.3 = 17.3 .3 3

(c)

2.8

0.8 2

4 0

The value value of o the th digit 4 is 40. he value value of the digit 2 is 2. The Th value value of o the digit 8 is 0.8. The 40 0 + 2 + 0.8 0 = 42.8

23 0

ed uc ati on

What is the width of the button?

width of button = 9 tenths of a centimeter = 9 cm 10 = 0.9 cm

Ones ne 0

. Tenths .

The width of the button is 0.9 cm. m.

Re ga

What is the length of the crayon? n?

length off crayon = 7 cm + 5 tenths cm = 7 5 cm 10 = 7.5 cm

Ones 7

. Tenths .

The length ength of the t crayon is 7.5 cm.

2 31

Re ga le du ca tio n

What is the mass of the pineapple?

mass of pineapple ple = 1 kg + 3 tenths ten kg

0 4 kg

3k kg

= 1 3 kg 10 = 1.3 kg

1 kg kg

1 kg

2 kg

Ones 1

. Tenths nth .

The mass of the pineapple iss 1.3 kg.

What is the volume of water ater in the container? con

volume = 1 liter + 2 tenths liters =12 l 10

= 1.2 l

Ones 1

. Tenths .

The volu volume of w water in the container is 1.2 l.

23 2

Let’s Practice

Re ga le du ca tio n

1. Match.

.5 0.5

0.1

0.8

0.6

0.9

0.3

2 33

Draw an arrow to show the decimal on the number line.

Re ga le du ca tio n

(a) 0.2

0.5

(b) 0.7 0

(d) 1.6 0

0 0.5

1.5

(e) 14.3

14.5 14

15.5

(f) 11.8 8

23 4

Write the decimal represented by the place value disks. (a) 1

0.1

0. 0.1

0.1

0.1 0 0.

0.11

0.1

0.1 0

0.1

Re ga le du ca tio n

(b)

(c)

(d)

0.1 0

(e)

(f)

g) (g)

(h) h)

2 35

Write the value of the digit. (b)

(a)

12.7

Re ga le du ca tio n

3.6

(c)

(d)

215.6

0.5

Read and write the numbers value chart. mbers rs in the place p (a) The four is in the e ones nes place. plac The seven is in the e tenths place. pl p The two is in n the th tens place. plac Tens

Ones nes

. Tenths T

(b) The sixx is in the tenths place. ten t The he one is in the tens place. The he zero zero iis in tthe ones place. Tens

23 6

Ones

. Tenths

Find the length of the lines. cm

Re ga le du ca tio n

(a)

0 cm

(b)

0 cm

(c)

0 cm

(d)

0 cm

(e)

cm c

0 cm

2 37

Find the mass of the boxes. kg

Re ga le du ca tio n

(a)

0 4 kg

3 kg

1 kg

0 4 kg

3 kg

2 kg

1 kg

2 kg

(b)

0 4 kg

3 kg

1 kg

0 4 kg

3 kg

2 kg

1 kg

2 kg

(c)

0 4 kg

3 kg

1 kg

0 4k kg

3 kg

1k kg

2 kg

238

2 kg

Find the volume of liquid in the beakers. l

(a)

uc ati on

(b) 2l

Re ga l

(c)

1l 2 39

Write as words.

Re ga le du ca tio n

(a) 0.2 (b) 1.1

(e) 4.0

(f) 10.1 (g) 8.5

(h) 23.4

10. Write as decimals. (a) four tenths

(b) one and nd two wo tenths

(e) 2 1

(f) 5 6

(g) 1 3

(h) 3 7

110

24 0

Hands On

Re ga le du ca tio n

In small groups, visit each of the measuring stations your our teacher mes to the th has prepared. Record the lengths, masses and volumes nearest tenth in the table below.

Mass Station

Object

Mass Mas (kg)

A B

Length h Station Sta

Object

Length (cm)

A B

Volume Station V

Liqu Liquid

Volume (liters)

A B

2 41

At Home

Re ga le du ca tio n

1. Match.

0.1

1.7

0.1

16.1

0.1

0. 0.1

0.1

.1 0.1

0.1

0.1 0

0.1

24 2

10.7

2.6

1.4

6.2

Fill in the blanks.

28.1

Re ga le du ca tio n

(a)

(b)

(c)

The 2 is in the

place. It has a value lue of

The 8 is in the

place. It has a value of

The 1 is in the

place. It has as a value of

34.9

The 3 is in the

place. ce. It has a value of

The 4 is in the

place. It ha has a value of

The 9 is in the

place. ce. It has a value of

The 5 is in the e

place. It has a value of

The 6 iss in the th

place. It has a value of

e 9 is in the The

place. It has a value of

The he 3 is in the

place. It has a value of

the The 7 is iin th

place. It has a value of

5,693.7

2 43

Write the decimal that represents the colored part of the shapes.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

(e)

(f) (

244

Fill in the blanks on the number line.

Re ga le du ca tio n

(a) 0

0.5

(b)

0.5

1.5 15

(c)

4.5

5.5

Find the length of the e lines. es. cm

(a)

0 cm

(b)

c cm

0 cm

2 45

Draw arrows on the scales to show the mass of the boxes. (b)

Re ga le du ca tio n

(a)

2.4 kg

3.2 kg

0 4 kg

3 kg

1 kg

3 kg

2 kg

evel el of liquid in the beakers. Draw a line to show the level (a) 0.4 l

246

1 kg

(b) (b 1.6 l

Write as words.

Re ga le du ca tio n

(a) 0.1 (b) 2.6 (c) 1.8

(d) 5.9 (e) 8.8

(f) 100.2 (g) 40.4

(h) 20.0

Write as decimals.

(a) one and seven tenths even en te ten

(b) three and two tenths tenth

(e) 2 2

(f) 7 1

(g) 1 5

(h) 13 6

110

2 47

Anchor Task

248

Hundredths

Let’s Learn

ed uc ati on

A square is divided into 10 equal parts. 6 of the parts are colored blue. 0.6 of the square is blue.

6 parts = 6 tenths en = 6 10 1 = 0.6

6 of the square squ 0.6 is blue.

00 equal equa parts. The same square is then divided into 100 w. 4 of the parts are colored yellow. 4 partss in 4 100 iss .

4 parts = 4 hundredths 4 100 = 0.04

100

0.04 of the square is yellow.

eg a

Let's find the total otal al amount the t ssq square has been colored. 6 + 4 = 60 0 + 4 10 100 100 00 100 10

= 644 = 0.64 100

6 10

= 100 They are equivalent fractions!

0.6 + 0.04 = 0.64 We say: We write: write

zero ze ero point p six four 0.64

0.64 of the square is colored in total. 2 49

47 parts of the whole are colored orange.

Re ga le du ca tio n

1 whole 47 parts = 47 hundredths =

47 100

= 0.47

We say 0.47 as ‘zero ero point four fo seven’.

0.40

0.45 5

0.47 47

Ones

Tenths

Hundredths dths

0.50

re colored olored orange. ora o 82 parts of the whole are 1 whole

82 parts = 82 hundredths =

82 100

= 0.82

We say 0.82 as ‘zero point eight two’.

0.80 80

2 50

0.82 0.8

0.85

0.90

Ones O

Tenths

Hundredths

There are 10 hundredths in 1 tenth. 0.01 0.1

0.1 0.01

0.01

0.01 .01

0.1 1

ed uc ati on

0.01

Write and say the decimal represented by the place valu value disks. 1

0.1

0.01

Ones

Tenths

Hundredths

1.11 one point one o one

1 0.1

1 0.011

Ones

Tenths

Hundredths

0.011 0.0

4.26 four point two six 0.01

0.01

0.011 0.0

0 01 0.0 0.01

0.1

0 0.1

0.01 0

0.011 0.0

0.01 0.0

0.01

0.01 0 01

0.01

Ones

Tenths

Hundredths

0.39 zero point three nine

2 51

Let's find the value of each digit in the number. 2 . 5

Re ga le du ca tio n

(a)

0. 0

0. 5 2

The value of the digit 2 is 2. The value of the digit 5 is 0.5. The value of the digit 3 is 0.03. 2 + 0.5 + 0.03 = 2.53

(b)

5 9. 2

0. 0

0. 2 9

The value of the digit 5 is 50. i 5 The value ue of the digit 9 is 9. The value digit 2 is alue e of the digi i 0.2. The value digit 8 is 0.08. e of the di 50 + 9 + 0.2 + 0.08 = 5 59.28

252

Write the amounts of money as decimals.

Re ga le du ca tio n

When writing dollar amounts, we s, w always include de the hundredths. dths.

$1 = 100¢

10 100 = $0.1

0.1 = 0.10

= $0.10

10¢ = $0.10 0.10 0

10¢ = $

$1 = 100¢

7 100 .07 = $0.07

¢=$ 7¢

45 100 = $0.45

45¢ = $

sa m

$1 = 100¢

100¢ + 16¢ = 116¢

116 100 = $1.16 =$

253

Let’s Practice Match.

Re ga le du ca tio n

0.81

0.96

0.77

0.22

0.60

0.06

254

Draw an arrow to show the decimal on the number line.

(b) 0.08 0

(d) 1.67 1.5

ed uc ati on

(a) 0.03 0.05

0.1 0.11

0.05

0.10

2.35

2.4

2.45

2.5

1.55 5

1.6

1.65

1.7

(e) 3.19 3

3.05

3.1

3.15

3.2

3.25

3.3

5.45

5.5

5.55

5.6

5.65

5.7

(f) 5.42 42

5.4

255

Write the decimal represented by the place value disks. (a) 1

0.1

0.1 0.01 0.01

Re ga le du ca tio n

(b)

0.1

0.11

0.01 0.01 0.01 0.01 0.01

(c)

0.1 .1 0.0 0.011 0.0 0 0.011 0 0.01 0.01

(d)

0.1 0.01

0.1

(e)

0.1 01

0.1

0.1 0

0.1 0.01 0.01 0.01

0.01 01 0.0 0.011 0.01 0.01 0.0 0.011 0.01 0

(f)

10 0

25 6

10 0.01 0.01 0.01 0.01 0.01 0.01

Write the value of each digit. Then add the values. 1 . 6

Re ga le du ca tio n

(a)

(b)

4 9. 5

1 . 7

(c)

257

Check to show the amount of money.

Re ga le du ca tio n

(a) $0.45

(b) $0.26

(d) $0.37

(e) e)) $0.20 0.20

2 58

Add the fractions. Then write as a decimal. (a)

5 6 + = 100 100 100

(b)

5 19 + = 100 100 100

eg al ed uc ati on

= 0.

= 0..

(e)

= 0. 0

61 53 + = 100 100 100

(f))

(g)

6 3 + = + 10 100 100 0 100

(h) (h

8 55 + = + 10 100 100 100

100 00

100

7 38 + = + 10 100 100 100

78 67 + = 100 100 1 10 100

= 0.

(i)

(d) 100 + 100 = 0 100

(j)

50 9 + = + 100 10 100 100

100

259

Write as words.

Re ga le du ca tio n

(a) 0.02 (b) 0.53 (c) 1.37

(d) 10.01 (e) 8.49

(f) 20.08

Add.

(a) 5 + 0.3 + 0.05 =

(b) 0.2 + 0.02 =

(d) ( 80 + 0.1 =

Write as decimals. cimals. als.

(a) three e hundredths undredths

nty-five hundredths hund hundr (b) twenty-five

260

(d)

82 100

(e)

11 100

(f)

202 20 100 00

(g) 100

345

Solve It!

Re ga le du ca tio n

Color the circles to show each number. Color a circle green to show 0.01. Color a circle red to show 0.1. Color a circle blue to show 1. Color a circle yellow to show 10. The first one has been done for you.

(a)

21.4

(b)

seventeen point four six sevent seventee

2 61

(c)

(d)

du ca tio n

fifty-eight point three one

Re g

forty rtyy point zer zero six

2 62

At Home Match.

Re ga le du ca tio n

0.1

0.1 0.01 0.01 0.01 0.01

0.01 0.01 0.01 0.01 0.01

11.41

0.01 0.01 0.01

0.1

11.0 11.04

0.1

0.1 .11

01 0.1

1.04

0.01

0.01 0.01 .0 01 0.0 0.01 0.01 0 01

10 0

0.1

0.01 0.0 01 0.0 0.01 0.01 0.01 0

0.1

0.1 0.01

0.24

10.41

1.08

2 63

Write the value of each digit. Then add the values. 3. 2

Re ga le du ca tio n

(a)

(b)

8 . 9

4 2 . 7

264

(c)

Write the decimal that shows the colored part of the shapes.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

(e)

(f) (

2 65

Fill in the blanks on the number line.

Re ga le du ca tio n

(a) 0

0.05

0.1

0.2

(b)

(c)

4.1

4.05

4.15

4.20

(d)

2.4

2.45

2.5

2.55 2

2.6

2.65

2.7

(e)

8.11

8.2

8.3

8.4

7.8

7.9

8.1

(f)

26 6

sa m

pl e

sa m

Re ga le du ca tio n

5. Match.

$0.76

$1.13

$5.05

$1.25

sa m

pl e

$0.38

$1.01

2 67

Add the fractions and write the sum as a decimal. 5 6 + = 100 100

Re ga le du ca tio n

(a)

(b) 100 + 100 = 4

(d) 100 + 10 =

Write as words. (a) 2.04 (b) 1.56

(d) 10.70

Write as decimals. cimals. mals.

(a) six hundredths undredths redths

(b) fourteen hundredths ourteen en hundredt hundre 177

(e) 100

268

(d) 100

(f)

528 100

Comparing Decimals

tio

Anchor Task

2 69

Let’s Learn

Re ga le du ca tio n

Compare 1.4 and 1.63. Which number is smaller?

Let's write the numbers in a place value chart. Ones

Tenths

Hundredths

Start art by paring the comparing gits in the digits highest ghest place. plac

Compare the values from left to right. ght. The values in the ones place are the same. ame. Ones

Tenths

Hundredths edths

If the digits in the same place are the same, move on.

Move on to compare are e the digits d in the tenths place. Ones

Tenths nths

Hu Hundredths

4 tenths hs iss smaller than 6 tenths. So, 1.4 is smaller than th 1.63. We write: write 1.4 4 < 1.63 1.6

27 0

Compare 4.17 and 4.13.

Re ga le du ca tio n

Let's write the numbers in a place value chart. Ones

Tenths

Hundredths

hs place are the t same. The values in the ones place and the tenths undredths edths place. plac Move on to compare the digits in the hundredths Ones

Tenths

Hundredths

an 3 hundredths. hundredt 7 hundredths is greater than 4.17 > 4.13

4.13 < 4.17

We can com compare he decima the decimals on a number line too!

4.13

4.1

4.17

4.2

2 71

Let's compare decimals on a number line.

Re ga le du ca tio n

(a) Compare 0.01 and 0.09. 0.01

0.09 09

0.05

0.1 0.1

0.09 > 0.01

0.01 < 0.09

0.09 is greater than 0.01

0.01 than 0.09 .01 is smaller sma

(b) Compare 1.3 and 1.27.

1.27

1.2

1.3

1.4

1.3 > 1.27 7

1.27 < 1.3

1.3 is greaterr than 1.27

1.27 is smaller than 1.3

6.6

6.7

6.81 > 6.69

6.81 is greater than 6.69

27 2

6.81

6.8

6.9

6.69 < 6.81

6.69 is smaller than 6.81

Let’s Practice Write the decimal represented by the place value disks. ks. Check the greater number.

Re ga le du ca tio n

(a)

0.1

0.1 .1

0.11

0.1

0.1 .1

0.1

0.1 0

0.1

0.1 0.01

0.1 0 0. 0.01 0

(b)

(c)

0.1 .1 0.0 0.011 0.01 0 0 1 0.0 0.0 0.011 0

((d)

0.0 0 011 0.0 0.011 0.011 0.011 0.01 0 0.01

0.011 0.011 0.011 0.01

0.1 0.011 0.011 0.011 0.01

2 73

Write the numbers in the place value chart and compare. p

Re ga le du ca tio n

(a) Compare 1.5 and 2.04 Ones

Tenths

Hundredths

. .

(b) Compare 6.49 and 6.94 Ones

Tenths

Hundredths redth

. .

On Ones

. . .

27 4

Tenths

Hundredths

Write the numbers on the number line and compare.

Re ga le du ca tio n

(a) Compare 0.04 and 0.06.

0.05

is greater than

0.1

(b) Compare 4.25 and 4.5.

4.2

4.3

is smaller llerr than

4.4

4.5

1.2

1.3

1.0 0

1.1

is smaller than

2 75

Circle the numbers that are greater than 2.6.

2.67

2.58

3.02

2.5

1.69

7.05

2.22

Re ga le du ca tio n

Write the fractions as decimals and compare. ompare. pare. 32

43 = 100

5 = 10

4 = 100

(a) 100 = (b)

Use the words is greaterr than, smaller than and than han,, is sma is equal to to fill in the blanks. ks (a) 0.5

(b) 13.03

13.05.

10.61.

(d) 7.69

7.69.

(e) 0.04

0.06.

(f) f) 105.38 5.38

2 76

1.2 1.2.

10.83.

(g) 30.11

30.11.

(h) 22 226.1 2 26.1

226.01.

Hands On

Re ga le du ca tio n

Play Decimal Compare! in pairs. Roll a 10-sided dice 3 times es to ox and d have ha create a 3-digit decimal. Write the number in the box git decimal. ecimal. your partner repeat the steps to create their 3-digit gam ga Compare your numbers. The greater number wins! Play 5 games to determine the overall winner.

&GEKOCN %QORCTG ORCT ORCTG

Game 1

Game 2

Game 3

Game 4

Game ame 5

Player 1

Player Play 2

Player 1

Player 2

Playerr 1

Player 2

Player ayer 1

Player 2

Player Play 1

Player 2

2 77

At Home Add the place values and compare.

Re ga le du ca tio n

(a) 1 + 0.2 + 0.03 =

10 + 0.4 + 0.01 = >

(b) 30 + 5 + 0.6 + 0.07 =

30 + 5 + 0.8 + 0.06 = >

(d) 300 + 80 0.01 0 + 2 + 0.7 + 0.0 0. 1 =

300 0.04 = 0 + 80 + 2 + 0.7 + 0 >

2 78

Write the numbers in the place value chart and compare. p

Ones

. . .

ed uc ati on

(a) Compare 0.04 and 1.01 Tenths

Hundredths

is greater than

(b) Compare 12.5 and 12.48 Tens

Ones

Tenths

Hundredths

. .

Re ga

iss smalle smaller sma than an

pare 70.07 and 70 (c) Compare 70.03 Tens ns

Ones

is greater than

Tenths

Hundredths

. .

2 79

Draw an arrow to show the position of the numbers on the number line. Fill in the blanks.

ga le du ca tio n

(a) Compare 3.14 and 3.21.

3.1

3.2 .2 2

3.3

2.2

2.3

9.7

9.8

7.5

7.6

(b) Compare 2.24 and 2.16.

2.11

a 9.62. 62. (c) Compare 9.77 and

9.6

9.5

d) Compare ompare 7.41 and 7.43. (d)

7.3

7.4 >

280

Circle the numbers that are smaller than 0.8.

0.21

1.73

0.59

0.1

0.92

0.78

0.09

Re ga le du ca tio n

Write the fractions as decimals and compare. mpare. (a)

87 = 100

179 = 100

(b)

1 = 10

25 = 100

130

40 = 100 00

195 5 = 100 00

(d) 10 =

Use the symbols bols >, < and = to fill in the blanks. (a) 1.1

2.02 02

(b) 14.5

74 (c) 7.74

6.74

(d) 10.88

1.98

(e)) 3.15 15

3 3.15 .15 15

(f) 12.01

1.28

(g) 5.31 (g 5

(h) 6.48

2 81

Looking Back Write the value of the digit.

Re ga le du ca tio n

(a)

3.64

(b)

12.78

(c)

95.16

(d)

6.05

Write the value of each digit. it. Then add ad a the values. (a)

1 . 4

(b)

5. 9

+ 282

Find the length of the lines. cm

Re ga le du ca tio n

(a)

0 cm

(b)

0 cm

Check to show the amount unt of money. (a) $0.40

(b) $0.36 6

2 83

Write as words.

Re ga le du ca tio n

(a) 0.71 (b) 2.06 (c) 35.9

Write as decimals.

(a) one and four tenths

(b) seventy and fifty-one hundredths dredths dths

43 3

(d) 100

(e) 25

7 100

(f) 2

Write the fractions n as decimals ns ecimal and compare. (a)

3 = 100 3

(b) 10 =

10 103 = 100

280 28 = 100

Use e the he symbols >, < and = to fill in the blanks.

(a) 0.3

(b) 1.5

4.15

(d) 0.18

0.45

(f) 16.01

16.09

(e) 55 55.55 5 5.55

284

16 100

55.55

1.06

Let's Do Mathematics 4 – Worktext A

Articles inside

The digit in the ones place is 5. It represents