Let's Do Mathematics 3 – Worktext B by Regal_Education

n ca t Wo r k t e xt x

for le arne arners 8 - 9 y year ears old

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

Numbers to 10,000

Anchor Task

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

Let’s Learn n

Let’s Learn

When we take a whole and divide it into equal parts, we get fractions. The whole orange is cut into 2 equal pieces. Each piece is a half which we write as 1 .

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 new nts and nd observations when w concepts pts are e introduced. introduce

Let’s cut an apple

into 4 equal pieces . Each piece is a quarte r.

2 halves make 1 whole.

1 4

1 whole

1 2

1 whole

half

The numbers of a

1 2

half

fraction have specia l names.

1 2

quarter

1 4

quarter

1 2

1 4

quarter

1 4

quarter

4 quarters make 1 whole.

1 4

The top number is called the numerator.

The bottom numb er is called the denom inator. A half has a n numerator of 1.

...and a denominator of 2!

Ethan eats 3 pieces of the apple. We say he eats 3 quarte apple. We can write rs of the this as a fraction 3 . 4

1 4

I ate 3 quarters of the apple!

1 4

212

213

Let’s Practice

and her baby A mother elephant g. of 4,670 kg. have a combined mass of 482 kg The baby has a mass is the mother? How much heavier

Let’s Practice m drive 1,205 km A truck driver has to stops for a to deliver his load. He destination. rest 478 km from his d? How far has he travele

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.

Step 1 mother. Find the mass of the ?

478 km trip remaining

trip traveled

mother

baby

– –

Re ga le du ca tio n

1,205 km

–

The truck driver has

traveled

–

km.

g kg.

The mother has a mass

s carnival, At the school athletic 4,675 the red team scored scored points. The blue team more 3,858 points. How many score points did the red team than the blue team?

Step 2 . difference in masses Subtract to find the ?

baby

–

mother m

red team

blue team

–

kg heavier than her

is m The mother

–

more points

eam scored The red team

baby.

139

am. team. than the blue team

138

(b) Home At

Count the number of different creatu re in the garden. Record your data on the next page.

At Home

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.

Repre Repressent ent your data in the

bar graph below.

Number of Creatu res

10 8

272

Hands On

do an activity.

Tell your friends the time you

One friends shows the time

using their arms.

The other friend shows the

time on a clocks.

roles h roles. ch Switch

273

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

Solve it!

Riley spent her summe r vaction in Europe. Complete the division equations and match h the letters to find the first city she visited. T

Solve It!

0 90 9

6÷2=

6÷3=

Activities that require learners earners ers to apply logical lo reasoning and problem-solving. are often em-solving. solving. Problems Proble posed which do not for solving ot have e a routine strategy strate s them. Learners are encouraged ncouraged to think creatively and apply a range of problem-solving roblem-solving heuristics. heu

8÷2=

6÷1=

14 ÷ 2 =

15 ÷ 3 =

279

Looking king Back

Looking Back

Find the area of each figure in square (b) (a)

fi h figure. Find the perimeter off the

12 m

units.

11 m

10 m

Consolidated olidated practice w where learners demonstrate on a monstrate their understanding underst und range nge of concepts taught taugh within a unit.

Area =

square units.

17 m

square units.

Perimeter =

(d)

(c)

figure. Find the area and perimeter of each

1 cm

Area =

square units.

Area =

Find the area of the rectangles. (b) (a) 12 cm

square units.

10 m

4 cm

Area =

Perimeter =

Area =

191

190

iii

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Contents 6 Division (2)

Dividing by 6 Dividing by 7 Dividing by 8 Dividing by 9 Word Problems

7 Measurement

g Mass ss Introduction to Measuring Measuring Mass in Kilograms Grams grams ms and G Measuring Volume rd Problem Mass and Volume Word Problems

8 Time

Telling Time to the Minute im Duration of Time

9 Geometry

nizing g Quadr Quadrilate Recognizing Quadrilaterals wing Quadrilaterals Quadrila Quadrilatera Drawing

Perim 10 Area and Perimeter

Introduction roduction to Area Measuring Ar Area Area of Rec Rectangles Introdu Introducti Introduction to Perimeter Area an Are and Perimeter

2 3 9 15 21 27

40 40 49 61 73

84 84 102 128 129 138

146 147 154 169 176 188

11 Fractions

200 200 2 218 2 23 236 244 252

a ti

12 Data and Graphs

Equal Parts Parts of a Whole Fractions on a Number Line Comparing Fractions Equivalent Fractions

Picture Graphs With Scales Bar Graphs With Scales Reading and Interpreting Bar Graphs Generate Data for Line Plotss

264 264 276 282 288

Division (2)

Anchor Task

Dividing by 6

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Let’s Learn

There are 18 strawberries. The strawberries are divided vided ed into equal equ oup? How many man ma groups. How many strawberries are in each group? groups of strawberries are there?

18 ÷ 6 = 3 groups of There are 6 gr group strawberries. are 3 rawberries. There rawbe Th strawberries berries in each group. berr

18 ÷ 3 = 6 There are 3 groups of strawberries. There are 6 strawberries in each group.

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There are 42 blocks. The blocks are divided into equal groups. How many blocks are in each group? How many groups ps off blocks are there?

42 ÷ 6 = 7 42 ÷ 7 = 6 There There are 7 groups of blocks. ere are 6 groups group of o blocks. There here are 7 blo blocks in each group. There are 6 blocks in each group.

Let’s Practice The balloons are grouped in 6s. Fill in the blanks.

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groups of

(a) There are

balloons. balloons balloon

equation (b) Complete the division equation. ÷

Circle groups of 6 cubes ubes es and complete com c the division equation. (a)

÷6=

(b)

÷6= 5

Circle groups of 6 dots and write a division equation.

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(a)

(b)

Complete the division. (a) 6 ÷ 6 =

(b) (b 12 ÷ 6 =

(d) 24 ÷ 6 =

(e) 30 ÷ 6 =

(f) 36 ÷ 6 =

nu Fill in the missing numb numbers.

(a) 42 2÷

(b)

÷6=3

(d)

÷6=4

At Home The presents are grouped in 6s. Fill in the blanks.

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(a) There are

groups of

presents. prese

n equation. quation. (b) Complete the division ÷

Circle groups of 6 cubes the division equation. bes es and complete co (a)

÷6=

(b)

÷6=

Circle groups of 6 suns and write a division equation.

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(a)

(b)

Complete the division.

(a) 42 ÷ 6 =

(b) (b 30 ÷ 6 =

(d) ( 48 ÷ 6 =

(e) 60 ÷ 6 =

(f) 54 ÷ 6 =

e missing numb num e Fill in the numbers.

(a) 54 ÷

c)) 6 ÷ 6 = (c)

(b)

÷6=4

(d)

÷6=6

Dividing by 7

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Let’s Learn

There are 28 pieces of candy. The candies are divided into equal groups. How many candies are in each group? How many groups of candies are there?

28 ÷ 4 = 7 There of candies. re are 4 groups gro There are in each re 7 candies ca group.

28 ÷ 7 = 4 There are 7 groups of candies. There are 4 candies in each group. 9

Re ga le du ca tio n

There are 56 peanuts. The peanuts are divided into equal groups. How many peanuts are in each group? How many groups of peanuts are there?

56 ÷ 8 = 7 There of peanuts. ere are 8 groups gro There are 7 peanuts in each pe group.

56 ÷ 7 = 8 There are 7 groups of peanuts. There are 8 peanuts in each group.

Let’s Practice The hats are grouped in 7s. Fill in the blanks.

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(a) There are

groups off

hats.

(b) Complete the division equation. ÷

Circle groups of 7 cubes ubess and complete com co the division equation. (a)

÷7=

(b)

÷7=

Circle groups of 7 dots and write a division equation.

Re ga le du ca tio n

(a)

(b)

Complete the division.

(a) 35 ÷ 7 =

(b) 42 4 ÷7=

(d) (d 14 ÷ 7 =

(e) 49 ÷ 7 =

(f) 28 ÷ 7 =

Fill in the he missing numbers. numb num e

(a) 70 ÷

= 10

(b)

÷7=4

(d)

÷7=3

At Home The keys are grouped in 7s. Fill in the blanks.

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groups of

(a) There are

keys. keys

ation. on. (b) Complete the division equation. ÷

Circle groups of 7 cubes es and d complete comple compl the division equation. (a)

÷7=

(b)

÷7= 13

Circle groups of 7 snowflakes and write a division equation.

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(a)

(b)

Complete the division.

(a) 70 ÷ 7 =

(b) 63 6 ÷7=

(d) (d 7 ÷ 7 =

(e) 56 ÷ 7 =

(f) 14 ÷ 7 =

Fill in the numbers. e missing ssing numb num er

9÷ (a) 49

(c)) 21 ÷ 7 =

(b)

÷7=5

(d)

÷7=4

Dividing by 8

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Let’s Learn

There are 24 starfish. The starfish are divided into equal groups. How many starfish are in each group? How many groups of starfish are there?

24 ÷ 8 = 3 There of starfish. re are 8 groups gro There are in each re 3 starfish st group.

24 ÷ 3 = 8 There are 3 groups of starfish. There are 8 starfish in each group. 15

Re ga le du ca tio n

There are 32 shells. The shells are divided into equal groups. How many shells are in each group? How many groups of shells are there?

32 ÷ 4 = 8 There are of shells. re 4 groups g There are 8 shells in each group.

32 ÷ 8 = 4 There are 8 groups of shells. There are 4 shells in each group.

Let’s Practice The flowers are grouped in 8s. Fill in the blanks.

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(a) There are

groups of

flowers.

(b) Complete the division equation. uation. on. ÷

Circle groups of 8 cubes es and d complete comple compl the division equation. (a)

÷8=

(b)

÷8=

Circle groups of 8 dots and write a division equation.

Re ga le du ca tio n

(a)

(b)

Complete the division.

(a) 56 ÷ 8 =

(b) 8 ÷ 8 =

(d) (d 16 ÷ 8 =

(e) 72 ÷ 8 =

(f) 24 ÷ 8 =

Fill in the e missing ssing numbers. numb num er

8÷ (a) 48

(c)) 64 4÷8=

(b)

÷8=8

(d)

÷8=2

At Home The bags are grouped in 8s. Fill in the blanks.

Re ga le du ca tio n

(a) There are

groups of

bags. gs.

n. (b) Complete the division equation. ÷

Circle groups of 8 cubes and nd complete the t division equation. (a)

÷8=

(b)

÷8=

Circle groups of 8 triangles and write a division equation.

Re ga le du ca tio n

(a)

(b)

Complete the division.

(a) 64 ÷ 8 =

(b) 16 1 ÷8=

(d) (d 48 ÷ 8 =

(e) 56 ÷ 8 =

(f) 72 ÷ 8 =

Fill in the e missing ssing numbers. numb num er

6÷ (a) 56

(c)) 32 2÷8=

(b)

÷8=2

(d)

÷8=3

Dividing by 9

Re ga le du ca tio n

Let’s Learn

There are 27 shuttlecocks. The shuttlecocks are divided into equal groups. How many shuttlecocks are in each group? How many groups of shuttlecocks are there? e?

27 ÷ 3 = 9 There are 3 groups of lecocks. cks. shuttlecocks. ere are 9 shuttlecocks shuttleco shutt There in n each group.

27 ÷ 9 = 3 There are 9 groups of shuttlecocks. There are 3 shuttlecocks in each group.

Re ga le du ca tio n

There are 54 marbles. The marbles are divided into equal groups. How many marbles are in each group? How many groups of marbles are there?

54 ÷ 6 = 9 There re are 6 groups group of marbles. There ere are 9 marbles marble in each mar group.

54 ÷ 9 = 6 There are 9 groups of marbles. There are 6 marbles in each group.

Let’s Practice The pencils are grouped in 9s. Fill in the blanks.

Re ga le du ca tio n

(a) There are

groups off

pencils. pencils

(b) Complete the division equation. ÷

Circle groups of 9 cubes ubes es and complete com co the division equation. (a)

÷9=

(b)

÷9=

Circle groups of 9 dots and write a division equation.

Re ga le du ca tio n

(a)

(b)

Complete the division.

(a) 18 ÷ 9 =

(b) (b 45 ÷ 9 =

(d) 9 ÷ 9 =

(e) 27 ÷ 9 =

(f) 90 ÷ 9 =

nu Fill in the missing numb numbers.

(a) 54 4÷

(b)

÷9=4

(d)

÷ 9 = 12

At Home The soccer balls are grouped in 9s. Fill in the blanks. ks.

Re ga le du ca tio n

(a) There are

groups of

soccer ba balls.

uation. on (b) Complete the division equation. ÷

Circle groups of 9 cubes bes and complete comp the division equation. (a)

÷9=

(b) (b

÷9=

Circle groups of 9 hearts and write a division equation.

Re ga le du ca tio n

(a)

(b)

Complete the division.

(a) 27 ÷ 9 =

(b) 81 8 ÷9=

(d) (d 72 ÷ 9 =

(e) 45 ÷ 9 =

(f) 90 ÷ 9 =

Fill in the e missing ssing numbers. numb num er

3÷ (a) 63

(c)) 81 ÷ 9 =

(b)

÷9=2

(d)

÷9=3

Word Problems

ca tio n

Let’s Learn

Re ga le d

Riley reads the same number of pages of her storybook rybook ook each y pages does she night. If she reads 24 pages in 6 days, how many g read each night?

24 pa pages page

24 ÷ 6 = 4 Riley reads 4 pages agess each night. nig

Mrs. Smith has 45 stickers. stickers She shares among 9 pupils. es the e stickers equally equ e pils. How many any y stickers does each pupil receive?? ?

45 stickers

45 ÷ 9 = 5 Each pupil receives 5 stickers.

ed uc ati on

Jordan buys a box of cupcakes for $24 to share with his friends. If one cupcake costs $3, how many cupcakes are in i the e box? ox?

$24

24 ÷ 3 = 8 8 cupcakes are in the box.

Re g

e puts uts 10 flowers flowe into each vase. Keira has 50 flowers. She How many vases does Keira a need?

0 flowers wers 10

50 ÷ 10 = 5 Keira needs 5 vases.

? vases

Let’s Practice Ethan collects 30 eggs on a farm. He helps pack them into cartons. Each carton holds 6 eggs. How many cartons does he need to pack all of the eggs?

Re ga le du ca tio

Ethan needs

cartons to pack all of the eggs.

tons to o put on shirts. Mrs. Choi buys 27 buttons tons. s. Each shirt has 9 buttons. e make in i total? How many shirts did she

Mrs. M s. Choi made Mr m

shirts in total.

Sophie buys 5 identical picture frames for $35. Find the cost of one picture frame.

Re ga le du ca tio

One picture frame costs $

The school cafeteria has seats ats for 54 people. The seats are arranged ed so that there are 6 seats per er table. able. How many tables are e there here in the th t cafeteria? Draw model to he help find wam the answer.

There are 30

tables in the cafeteria.

Halle is saving her money to buy a ukulele. She can save $9 per week. If the ukulele costs $72, how many weeks must she save her money? Draw a model to help find the answer.

Re ga le du ca tio

Halle must save her money ney for

weeks. w

Donuts are sold in boxes oxess of 8. Michelle buys 48 donuts. uts. s. es d do he bu How many boxes does she buy?? fin the answer. Draw a modell to help find

Michelle buys

boxes of donuts. 31

At Home

Class 3A goes on a field trip to the dinosaur museum. eum.. They take mini vans which can seat 6 pupils. There are 36 pupils in class 3A. How many vans will they need?

Re ga le du ca

Class 3A will need

Dominic is cleaning ing his room. He packs his 54 cars into 4 toy car c o boxes. If each box can cars, an hold 9 cars ca how many boxes need? xes does he h n

Dominic nic needs

mini ni vans.

boxes to pack his toy cars.

Riley is baking chocolate chip cookies. She adds 5 chocolate chips to each cookie. She uses a total of 40 chocolate chips. How many cookies does she bake?

Re ga le du ca tio

Riley baked

cookies. s.

Blake shares $24 equally amongst qually ly amon amongs his three brothers. How much money ney does do each brother receive? ve?

Each brother bro receives $

Looking Back The balloons are grouped in 7s. Fill in the blanks.

Re ga le du ca tio n

(a) There are

groups of

balloons. balloon

equation (b) Complete the division equation. ÷

The bags are grouped ped in 8s. Fill in the blanks.

(a) There are

groups of g

b) Complete omplete the division d (b) equation. ÷

bags.

Circle groups of 6 cubes and complete the division equation. q

Re ga le du ca tio n

÷6=

Circle groups of 9 cubess and d complete complet comple the division equation.

÷9=

Divide by 6. Complete the equations. (a) 24 ÷ 6 =

(b) 54 ÷ 6 =

(d) 12 ÷ 6 =

(e) 60 ÷ 6 =

(f) 36 ÷ 6 =

(g) 18 ÷ 6 =

(h) 6 ÷ 6 =

(i)

(j)

Re ga le du ca tio n

48 ÷ 6 =

30 ÷ 6 =

ons. Divide by 7. Complete the equations. (a) 7 ÷ 7 =

(b) 42 ÷ 7 =

(d) 14 ÷ 7 =

(e) 21 ÷ 7 =

(f) ( 70 ÷ 7 =

(g) 49 ÷ 7 =

(h) (h 28 ÷ 7 =

(i)

(j)

63 ÷ 7 =

56 ÷ 7 =

mplete the eq Divide by 8. Complete equations. (a) 8 ÷ 8 =

(b) 32 ÷ 8 =

(d) 56 ÷ 8 =

e) 40 0÷8= (e)

(f) 16 ÷ 8 =

(g) (g 72 ÷ 8 =

(h) 80 ÷ 8 =

(i)

(j)

24 ÷ 8 =

48 ÷ 8 =

Divide by 9. Complete the equations. (a) 18 ÷ 9 =

(b) 45 ÷ 9 =

(d) 9 ÷ 9 =

(e) 27 ÷ 9 =

(f) 90 ÷ 9 =

(g) 63 ÷ 9 =

(h) 36 ÷ 9 =

(i)

(j)

Re ga le du ca tio n

81 ÷ 9 =

72 ÷ 9 =

Fill in the blanks.

(a) 40 ÷ 10 =

(b) 32 ÷ 4 =

÷ 10 = 7

(e)

(g) 49 ÷ 7 = (i)

(k)

÷6=6

(o) 9 ÷

÷8=2

(s) 48 ÷ 8 = (u) 64 ÷ (w))

÷5=3

(j) (

12 ÷

(l)

÷7=6

(n) 28 ÷ 7 =

(m) 2 ÷ 2 =

(q)

(f)

(h) (h 81 ÷ 9 =

= 10 1

100 ÷

(d) 24 ÷

(p) 24 ÷

(r)

÷9=4

(t) 90 ÷ 10 =

÷3=9

(v) 18 ÷

(x)

÷ 10 = 1

Re ga le du ca tio n

10. An egg carton can hold 10 eggs. How many such cartons are needed to pack 70 eggs?

egg cartons are needed d to pack 70 eggs. e

11.

Ethan bought 6 tickets to $42. o the e fair for $4 Find the cost of 1 ticket.

The e cost ost of 1 ticket is $

Re ga le du ca tio

12. Sophie made pizza slices to share equally among her 4 friends. She cooked a total of 24 slices. How many slices did each friend receive?? Draw a model to help find the answer.

Each of Sophie’s friends received eived

pizza slices.

13. Ethan buys 64 beads project. ds for or an art pr The beads are sold in packs of 8 beads. How many such packs does Ethan buy? h pa pac oes E

Ethan bought boug

packs of beads.

Measurement

Introduction to Measuring Mass ass Anchor Task

Let’s Learn

tio n

Compare the mass of the ball and the toy truck.

du c

The ball is as hea heavy tr as the toy truck.

Re ga

Compare the mass of the spinning top p and the soft toy. The soft toy is lighter than the spinning top.

Compare the mass of the toy boat and the toy airplane. The toy airplane is heavier than the toy boat.

Each

has a mass of 1 unit. Find the mass of the pen.

du ca tio n

The pen n has a mass of 2 uni units.

Find the mass of the book.

Re ga l

The book has a mass of 5 units.

Find the mass of the he shoe.

The shoe has a mass of 8 units.

Let’s Practice Use the word groups 'is heavier than', 'is lighter than' n' or 'is as heavy as' to fill in the blanks.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Each cube has a mass of 1 unit.

Re ga le du ca tio n

(a) What is the e mass of the glue stick?

units.

(b) What iss the mass of the scissors?

units.

(d) What is th the mass of the notepad?

units.

((e) Which object is the heaviest?

(f) What W is the combined mass of the glue stick and the crayons?

units.

Solve It! Find the mass of each object.

Re ga le du ca tio n

(a)

The

has a mass off

(b)

The

has a mass of

Check the set of balls that will make the balance level.

(b)

ed uc ati on

(a)

At Home Check the heavier object. If they have the same mass, s, circle both objects. (b)

Re ga le du ca

(a)

tio n

(c)

(d)

Check the lighter box. Iff they have ha the same mass, circle both boxes. (a)

(b)

(c))

(d)

Each cube has a mass of 1 unit. Write the mass of each object.

Re ga le du ca tio n

(a)

units

(b)

units

(c)

units its

(d)

units un

Measuring Mass in Kilograms and Grams

ga le du ca tio n

Let’s Learn

Dominic measures the mass of a pineapple by placing ng it on the scale. The pinea pineapple weighs 1 kg.

0 4 kg

3 kg

1 kg

2 kg

We say: We write:

1 kilogram. 1 kg

Here are some things gs that we measure in kilograms.

Can you guess the mass of each object?

What is the mass of the apples?

Re ga le du ca tio n

The mass of the kg appless is 1 kg.

0 4 kg

3 kg

0 4 kg

3 kg

1 kg

2 kg

What is the mass of the oranges?

The mass of the oranges is 3 kg.

0 4 kg

3 kg

0 4 kg

3 kg

1 kg

2 kg

What is the mass ss of the potatoes? p

The mass of the potatoes is 7 kg.

10 kg

9 kg

1 kg

8 kg

2 kg

7 kg

3 kg

10 kg

9 kg

1 kg

8 kg

2 kg

7 kg

3 kg

6 kg

4 kg

5 kg

6 kg

4 kg

5 kg

Re ga le du ca tio n

For objects lighter than 1 kg, we can measure their mass in grams. The cupcake weighs 80 g.

0 500 g

400 g

300 g

We say: We write:

100 g

200 g

80 grams. 80 g

There are 1,000 g in 1 kg.

The mass of these e objects is measured in grams.

The popcorn has a 0 gram mass of 100 grams.

Re ga le du ca tio n

What is the mass of the popcorn?

0 500 g

400 g

100 g

0 500 g

400 g

100 g

300 g

200 g

The bread has a mass of 300 grams.

What is the mass of the bread?

0 500 0 g

400 0g

100 g

0 500 g

400 g

100 g

300 g

200 g

The eggs have a mass of 450 grams.

What is the mass ss of the eggs? e

0 500 g

400 g

100 g

0 500 g

400 0g

100 g

300 g

200 g 20

200 g

Fill in the blanks. (b)

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(a)

tio n

Let’s Practice

0 4 kg k

0 4 kg

3 kg

1 kg

2 kg

1 kg

2 kg

The washing powder

The pumpkin has a Th

kg.

has a mass of

(c)

kg.

mass of

(d)

10 kg

9 kg

10 kg

1 kg

9 kg

1 kg

8k kg

2 kg

8 kg

2 kg

7 kg

3 kg

7 kg

3 kg

6 kg

4 kg

6 kg

5 kg

4 kg

5 kg

roast turkey has a The ro

The bag of potting mix

mass of m

has a mass of

kg.

(f)

Re ga le du ca t io n

(e)

0 500 g

400 g

0 00 g 500

100 g

300 g

400 g

200 g

300 g

The bowl of noodles has

(g)

mass of

(h)

0 500 g

400 g

0 500 g

100 g

300 g

200 00 g

The pencil case ca has a

a mass of

100 10 g

0g 200

400 g

300 g

100 g

200 g

The orange range has a mass

The tablet computer has

off

a mass of

g. g

Some ome boxes boxe are placed on scales to measure their masses. A

du ca tio n

0 500 g 400 g

100 g

3 kg

300 g

200 g

0 500 g

0 4 kg

400 g

100 g

1 kg

300 g 30

200 g

2 kg

0 500 00 g

0 4 kg 3 kg

400 g

0 4 kg

100 g

1 kg

3 kg 300 g

1 kg

200 g

2 kg

(a) What hat is the mass mas of Box E? b) What is the th mass of Box C? (b) (c) What iis the mass of Box F? d) Which W (d) box is the heaviest? (e) Which box is the lightest? 55

Check the mass that is the best estimate for each object. (b)

Re ga le du ca tio n

(a)

8 kg

10 g

(c)

4 kg k

1100 g

2 kg

5 kg

10 g

10 kg

(d)

1 kg

50 g

(e)

(f)

600 kg g

6 600 0 g

(g)

(h)

2 kg 56

250 g

Hands On

0 500 0g 400 g

100 00 g

Re ga le du ca tio n

Use a scale to measure the mass of objects found in your classroom. Estimate the mass of each object before measuring.

Object

Estimated Estim Mass

300 g

200 00 g

Actual Mass

pencil

notebook textbook k scissors cissors eraser rase

pencil case

At Home Fill in the blanks.

Re ga le du ca tio n

(a)

(b)

10 kg

9 kg

0 kg 4k

1 kg

8 kg

2 kg

7 kg

3 kg

6 kg

3 kg

1 kg

4 kg

5 kg

2 kg

The kettle bell has a

The blender has a mass

mass of

kg.

(c)

kg.

(d)

0 500 g

400 g

300 g

0 500 g

100 0g

400 g

200 g 2

300 g

The snow globe has a T mass of

100 g

200 g

The toy robot has a mass of

Draw to show the mass on the scales. (b) 1 kg

(a) 400 g

0 500 g 400 g

0 kg 4k

100 g

Re ga le du c

3k kg g

300 g

1 kg

200 g

2 kg

(d) 200 g

10 kg

9 kg k

1 kg k

8 kg

2 kg

7 kg k

3 kg

6 kg k

4 kg

0 500 g

400 g

300 g

100 g

200 g

5 kg

Check the mass that is the best estimate for each object. (b)

Re ga le du ca tio n

(a)

1 kg

10 g

(c)

15 kg

250 g

25 kg

(d)

1 kg

500 g

Circle the appropriate unit of mass to measure each object. m (a) A television

grams

kilograms

(b) A sandwich h

grams

kilograms

grams

kilograms

(d) A stapler apler

grams

kilograms

(e) A brick

grams

kilograms

(f) (f A person pers

grams

kilograms

(g) A mango

grams

kilograms

(h) A microwave

grams

kilograms

Anchor Task

Measuring Volume

Let’s Learn

Re ga le du ca tio n

Each of the containers below have an amount of colored water.

The amount of water in each containerr is ca called the volume of water.

Halle poured the water from Container into Container B. ontainer A in She then poured the water back Container A. k into Co Did the volume of water change? ange?

Container er A

Container B

Container A

When the water is poured into different containers, the volume remains the same!

ed uc ati on

Container A and Container B are the same size. Compare the volume of water in the containers.

Container A

Container er B

The volume of water in Container A is lesss than the volume of water in Container B. The volume of water in Container B is greater than the volume of water in Container A A.

The glasses below are of the same the volume ame size. Compare Com of water in each glass. Arrange the glasses glasse in order from the smallest volume to the greatestt volume. volume

Re ga l

smallest volume

greatest volume

uc ati on

The carton below contains 1 l of orange juice. This is the symbol for liters.. We write 1 liter ter as 1 l.

Re ga

These containers contain more than 1 liter of liquid. liqu d.

These containers ers contain contai less than 1 liter of liquid.

Let’s Practice Some water was poured into identical beakers. Check the beaker with the greater volume of water.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

he smallest volume of liquid. Circle the beaker with the (a)

(b)

(c)

The liquid in each container was poured into 1-liter beakers. Find the volume of liquid from each container.

Re ga le du ca tio n

(a)

(b)

(c)

Check to describe the volume of liquid in each container.

Re ga le du ca tio n

(a) Large bottle of sports drink

less than 1 l

more than 1 l

about 1 l

(b) Bath tub

less ss than 1 l

more th than 1 l

about bou 1 l

lesss tha than 1 l

more th than 1 l

abou 1 l about

(d) Perfume erfume bottle

less than 1 l

more than 1 l

about 1 l

Solve It! Find the volume of water in each container.

Re ga le du ca tio n

Arrange the containers from the smallest volume to the c greatest volume. vo

smallest alle

greatest

Tick the bottles used to fill the containers.

Re ga le du ca tio n

er. (a) Dominic poured 13 l of water into the blue container.

12 l

113 3l

(b) Keira poured 16 l of water into o the yellow container.

3l 13

16 l

12 l

28 l

At Home Some water was poured into identical glasses. Check the glass with the smaller volume of water.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

e greatest greate volume of water. Circle the glass with the

(a)

(b)

The liquid in each container was poured into 1-liter beakers. Find the volume of liquid from each container.

Re ga le du ca tio n

(a)

(b)

(c)

Check to describe the volume of liquid in each container.

Re ga le du ca tio n

(a) Bottle of hand wash less than 1 l les

more than 1 l mo

ab about 1l

(b) Water cooler bottle

less than 1 l

more than 1 l

about 1 l

less than 1 l

more than 1 l mo

about 1 l

ttle of eye dro (d) Bottle drops

less than 1 l

more than 1 l

about 1 l

Mass and Volume Word Problems

Re ga le du ca ti n

Let’s Learn

Riley buys an apple and a mango for lunch. The apple has a mass of 125 grams and the mango has a mass of 236 grams. What is the combined mass of the fruits? 125

236

mass of apple

mass of mango

2 5

+ 2 3 6 3 6

125 + 236 = 361 So, the combined mass of the fruits is 361 36 grams. A brick has a mass of 5 kg. Mr. Cordner orders 9 such bricks to fix a wall. What is the total mass ass of the bricks? bi 5 kg

5 x 9 = 45 The e total mass of the bricks is 45 kg.

Re ga le du c

The elephant has a mass of 2,750 kg. The car has a mass of 1,349 kg. How much heavier is the elephant than the car?

2,750 kg

mass of elephant

mass of car 1,349 kg

2,750 – 1,349 = 1,401 The elephant is 1,401 kg heavier than the car. h 8 identical paper clips joined in a chain. lips are join The mass of the chain is 24 g. Find the mass of 1 paper clip. ?

24 g

24 ÷ 8 = 3 ass of 1 paper clip is 3 g. The mass

2 7 5 0 – 1 3 4 9 1

4 0 1

ed uc ati

Ethan's bucket holds 9 liters of water. He uses 8 buckets to help p wash his father's car. How many liters of water does he use in total?

9 x 8 = 72 Ethan uses 72 l of water in total to wash his father's car. f

Re ga

An inflatable swimming pool holds olds 2,150 l of water. Some children jump in the pool and spill spil 270 l of water. What volume of water remains mains in the pool? p

2,150 l

volume be before spill

volum volume after spill

spilled

270 l

–

1 5 0

2 7 0 1

8 8 0

2,150 – 270 = 1,880 There is 1,880 l of water remaining in the pool. 75

844 l milk in store

du ca tio n

A store has 844 l of milk. An order of 1,260 l is delivered to the store. Find the total volume of milk. 1,260 l

milk delivered ?

2 6 0 8 4 4

1 0 4

844 + 1,260 = 2,104 The store has a total of 2,104 l of milk.

Re ga

Mrs. Kim needs to buy 28 liters of paintt to paint her h garden fence. She buys the paint in 4 identical tins. What is the volume of paint in each tin? tin

28 l

28 ÷ 4 = 7 Each ch tin contains 7 l of paint.

Let’s Practice A dairy farmer gets 27 l of milk from his cows in the morning. He pours the milk into identical containers that hold 9 l. How many containers does he need to hold all of the milk?

Re ga le du ca t

The dairy farmer needs

containers. cont

ss of 2,087 kg. A pickup truck has a mass 963 kg of soil is loaded aded into the back of the truck. ruck. What is the mass now? ss of the truck t

pickup truck

soil

The pi pickup truck now has a mass of

In 1 day, a juice shop sells 563 l of orange juice and 395 l of carrot juice. e. How many more liters of orange juice e does the shop sell than carrot juice?

Re ga le du ca tio n

orange juice

carrot juice

–

The juice shop sells

l more oran orange juice than carrot juice.

flou A bakery orders 8 bagss of flour. Each bag has a mass of 5 kg. Find the total mass ass of flour ordered.

The total mass of flour ordered is 78

–

kg.

At Home Halle's fish tank can hold 24 l of water. She cleans the tank and refills it using a 4 l container. How many such containers of water must she pour to fill the tank? Draw a model to help find the answer.

Re ga le du ca ti

containers are needed ed to fill the fish tank.

A chocolate factory orders to make their ders ingredients ing chocolate. They order 980 or 0 kg of sugar and 1,865 kg of cocoa. What is the total mass of the ingredients? Draw a model to help find fin the answer.

The total to mass of the ingredients is

kg.

Julian buys 1,550 kg of concrete and 865 kg of stones to repair the driveway to his house. How many more kilograms gram of concrete did he buy than stones? Draw a model to o help find the answer.

Re ga le du ca tio n

Julian bought

g a 6 l bucket. buck Dominic fills a tub using int the tub. He pours 7 buckets of water into What volume of water iss in the tub? Draw a model to o help find the answer.

There are

more kilogram kilograms of concrete than stones.

l of water in the tub.

Looking Back Check the heavier box. If they have the same mass, circle both boxes.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

Fill in the blanks.

(a)

(b)

10 kg g

9 kg

0 500 g

1 kg

8k kg

2 kg

7 kg

3 kg

6 kg

400 g

300 g

4 kg

100 g

200 g

5 kg k

The Th school bag has a

The cake has a

mass of

kg.

g. 81

Circle the appropriate unit of mass to measure each object. (a) A table

grams

(b) A cupcake

grams

kilograms ms

grams

kilograms ograms

(d) A bookshelf

grams

kilograms ilograms

kilograms

Re ga le du ca tio n

Check the beaker with the greater volume me of liquid. liqu

(a)

(b)

e smallest volume of liquid. Check the beaker with the

The water from the watering can was poured into 1-liter beakers. w Find the volume that was in the can. olume of water w

Circle to describe the volume of a kitchen sink. more than 1 l

about bout 1 l

Re ga le du ca tio n

less than 1 l

Circle to describe the volume of a coffee cup. less than 1 l

more than 1 l

about ou 1 l

Sugar comes in a box containing 8 packs. The total mass of the box is 32 kg. ar? What is the mass of 1 such pack of sugar? er. Draw a model to help find the answer.

The mass of 1 pack of sugar is

ol con 10. A swimming pool contains 3,875 l of water. avy rain, th After some heavy the volume of water in the pool increases 4,183 l. reases to 4 me of wate What volume water did the rain add to the pool? odel to help find the answer. Draw a model

The rain added

of water to the pool.

Time

ati on

Telling Time to the Minute Anchor Task

It’s ’s 23 minutes past p 10.

It’s ten twenty-three.

It’s 23 minutes after 10 o’clock.

Let’s Learn

ed uc ati on

1 minute

On a clock, it takes the minute nute hand 1 minute mi m to move from one marking to the next. It takes kes 5 minutes to move from one number to the next. There are 60 minutes es in one o hour. hour It takes the minute hand 1 hour to move once around ound the clock. clo c It’s 10:13. It’s 7:56.

du ca tio n

It is 6:12 a.m. It is 12 minutes past 6 o’clock in the morning. Jordan wakes up at 12 minutes ess past 6. 6

It iss 3:2 p 3:26 p.m. min It is 26 minutes past 3 o’clock in the afternoon. es home at 26 minutes past 3. Jordan rides

du ca tio n

It is 10:47 a.m. n the morning. morning It is 13 minutes until 11 o’clock in y the p tes to 11. Halle p plays piano at 13 minutes

Itt is 8:52 p.m. It is 8 minutes until m un 9 o’clock at night. Halle watches television at 8 minutes to 9. watc

Let’s Practice Match.

Re ga le du ca tio n

6:13

5:39

1:07

9:33

8:55

Match.

Re ga le du ca tio n

8 minutes nutes past 10

minutes to 7 12 m

18 minutes to 9

12 minutes past 7

3 minutes past 12

Fill in the blanks.

Re ga le du ca tio n

(a)

It is

minutes past

(b)

It is

minutes nutes to

(c)

It is It iis

minutes to

Re ga le du ca tio n

(d)

It is

minutes to

(e)

It is

minutes inu inute past st

(f)

It is It is

minutes to

Write ‘past’ or ‘to’. (b)

Re ga le du ca tio n

(a)

6 minutes

23 minutes

17 minutes

d) (d)

(c)

16 minutes

10.

(e)

(f)

9 minut minutes

12 2 minutes

Draw hands on the clocks to show the time. (b) 15 minutes to 11

Re ga le du ca tio n

(a) 11 minutes past 6

nutes es past 1 (d) 28 minutes

(e) 22 minutes to 3

2 minutes min m (f) 12 past 9

Fill in the blanks. s.

minut utes es to 8 is (a) 4 minutes

(b) 24 minut minutes es past 12 is

(d) 7:39 is

minutes to

(e) 12: 12:02 is

minutes past

(f) 10:47 is

minutes to

. 93

Hands On Tell your friends the time you do an activity.

One friends shows the time using their arms.

The other friend shows the time on a clock. k k.

Switch roles.

tio n

I play the violin at 25 minutes past 9.

(b) Home At Match.

Re ga le du ca tio n

12:22

12:11

2:55

1:07

11:51

Match.

Re ga le du ca tio n

9 minutes es to o4

9 minutes past 4

26 minutes to 11

2 minutes past 2

14 minutes to 12

Fill in the blanks.

Re ga le du ca tio n

(a)

It is

minutes past

(b)

It is

minutes utes to

(c)

It is It iis

minutes past

Draw the minute and hour hands to show the time. (b) 27 minutes to 11

Re ga le du ca tio n

(a) 1 minute past 8

nutes es past 6 (d) 28 minutes

(e) 21 minutes to 5

(f 4 minutes min mi (f) past 7

Fill in the blanks. s.

minut utes to 2 is (a) 16 minutes (b) 4 minut minutes es to 11 is

(d) 2:54 is

minutes to

(e) 8:29 8:2 is

minutes past

(f) 10:33 is

minutes to

Hands On Roll the dice. Move your counter the number of spaces paces es shown on the dice.

ti Say the time using ‘past’ and ‘to’. If you say the incorrect time, go back to the start.

er. The first player to the finish is the winner.

ati on

Solve It!

ed uc ati on

Check the correct clock.

(a) Wyatt worked in the garden for 25 minutes. He finished ished gardening? gardening at 5:00 p.m. What time did Wyatt sstartt g gardenin

(b) Riley started playing the e guitar at a midday. She played the guitar y stop pp y g the guitar? for 18 minutes. Wha What time Riley playing Wh e did R

100

le du ca tio n

(c) Jordan started fishing at 4 o’clock. He caught his first fish 46 minutes later. What time did Jordan catch his first fish? sh?

(d) Chelsea watched a 30-minute show. She finished -minute television te watching the show ow at 8:15 :15 p.m. What time did the show start?

1 01

Duration of Time

Re ga le du ca tio n

Let’s Learn

Mr. Jenkins puts a pizza in the oven at 7:30 p.m. He removes the pizza at 7:48 p.m. zza? za? How long does it take Mr. Jenkins to cook a pizza?

5, 10, 15, 16, 17, 18.

1 18 17 16

It takes Mr. Jenkins Jenk 18 minutes to cook a pizza. +5

7:30 1 02

7:45

7:48

Re ga le du ca tio n

Riley started running at 9:10 a.m. m. She ran for 5 kilometers. She finished at 9:47 a.m. How long does it take Riley to run 5 kilometers?

47 – 10 = 37

37 minutes

9:47

9:10

n 5 kilometers. kilome kilom Riley took 37 minutes to run How long is it from 4:30 p.m. p.m to 5:15 p 5 p.m.? 30 m minutes

15 minutes m

45 min minutes

30 0m min

4:30

15 min

5:00

5:15

30 + 15 5 = 45 4 It is 45 minutes nut from 4:30 p.m. to 5:15 p.m.

1 03

Let’s Practice Fill in the blanks.

Re ga le du ca tio n

m. to o 6:48 a.m.? a.m (a) How many minutes are there from 6:25 a.m.

minutes

e there from 1:20 1:1:2 p.m. to 1:48 p.m.? (b) How many minutes are

minutes utes

w many minutes minut a (c) How are there from 8:55 a.m. to 9:10 a.m.?

minutes

104

Re ga le du ca tio n

(d) How many minutes are there from 12:35 a.m. to 12:56 a.m.?

minutes

om 11:05 p.m. p.m to 11:23 p.m.? (e) How many minutes are there from

minutess

(f) How many ny minutes are a there from 10:10 a.m. to 10:36 a.m.?

minutes minu m

1 05

Fill in the blanks. Use the time line to count on.

Re ga le du ca tio n

8 p.m.? (a) How many minutes are there from 1:05 p.m. to 1:48

minutes

es are there from fro 3:15 a.m. to 3:56 a.m.? (b) How many minutes

minutes m minu

106

Re ga le du ca tio n

minutes

re between betwee the times? How many minutes are there Fill in the blanks. 52 a.m. (a) 3:45 a.m. and 3:52

(b) 2:45 p.m. and p.m. nd d 12:59 12:5 12 m d 1:43 a.m. a.m (c) 1:05 a.m. and

(d) 4:20 a.m.. and 4:42 a.m a.m.

Fill in the blanks. blank blan s.

(a) a) What time is it 14 minutes after 2:30 p.m.?

(b) What tim (b time is it 41 minutes after 8:10 p.m.?

time is it 19 minutes after 9:05 p.m.? (c) What tim

(d) Wha What time is it 38 minutes after 11:10 p.m.?

1 07

Fill in the blanks.

le du

(a) Riley leaves her home at 7:25 a.m. She arrives at school at 7:52 a.m. How long did it take Riley to get to school?

It took Riley

minutes tes to get to school.

artss at 2:10 p.m (b) Science class starts p.m. and finishes at 2:55 p.m. ence cla How long is the science class?

science class is Th sc The

108

minutes long.

Re ga le du

tio n

Ethan finished jogging ng at

to her garden at 5:05 p.m. (d) Chelsea goes into er ducks for fo 52 minutes, then goes inside. She plays with her What time do go inside? does Chelsea elsea g

Chelsea C hels goes inside at

1 09

(b) Home At Fill in the blanks.

Re ga le du ca tio n

m. to o 3:21 a.m.? a.m (a) How many minutes are there from 3:05 a.m.

minutes

(b) How many minutes are e there from 2:45 2: p.m. to 3:18 p.m.? 2

minutes tes

minutes

110

Re ga le du ca tio n

(d) How many minutes are there from 7:35 a.m. to 8:12 a.m.?

minutes

e from om 3:30 p.m. p.m to 3:45 p.m.? (e) How many minutes are there

minutes

ny minutes nutes are a there from 1:50 a.m. to 2:28 a.m.? (f) How many

minutes min

111

Fill in the blanks. Use the time line to count on.

Re ga le du ca tio n

(a) How many minutes are there from 4:15 p.m. to 4:411 p.m.?

minutes

tes are there from f (b) How many minutes 9:55 a.m. to 10:10 a.m.?

minutes min

112

Re ga le du ca tio n

minutes

here re between the times? How many minutes are there Fill in the blanks. (a) 1:45 a.m. and 1:52 2 a.m. m.

d 112:59 p.m. (b) 12:15 p.m. and :39 a.m a (c) 5:15 a.m. and 5:39 a.m.

(d) 9:20 a.m. m. and 9:43 a.m. a

Fill in the blank blanks. blan s.

a) What time is it 29 minutes after 2:30 p.m.? (a)

(b) (b What time tim is i it 41 minutes after 2:05 p.m.?

(d) What Wha time is it 16 minutes after 12:35 p.m.?

1 13

Fill in the blanks.

ed uc ati on

(a) Blake takes a nap at 3:05 p.m. He wakes up at 3:48 p.m. How long was Blake asleep?

Blake was asleep for

minutes. minu

Re g

aking ng a pizza at 5:15 p.m. (b) Sophie started making aking g the pizza piz at 5:51 p.m. She finished making How long did it take ke e Sophie to make the pizza?

Sophie took S Soph

114

minutes to make the pizza.

le du

tio n

Wyatt reached the waterfall erfall at

Re g

(d) Halle’s English exam xam m started at a 10:15 a.m. xam am in 43 minutes. She finished the exam What time did Halle Ha finish nish i h the English exam?

Halle Ha H lle finished the English exam at

. 1 15

Let’s Practice Fill in the blanks.

Re ga le du ca tio n

m. to o 10:15 p.m.? p.m (a) How many minutes are there from 9:25 p.m.

min

9:25 p.m. +

min

10:00 p. p.m p.m.

10:15 p.m.

minutes

(b) How many minutes are there min the from 5:50 a.m. to 6:30 a.m.?

min

5:50 a. a.m. +

minutes 116

min

Re ga le du ca tio n

min

min in

1:35 p.m. +

minutes

(d) How many minutes 11:45 a.m. to 12:40 p.m.? tes are there from ffr

m min

min

11:45 45 a.m. +

minutes m

1 17

Fill in the blanks.

Re ga le du ca tio n

0 a.m. (a) Ethan started opening his birthday presents at 11:50 He finished opening at 12:35 p.m. p g his presents p p How long did Ethan spend opening his prese presents? sents? ts?

Ethan spent

minutes utes openin opening his presents.

eaning ning her bedroom be bed (b) Sophie started cleaning at 4:45 p.m. as spotlessly spotless clean c Her bedroom was at 5:25 p.m. How long did it take ke e Sophie to clean her bedroom?

Itt took too Sophie

118

minutes to clean her bedroom.

Re ga le d

ion

Wyatt reached the cave at

ce e m starte (d) Halle’s science exam started at 2:10 p.m. ed the ex e She finished exam in 58 minutes. What time tim me did Halle Ha H lle le fin ffinish nish the science exam?

Halle Ha H lle finished the science exam at

. 1 19

Solve It!

Re ga le du ca tio n

Use the map on the next page to answer the questions. ns. 1.

Sophie left the camp site at midday. She hiked via the cave to the waterfall. What time did she arrive at the waterfall? terfall?

Sophie arrived at the waterfall at

Blake left the camp site at 3:10 0 p.m. m. He hiked hike past the pond and the waterfall to the forest. est. What time did Blake arrive at the forest?

Blake arrived at the forest fore at

Keira left the e camp site at 8:00 a.m. She passed the pond, rocks and forest on the way to the waterfall. What time did th w Keira arrive waterfall? ve at the wate w

Keira ra arrived arriv at the waterfall at a

120

35 min

25 min

le d

10 min

15 min

30 min

35 min

121

(b) Home At Fill in the blanks.

Re ga le du ca tio n

(a) How many minutes are there from 6:35 p.m. m. to 7:20 p.m.? p.m

min

6:35 p.m. +

min

7:00 00 p.m.

7:20 p.m.

minutes

(b) How many minutes are there min the from 11:45 a.m. to 12:30 p.m.?

min m

11:45 a.m. a. +

12:00 p.m. =

minutes 122

min

12:30 p.m.

Re ga le du ca tio n

min

3:20 p.m. +

min m

4:00 p.m. 4:10 p.m.

minutes

(d) How many minutes 10:45 a.m. to 11:40 a.m.? es are there from fr f

mi min

min

10:45 a.m. +

minutes m

123

Fill in the blanks.

Riley spent

ed uc ati on

40 a.m. (a) Riley arrived at her grandmother’s house at 9:40 She left at 10:15 a.m. How long did Riley spend at her grandmother’s grandmothe her’s ’s house?

minutes nutes at her grandmother’s house.

omework at a 4:25 p.m. (b) Jordan started hiss homework 20 p.m. He finished at 5:20 homework? How long did Jordan d dan an spend d doing his homew

Jordan J orda spent

1 24

minutes doing his homework.

ed uc ati on

(c) Halle started playing her ukulele at 10:25 a.m. She played the ukulele for 50 minutes. What time did Halle stop playing the ukulele?

Halle stopped playing ng the he ukulele at

Re g

e swimmi swimm swimmin (d)) Ethan arrived att the swimming pool at 12:45 p.m. He swam for 55 minutes, nutes, then th left. What time did Ethan E leave leav le av the swimming pool?

Ethan left the swimming pool at Et

. 125

Looking Back Fill in the blanks.

Re ga le du ca tio n

(a)

It is

minutes past

(b)

It is

minutes tes to

Draw the the time. e clock ock hands to show s (a) 277 minut minute nu e past ast 8

1 26

(b) 12 minutes to 12

Fill in the blanks. (a) 21 minutes to 7 is

(b) 18 minutes to 3 is

Re ga le du ca tio n

Fill in the blanks.

(a) There are

minutes between 4:45 a.m. and 4:52 a.m.

(b) There are

minutes between en 12:30 :30 p.m. and a 12:54 p.m.

Fill in the blanks.

(a) How many minutes are there from 6:45 6:4 p.m. to 7:35 p.m.? 6

minutes. utes.

(b) How w many any minutes minute are a there from 12:40 p.m. to 1:25 p.m.?

minutes.

127

Geometry

Anchor Task

1 28

tio n

Recognizing Quadrilaterals

Re ga le du ca tio n

Let’s Learn

Observe the lines on each side of the ruler. a Notice that the distance between the two lines iss the same at art and do not any point. Lines that are an equal distance apart meet are called parallel lines.

We say: AB is parallel to CD. We write: AB CD

We say: parallel to GH. EF is p write: We w EF GH

The distance between IJ and KL does not stay the same. IJ is not parallel to KL.

129

Identify the pairs of parallel lines. N

Re ga le du ca tio n

MN is parallel to OP. MN OP

QR is parallel to ST. QR ST

AB is parallel to CD. A AB CD

Recall that squares, rectangles, trapezoids pezoids and an parallelograms are quadrilaterals. A quadrilateral has 4 straight straigh sides and 4 angles. rectangle

square

side de

ang angle

apezoid zoid trapezoid

parallelogram

side

angle

130

Let’s look at some different types of quadrilaterals.

Re ga le du ca tio n

quadrilaterals trapezoids

parallelograms

• at least 1 pair of parallel sides

• 2 pairs of parallel sidess

• no p parallel ara sides

rectangles

rhombi rhom rho

• opposite sides of equal length gth

• all sides of equal length

ssquares

• all angles and sides are equal

1 31

Let’s Practice Check the pairs of lines that are parallel.

Re ga le du ca tio n

W Y

L N

Q S

132

How many pairs of parallel allel lines does d each shape have?

(a)

(b) b))

(c)

(d)

(e)

(f)

(a) Check the shapes that are quadrilaterals.

Re ga le du ca tio n

(b) Explain is ain why why a square squ i a type of rectangle.

1 33

Choose a word from the box that best describes each shape. rectangle trapezoid

rhombus quadrilateral al

Re ga le du ca tio n

square parallelogram

1 34

(a)

(b)

(c)

(d (d)

(e)

(f)

Hands On

Re ga l

Work in pairs and identify objects around the schoolyard ard that elow. have a quadrilateral shape. List them in the table below.

Object bject

Quadrilateral

1 35

At Home Complete the key and color the shapes.

Re ga le du ca tio n

squares

1 36

rectangles

rhombi

trapezoids apez

Circle the word that best describes the shape.

Re ga le du ca tio n

(a) square

rectangle ctangle

rectangle ectangle ang

rhombus

rhombus rh

square

parallelogram

square

(b)

(c)

(d)

1 37

Drawing Quadrilaterals

Re ga le du ca tio n

Let’s Learn

Keira uses dot paper to draw some quadrilaterals. s. She chooses 4 dots. Then she uses a pencil and ruler to draw lines and connect the dots.

Can you name the pink shape?

Michelle draws some quadrilaterals adrilaterals rilateral on a piece of grid paper. She chooses 4 points where the g grid lines cross. Then she uses ts w wh a pencil to connect ct the he points. poin po

What color is gle? the rectangle?

1 38

Let’s Practice Draw 3 squares on the dot paper.

Draw 3 rectangles on the he grid paper. pap

Re ga le du ca tio n

1 39

Draw 3 parallelograms on the dot paper.

Re ga le du ca tio n

140

Draw 2 quadrilaterals on paper n the e grid pape pap that are not squares, rectangles or parallelograms. ograms. ms. Explain Explai how they are different.

Work in pairs.

ca tio n

Hands On Draw a quadrilateral on the dot paper below.

ake it on a Have your partner name the shape and make geoboard. Switch turns.

Re ga le

1 41

At Home On the dot paper, draw a square, a rectangle and d a rhombus. rhombus hombus Label each shape.

Re ga le du ca tio n

142

On the grid paper, draw a parallelogram, a square and a trapezoid. Label each shape.

Re ga le du ca tio n

1 43

Looking Back Check the shapes that are quadrilaterals.

Re ga le du ca tio n

1 44

Check 1 or more names for each shape. (a) square uare

rectangle

trapezoid

rhombus

parallelogram paralle

quadrilateral drilateral teral

square

rectangle ectangle gle

trapezoid

rhombus ombus

parallelogram

quadrilateral quad

square

rectangle re

trapezoid

rhombus

parallelogram

Re ga le du ca tio n

quadrilateral

(b)

(c)

(a) Draw aw a trapezoid trapezo trapezoid..

(b) Draw a parallelogram.

1 45

Anchor Task

146

Area and Perimeter

Let’s Learn

ed uc ati on

Introduction to Area Michelle uses square tiles to make some figures. She counts the number of tiles used to make each shape. Count the squares used to make each figure!

6 square tiles les

3 square tiles

5 square tiles

vered d by a shape sha sh The amount of surface covered is called area. We say: n area ea of 6 square sq s The green figure has an tiles. a area rea ea of 3 square tiles. The yellow figure hass an ar of 5 square s The red figure has an area tiles. e yellow ellow and blue b Riley uses some tiles to make a figure.

Each blue tile has half the area of a yellow square tile

ou find ind the area of o her figure? Can you

iles can ca combine to make 1 square tile. 2 blue tiles Riley’s figure has an area of 4 square tiles. 1 47

1 unit

The square grids below are made of squares that have a side length of 1 unit.

Re ga le du ca tio n

1 unitt

are grid paper pap Halle draws and shades a figure on a sheet of square paper. What is the area of the shaded figure? To find the area of the shaded figure, count haded figure thee number of square units it ffills up.

Area A = 20 square units.

Keira draws and shades de a figure on o a sheet of square grid paper. What is the area off the shaded sh s d figure? f To find the area of the shaded figure, add the number of square units and nu half square units.

Area B = 8 square units + 4 half square units. squ = 10 square units. s

148

Let’s Practice Find the area of each figure.

Re ga le du ca tio n

Area =

square units.

Area =

square units.

square u units. units

Area =

square units.

1 49

The figures are inside a grid made up of square tiles.

Re ga le du ca tio n

(a) Find the area ea of each figure. fig Area A =

squ square units.

Area B =

square units.

Area rea C =

ssquare units. squ

Area D =

square units.

Area rea E =

ssquare units.

Area F =

square units.

has the greatest area? (b) Which figure fig (c) Which W fig figure has the smallest area?

150

Solve It!

Re ga le du ca tio n

The blue figure has an area of 16 square units. are Color 3 more figures that have a different shape butt the same area.

Make sure the figu figures do not overlap or share any squares.

1 51

At Home Find the area of each figure.

Re ga le du ca tio n

(a)

(b)

Area =

square units.

Area =

square units.

Area =

square units.

(c)

(d)

Area =

square un units.

(e)

(f)

Area =

152

Area ea =

square units.

Complete the following. N

Re ga le du ca tio n

(a) Circle the same area. cle 2 figures that th have h (b) Figure of Figur ure e R has an area a

square units.

c) Figur Figure e N has h an a area of (c)

square units.

(d) Figure Figure

has the smallest area.

e) Figure Fig e Figur (e)

has the greatest area.

153

Measuring Area

Re ga le du ca tio n

Let’s Learn

A square centimeter is an area equal q to a square e with a side length of 1 cm. The symbol for or square centimeterss is ccm2. 1 cm

1 cm

cm2

m We can use square centimeters as a unit of measurement for area. The square has a side length th off 3 cm. Let’s find the area of the square. are.

3 cm

The 3 cm square can be divided into nine 1 cm squares.

1 cm m

1 cm

The area ea of the square is 9 square centimeters. We say: 9 square y s ua centimeters. c We e write: write 9 cm cm2.

1 54

The pink rectangle has a height of 2 cm and width of 5 cm. 5 cm

Re ga le du ca tio n

1 cm 1 cm m

2 cm

It has an area of 10 cm2.

e length ngth of 1 cm. cm The squares in the grid below have a side

1 cm

Each figure re in the grid has an area of 12 cm2.

155

Re ga le du ca to n

A square meter is an area equal to a square with a side length of 1 m. The he sy symbol for square meters is m2. 100 cm 1m 100 cm

The yellow rectangle has height of 3 m and width of 4 m. 1m

The area of the rectangle le iss 12 square meters. We say: 12 square meters. eters. rs. We write: 12 m2.

he grid below have a side length of 1 m. The squares in the

Both figures in the grid have an area of 14 m2.

1 56

The symbol for square re inches iss in2.

Re ga le du ca tio n

This square has a side length of 1 inch. It has an area of 1 square inch. 1 in

1 in

in2

The blue rectangle has a height of 2 in and width of 3 in. 1 in

3 in

1 in

2 in

The area of the rectangle e is 6 square inches. in We say: 6 square inches. ches. s. We write: 6 in2.

e grid id below bel The squares in the have a side length of 1 in.

1 in

Both oth figures in the grid have an area of 8 in2.

157

1 ft

ft2

Re ga le du ca

12 in

A square foot is an area equal to a square with a side length of 1 ft. Thee symb sy symbol for square square feet is ft2. 12 in 1 ft

The green rectangle has height of 5 ft and width of 4 ft. 1 ft

4 ft

1 ft

5 ft

The area of the rectangle ctangle angle is 20 square feet. quare are feet. We say: 20 square We write: 20 ft 2.

es in n the grid below b The squares have a side length of 1 ft.

Both figures in the grid have an area of 13 ft 2. 1 58

1 ft 1 ft

Let’s Practice Find the area of each figure.

1 cm

Re ga le du ca tio n

(a)

1 cm

Area =

(b)

Area ea =

Area =

159

1 in

(c)

Re ga le du ca tio n

1 in

Area =

1 ft

(d)

Area =

Area = A

160

Area =

1 ft

Find the area of each rectangle. Make sure you write the correct area units.

Re ga le du ca tio n

(a)

1 cm

The square is made up of

1-cm squares. es. s.

Area =

(b)

The rectangle angle is made up

1 m of

1-m m squares squares. squar

ea = Area

The rectangle tangle is made m up of

1-m squares. sq

Area =

(d)

1 cm

The rectangle is made up of

1-cm squares.

Area =

1 61

Find the area of each figure. (a)

The figure iss made ade up

Re ga le du ca tio n

1 m of

1-m m squares. squares

Area =

(b)

1 cm

The figure is m made up of

1-cm 1 c squares.

Area =

(c)

1 cm

The figure is made up

1 cm

1-cm squares.

Area =

(d) d)

1 m The figure is made up

Area =

1 62

1-m squares.

(e)

The figure is made up 1-cm squares. uares. es.

Re ga le du ca tio n

1 cm

Area =

1 cm

(f)

The he figure gure is ma made up

1-m squares.

Area =

(g)

The figure is made up of

1-m squares.

Area =

(h)

1 cm

The figure is made up of

1-cm squares.

Area =

1 63

Hands On

Re ga l

Work in pairs. Take square centimeter tiles and build squares. Start with a square of side length 1 cm. c Add tiles to make a new square of side length 2 cm. Find the area of each square you make and fill in n the the table. table

Square Side Length

Numbe Number of 1 cm squares s

Area in cm2

1 cm

2 cm

3 cm 4 cm

5 cm

1 64

At Home Find the area of each figure. Make sure you write the correct area units.

Re ga le du ca tio n

(a)

Area =

(b)

(c))

1 cm

Area =

(d)

(e)

Area =

1 in

(g)

(f))

1 in

1 cm

Area =

1 65

(h)

1 ft

(i)

1 ft

Re ga le du ca tio n

1 ft

Area =

(j)

1 in

Area =

1 cm

(l)

(k)

1 cm

Area =

(m)

(n)

1 cm

Area = A

Area =

1 66

Find the area of each figure.

1 in

Re ga le du ca tio n

(a)

1 in

Area =

Area a=

Area =

1 ft

(b)

1 ft

Area =

Area = A

Area =

1 67

The grid is made of squares that have a side length of 1 cm.

Re ga le du ca tio n

(a) What is the area off the pink figure? figur figu

e figure gure that h (b) What color is the has an area of 13 cm2?

hat is the area area of the green square? (d) What

(e) 2 figures the same area. What is the area? igures have th

168

Area of Rectangles

Re ga le du ca tio n

Let’s Learn

Figure A is a rectangle. Find its area in square centimeters. ntimeters. eters.

Figure A

To find the area of a gle, we mu rectangle, multiply the ngth by the breadth. length

3 cm

6 cm

Area Figure A = length x breadth = 6 cm x 3 cm = 18 cm2

The area of Figure A is 18 cm2.

ectangle angle in square sq Find the area of each rectangle centimeters.

(a)

(b)

Figure B

6 cm

4c cm

Figure C

5 cm

rea Figure B = length l Area x breadth = 5 cm x 4 cm = 20 cm2

5 cm

Area Figure C = length x breadth = 5 cm x 6 cm = 30 cm2

1 69

Let’s Practice Find the area of each rectangle.

Re ga le du ca tio n

(a)

(b)

3 cm

6 cm

1 cm

2 cm

Area =

(c)

5 cm

(d)

4 cm

Area = A

Area =

(e)

6 cm

(f)

10 cm

Ar = Area

170

Area =

(g)

8 in

10 ft

(h)

Re ga le du ca tio n

2 in 8 ft

Area =

(i)

3 cm

7 in

(j)

5 in

7 cm

Area =

10 0 ft

(k)

6 in

(l)

4 ft

6 in

Area =

1 71

Find the area of each rectangle.

1 cm

Re ga le du ca tio n

1 cm

(a) What is the area off figure Q? Q

ure e has an area of 15 cm2? (b) Which figure

ure has the largest lar (c) Which figure area? What is its area? has h an area of

igures h (d) Which 2 ffigures have the same area? and

have the same area.

((e) What iis the area of figures Q and T combined? +

172

Solve It!

Re ga le du ca tio n

The figures are made by combining 2 or more rectangles. ngles. s. Find the area of each figure. Dividee the figure (a) intoo rectangles! F Find the rea of each rec area rectangle and com combine. 4 cm

4 cm

Working Wo

3 cm

8 cm

Area =

(b)

Working

Area =

1 73

At Home Find the area of each rectangle.

Re ga le du ca tio n

(a)

(b)

4 cm

3 cm

Area =

Area rea =

(c)

20 m

Area =

(d)

10 cm

(e) (

10 cm

Area =

Area = Ar

174

In what month is Wyatt’s birthday?? Find the area of each rectangle. as Then match the letters to the areas below to find out.

Re ga le du ca tio

4 cm

10 cm

12 cm

6 cm

3 cm

2 cm

12 cm m2

16 cm2

1 cm

60 cm2

6 cm2

16 cm2

12 m2

6 m2

1 75

Anchor Task

176

Introduction to Perimeter

Let’s Learn

Re ga le du ca tio n

Dominic draws two figures on a sheet of 1-cm square grid d paper. He adds the lengths of each side of the figures. The total distance around a figure is called the perimeter.

1 cm

ce of a continuous continu The distance line around a figure is the perimeter. Perimeter er A = 7 cm + 5 cm + 7 cm + 5 cm = 24 cm

Perimeter B = 5 cm + 2 cm + 3 cm + 4 cm + 2 cm + 6 cm = 22 cm

1 77

Re ga le du ca tio n

Find the perimeter of the triangle.

To find thee perimete perimeter angle, add tthe of the triangle, ngths of the sides. si lengths

20 m

12 m

16 m

Perimeter = 20 m + 16 m + 12 m = 48 m

Find the perimeter of the rectangle. ngle..

The perimeter of the rectangle is its length + breadth + length + breadth.

11 m

40 m

Perimeter = 40 m + 11 m + 40 m + 111 m = 102 m

Find the perimeter meterr of the square. squa sq re.

8 cm

Perimeter = 8 cm + 8 cm + 8 cm + 8 cm Perim = 4 x 8 cm = 32 cm

178

The perimeter of the square is equal to 4 times its length.

Find the perimeter of each figure. 1 cm

Re ga le du ca tio n

3 cm

2 cm

2 cm + 3 cm + 1 cm + 3 cm + 4 cm = 13 cm The figure has a perimeter ter of 13 cm.

3 cm

4 cm

4 m + 6 m + 6 m + 4 m + 6 m + 6 m = 32 m The figure of 32 m. e has as a perimeter perim

Find the perimeter of each h figure re formed forme with an elastic band on the geoboard.

1 cm

Perimeter ter A = 2 cm cm + 3 cm c + 2 cm + 3 cm = 10 cm Perimeter erimeter B = 4 x 2 cm erimete = 8 cm

Perimeter ter C = 1 cm + 1 cm + 1 cm + 1 cm + 2 cm + 1 cm + 4cm + 3 cm = 14 cm 1 79

Let’s Practice Find the perimeter of each figure. Show your working. king..

Re ga le du ca tio n

(a)

Working

3 cm

5 cm

Perimeter =

(b)

Working

5 cm

4 cm

m 3 cm

Perimeter =

(c)

Working

10 m

Perimeter = Pe Perime

180

(d)

Re ga le du ca tio n

Working

12 cm

Perimeter =

(e)

or Working

35 cm

50 cm

Perimeter = 3m

(f)

Working

Perimeter = P Perime

1 81

The figures below are inside 1-cm square grid paper.

Re ga le du ca tio n

182

(a) Find the perimeter of each figure. Working

Re ga le du ca tio n

Perimeter A =

Perimeter B =

Perimeter C =

Perimeter D =

Perimeter E =

Perimeter F =

Perimeter G =

Perimeter meter H =

(b) Which ich figure figure has ha the greatest perimeter? (c) c) Which figure fig igure has h the smallest perimeter?

(d) Which 2 figures fig have the same perimeter? Fig Figures

and

have the same perimeter.

(e) Which i figure has the greatest number of sides? 1 83

Solve It!

Re ga le du ca tio n

Ethan has a piece of wire that is 16 cm long. He wants to bend the wire to make a rectangle. e full length of Draw 4 different rectangles he can make that use the the wire in the grid below. 1c cm

1 cm

184

At Home Find the perimeter of each figure. Show your working. king..

eg al ed uc ati on

(a)

Working

5 cm

Perimeter =

7 cm

(b)

7 cm

Working

7 cm

Perimeter =

12 m

(c)

Working

Perimeter = Perim Perimete

1 85

Find the perimeter of each figure on the geoboard.

Re ga le du ca tio n

1 cm m 1 cm

Perimeter =

Perimeter = Per

186

Draw 2 different rectangles with a perimeter of 14 cm.

Re ga le du ca tio n

1c cm cm 1c

hat has a perimeter peri per Draw a figure with 6 sides that of 28 cm.

1 cm

1 87

Area and Perimeter

Re ga le du ca tio n

Let’s Learn

Find the area and perimeter of the rectangle. 1 cm

1 cm

Area

= 5 cm m x 3 cm 5 cm2 = 15

Perimeter eterr = 5 cm + 3 cm + 5 cm + 3cm = 16 cm

Compare the areas and perimeters meters eters of the figures in the geoboard. 1 cm

Area = 8 cm2 Perimeter = 12 cm m

1 cm

Area = 8 cm2 Perimeter = 16 cm

Area = 5 cm2 Perimeter = 12 cm

Figures A and an B same have the sa rea but bu different area rim perimeters!

188

Figures A and C have the same perimeter but different areas!

Let’s Practice Find the perimeter and area of each figure.

1 cm

Re ga le du ca tio n

1 cm

Area =

Perimeter =

Area rea =

Perimeter erim =

Area = A

Perimeter =

Area =

Perimeter =

1 89

Compare the areas and perimeters of the figures in the geoboard.

Re ga le du ca tio n

1 cm 1 cm

(a) Find 2 figures that have the same area. figures th tha Figures gures

and

both have an area of

cm2.

((b) Find 2 ffigures igur that have the same perimeter. Figures Fi

190

and

both have a perimeter of

cm.

Fill in the blanks.

1 cm

Re ga le du ca tio n

1 cm

Figure M

Figure L

Figure O

Figure N

F Figure P

(a) Each Each figure ffigu has a perimeter of (b) Figur Figures Fig e

and

cm.

have the same area of

cm2. 1 91

Solve It!

Michelle spent her vacation at her grandfather’s ranch. h. The map shows some of the features of the ranch.

guesthouse

gamess room

flower bed

Re g

herb garden

main ain house h

192

swimming pool

at on

Use your notebook to answer the questions below.

tool shed

Re ga le d

vegetable garden

(a) Find the area of the swimming wimming pool. (b) Find the perimeter ter of the guesthouse. gue mbined area ar of the guesthouse and (c) What is the combined games room? m?

(d) What is the e area of the main house? elle’s gra (e) Michelle’s grandfather wants to build a fence around the garden, the flower bed and the herb garden vegetable ga to keep the animals out. How many meters of fencing will he need? wm 1 93

At Home Find the perimeter and area of each figure.

1 cm

Re ga le du ca tio n

1 94

Area =

Perimeter =

Perimeter meter =

Area rea =

Area =

Perimeter = Perime

Perimeter =

1 cm

Compare the areas and perimeters of the figures in the geoboard. 1 cm

Re ga le du ca tio n

1 cm

(a) Find 2 figures that have the same area. figures th tha Figures gures

and a

both have an area of

cm2.

that have the same perimeter. (b) Find 2 ffigures igu Figure Fig Figures

and

both have a perimeter of

cm. 1 95

Looking Back Find the area of each figure in square units.

Re ga le du ca tio n

(a)

(b)

Area =

(c)

Area ea =

square units.

Area =

square units.

Area =

square units.

(d)

Area =

(d)

square units. squ squa nits i

(e)

Ar = Area

196

square units.

Find the area of each rectangle. (a)

(b)

10 m

Re ga le du ca tio n

12 cm 4 cm

Area =

20 in

(c)

6 in

Area =

(d)

3 cm

8 ft

(e)

8 ft

9 cm

Area =

A Area =

1 97

Find the perimeter of each figure. (a)

Re ga le du ca tio n

8 cm

12 cm

Perimeter =

5 cm

(b)

5 cm

Perimeter = Perime Perimet

5 cm

5 cm m

5 cm

(c)

12 m

11 m

10 m

17 m

Perimeter er =

1 98

Find the area and perimeter of each figure.

Re ga le du ca tio n

1 cm 1 cm

Area =

Perimeter =

Perimeter = Pe

Area =

Perimeter = Perime

Perimeter =

1 99

Fractions

Equal Parts Anchor Task

20 0

ion

Let’s Learn

Re ga le du ca tio n

Sophie takes a piece of paper and divides it into 4 parts. ts. Each part is the same size. The piece ce of paper is divided intoo equal parts.

4 equal parts

o been een divided divide into equal parts. These pieces of paper have also ach shape ha How many equal parts does each have?

4 equal parts

3 equal equa parts pa

8 equal parts

ha b These piecess of paper have been divided into parts of unequal sizes.

2 01

Sophie and Halle make a sandwich. To share the sandwich, they cut it into two equal parts. How much of the sandwich does each child get?

Re ga le du c

We get half each!

Each child gets one of two equal al parts. part We can express this as a fraction. tion ion..

Each child gets 1 , or one-half alf of the san sand sandwich. 2

A unit fraction is one equal qual al part of tthe whole. The top number of a unit fraction is always 1.. The bo bottom number of a unit fraction shows the number of equal equ parts. eq arts Blake folds a piece four equal parts. ece of paper into i What unit fraction one equal part? ction represents represen o 1 4

1 4

One-fourth is the same as one-quarter.

One part out o of o four is 1 , or one-fourth. 4

202

Let’s look at some unit fractions.

Re ga le du ca tio n

1 2

one-half

1 3

one-third

1 4

one-quarter

1 5

one-fifth

1 6

one-sixth

1 7

enth one-seventh

1 8

one-eighth

As a whole whol is divided d into more and more parts, the unit fraction representss a smaller and smaller part of the whole.

2 03

Let’s Practice Check the shapes that are divided into equal parts. s. Cross ross the shapes that are not divided into equal parts.

Re ga le du ca tio n

204

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Draw lines to divide the shapes into equal parts. (b)

Re ga le du ca tio n

(a)

two equal parts

(c)

four equal equ parts eq

(d))

five equal ual parts

(e)

three equal parts

(f)

six equal parts

eight equal parts

205

Circle the unit fractions.

Re ga le du ca tio n

206

Color and write the unit fraction. (b)

Re ga le du ca tio n

(a)

(c)

(d)

(e)

(f)

(g)

(h)

207

Write the unit fraction. (b)

Re ga le du ca tio n

(a)

208

(c)

(d) d)

(e)

(f)

(g)

(h)

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

Flick the paper clip to spin it.

Race your friends to name the unit fractions.

The first person to correctly name the fractions is the winnerr and makes the next spin.

uc ati on

209

Solve It!

Re ga le du ca tio n

Divide each square into quarters. Use a different way each time. The first one has been done for you. (a)

(c)

210

(b)

(d)

At Home Divide the shapes into equal parts.

Re ga le du ca tio n

(a) 2 equal parts.

ts. (b) 4 equal parts.

(d) 4 equ equal parts.

al parts. (e) 6 equal

(f) 4 equal parts.

211

Match the unit fractions.

1 2 1 3 1 4 1 5 1 6

1 Check the shapes hapes pes that show sh .

Re ga

ed uc ati on

212

Check the shapes that show 1 . 3

Re ga le du ca tio n

Check the shapes that show ow w 1 . 4

213

Check the shapes that show 1 . 5

Re ga le du ca tio n

214

Check the shapes that show w 1 . 6

Check the shapes that show 1 . 7

Re ga le du ca tio n

Check the shapes that show w 1 . 8

215

10. Fill in the blanks. The shape has

equal al parts. arts.

Re ga le du ca tio n

(a)

e shape hape is The unit fraction of the

(b)

The shape has as

equal parts. equ equa

The unitt fraction tion of th tthe shape is

(c)

The shape ha h has

The shape has

equal parts.

The unit fraction of the shape is

216

equal parts.

The unit fraction of the shape is

(e)

equal parts.

The uni unit fraction of the shape is

(d)

Solve It!

Re g

tio n

Michelle is having chicken and vegetables for dinner. She divides her dinner plate into five equal parts. She puts all of the peas in one equal part. What fraction of Michelle's dinner plate has peas? s? Draw a picture to show your understanding.

of Michelle's Miche dinner plate has peas.

217

Anchor Task

218

Parts of a Whole

219

Let’s Learn

Re ga le du ca tio n

When we take a whole and divide it into equal parts, we get fractions. The whole orange is cut into 2 equal pieces. es.

Each piece is a half, which we write as 1 . 2

2 halves lv make 1 whol whole.

1 whole

1 2

half

1 2

The numbers of a fraction have e special names. n

1 2

A half has a numerator n umerator of 1.

220

The top n number is called tthe numerator.

The bottom number is ca called the denominator.

... and a denominator of 2! d

Re ga le du ca tio n

Let’s cut an apple into 4 equal pieces. Each piece is a quarter.

1 whole

1 4

quarter

quarte quarter

quarter

4 quarters quarter w make 1 whole.

1 4

Ethan eats 3 pieces of the e apple. We W say he eats 3 quarters of the 3 apple. We can write e this as a a fraction frac . 4

1 4

I ate 3 quarterss of the apple!

1 4

221

du ca tio n

A pizza is cut into 4 equal slices. Jordan eats one slice. Let’s write the slice he ate as a fraction.

te as 1 . We write the fraction of pizza he ate 4

A farmer divides his field into 5 equal parts. He plants corn in two of the parts rts and wheat whe in the remaining parts.

Re g

1 5

2 5

Let's write e the quantity of each crop as a fraction. 2 of the field is i corn cor and 3 of the field is wheat. 5 5 2 and nd 3 make 1 whole. 5 5

222

1 5

3 5

1 5

Re ga le du ca tio n

What fraction of the shapes are colored? What fraction is not colored? Each part represents 1 . 4

3 parts are colored.

So 3 of the shape is colored. 4

1 part is not colored. ed.

So 1 of the shape ape iss not colored. color colo 4

Each part represent represents 1 . 6

2 parts artss are colored. colore

So o 2 of the sha shape is colored. 6

not colored. 4 parts are n

So 4 of th the shape is not colored. 6

Eac Each part represents 1 . 5

4 parts are colored.

So 4 of the shape is colored. 5

1 part is not colored.

So 1 of the shape is not colored. 5

223

Let’s Practice Write the numerator of each fraction.

Re ga le du ca tio n

224

(a)

1 4

(b)

3 5

(c)

2 6

(d)

4 7

(e)

1 8

(f)

2 3

(g)

1 5

(h)

3 4

( (i)

5 7

Write the denominator of each ach fraction. fractio

(a)

3 4

(b)

1 2

(c)

1 3

(d)

4 5

(e) (e

3 6

(f)

2 4

(g)

2 3

(h) (h

4 7

(i)

5 8

Match the fraction to its name in words.

4 7

four fifths

2 7

one third

1 3

enths fourr sevenths

4 5

fifth three fifths

3 5

one on half

3 4

two sevenths

1 2

five eighths

5 8

three quarters

Re ga le du ca tio n

225

What fraction of each pizza remains? (b)

Re ga le du ca tio n

(a)

226

(c)

(d)

(e)

((f)

(g))

(h)

Complete for each shape.

Re ga le du ca tio n

(a) is colored.

is nott colored.

is colored. d.

is n not colored.

is colored colored.

is not colored.

is colored.

is not colored.

is colored.

is not colored.

(b)

(c)

(d)

(e) (e

227

(f) is not colored. colore

Re ga le du ca tio n

is colored.

(g)

is colored. d.

is not colored.

is colored colored. colore

is not colored.

is colored.

is not colored.

is colored.

is not colored.

(h)

(i)

(j)j)

228

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

Flick the paper clip to spin it.

Race your friends to name the fractions.

The first person to correctly name the fractions is the winnerr and makes the next spin.

uc ati on

229

Hands On Play this game in pairs.

Roll 1 dice as the numerator and another dice as the denominator.

Re ga le du ca tio

I rolled a 1 then a 5. My fraction is 51 !

Color the matching fraction below.

If the fraction is not below, or already y colored, it's the other player's turn.

The first player to color all the fractions is the winner!

230

At Home Complete.

Re ga le du ca tio n

(a)

(b) (c)

(d) (e) (f)

has a numerator of

and a denominator minator ator of

has a numerator of

and a denominator enominator nominator o of

has a numerator of

and d a denomina denomin denominator of

has a numerator of

and d a denom den denominator of

has a numerator of

and a d denominator of

has a numerator or of

an and a denominator of

Circle the fraction greatest denominator. n with the grea (a)

(b)

1 2 2 3 1 7 3 5 6 8 3 4

1 2 4 7

4 5 1 8

2 7 5 6

3 4 2 3

Circle cle the fraction with w the smallest numerator. (a) (a b) (b)

6 7 1 2

5 8 2 5

4 6 3 4

3 5 4 5

231

Color to show the fraction. (b) two sixths

Re ga le du ca tio n

(a) three quarters

232

(d) one half

(e) four fifths

(f) four sixths

hree eighths (g) three

(h) five sixths

Divide into equal parts and color to show the fraction.

1 4

(b)

3 8

Re ga le du ca tio n

(a)

(c)

5 6

(d)

1 2

(e)

4 5

(f)

1 8

233

Write the fractions for each shape.

Re ga le du ca tio n

(a) is green.

iss blue.

is orange. ange. e.

is red.

is gree green.

is yellow.

is blue.

is purple.

is orange.

(b)

(c)

(d)

e)) (e)

234

Solve It!

Re ga le du ca tio n

Sophie, Michelle and Jordan each color a fraction of the he circle with w their favorite color. Together, they color the whole circle and their fractions actions ons are different from each other. Color the circle to show 1 possible way this can be done.

235

Fractions on a Number Line

al ed uc ati on

Anchor Task

Can you show fractions on a number line?

Number Line

I thinkk 21 sh should be in the center and 1. nter of 0 a

236

Let’s Learn Fold a piece of paper in half. The folded line is at the center of the paper.

Re ga le du ca tio n

1 2

folded line ne

wa We can find 1 on a number line in a similar way. 2

Divide the number line between en 0 and 1 into 2 equal parts. 1 2

1 2

is between en 0 aand 1 on a number line! lin

2 halves whole. es make 1 w thirds make 1 whole? How Ho w many th third ole?

237

Let’s divide a number line into 3 equal parts between 0 and 1. 1 3

1 3

Re ga le du ca tio n

1 3

2 3

1 3 of the way to 1. From 0, this is

2 3 of the way to 1.

From 0, this his iss

3 3 o the way to 1. of 3 =1 3 From 0, this is

The number line has been divided into 4 equal parts between 0 and 1. From 0, what is the he fraction at the green arrow?

Each mark on line is separated by 1 . n the number numbe num 4

1 4

3 4

The are 3 one quarter sections from 0 to the green arrow. There

So the green arrow is 3 . he gre 4

238

Let’s Practice Draw a point to show the fraction on the number line. ne.

Re ga le du ca tio n

(a) 1

(b) 1

(c)

1 4

(d) 5 6

(e) 3 4

(f) (f

3 6

239

Write the fraction shown on the number line.

Re ga le du ca tio n

(a) 0

(b)

(c)

(d)

(e)

f)) (f)

240

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

Re ga le du ca tio n

2 4

(b) 1 is represented by point

4 5

4 8

(d) 4 is represented resented ented by point p poin 4

2 4

represented repre by point (e) 5 is represen 7

241

At Home (a)

0 (b)

(c)

al ed uc ati on

1. Write the fraction.

(d)

242

Draw a point to show the fraction on the number line. 4

(b) 2

0 3.

ed uc ati on

(a) 1

Fill in the blanks.

(a) 2 is represented by point oint nt 6

3 6

(b) 3 is represented esented nted by point p po

Re ga

S 4 5

F 6 8

1 243

Comparing Fractions

Re ga le du ca tio n

Let’s Learn

Ethan and Dominic each bought a pizza of the same me size for lunch. lun lu After lunch, they compared how much pizza they ey had left. I have 21 of pizza left. the p

1 2

I have 31 of the pizza left.

1 3

Ethan has more pizza than han Dominic. Dominic

1 3

1 2

We say:

1 is greater th than 1 . 2 3

writ We write:

1 > 1 2 3

We say: say

1 is smaller s than 1 . 3 2

We write:

1 < 1 3 2

244

1 2

and 31 have a numerator of 1. They are unit fractions.

Let's compare some more unit fractions of the same size rectangle.

Re ga le du ca tio n

1 2

1 3

1 4

1 5

e off the fractio As the denominator increases, the size fraction decreases. We can see that 1 > 1 and 1 > 1 . 2

Compare other fractions you u see. ee. 1 2

1 4

1 > 1 2 4

1 2

1 5

We can use a number line to compare fractions!

1 < 1 5 2

1 5

1 3

1 > 1 3 5

245

1 7

uc ati on

4 circles of the same size are divided into 7 equal parts. Compare the colored fraction of each circle.

2 7

3 7

Each fraction has a denominator of 7.

4 7

Re ga le

As the numerator increases, the fraction increa becomes bigger! be

When the denominator ato is the ator e same, sam the size of the fraction increases as the numerator increases. umerato mera We can see that hat 4 > 3 and 1 < 2 . 7

Showing the fractions on a number mber line can help us compare!

246

1 7

2 7

3 7

4 7

Let’s Practice Fill in the blanks. (a)

ed uc ati on

The denominator of each fraction is is greater than

(b)

The denominatorr of each fr fraction is f

Re ga

is smaller maller ler than

(c)

denominator of each fraction is The denom de is i greater than

247

Write the unit fraction. Check the greater fraction

Re ga le du ca tio n

(a)

(b)

(c)

(d)

248

Circle the greater fraction.

6 7 3 5 6 8

5 7 2 5 4 8

(b)

1 4 2 7 2 5

3 4 5 7 5 5

1 6 1 7 1 4

1 8 1 3 1 5

Re ga le du ca tio n

(a) (c)

(e)

(f)

Circle the smaller fraction. (a) (c)

(e)

(d)

1 2 1 6 1 1

1 3 1 5 1 2

(b) (d) (f)

are the fractions fraction b Compare by writing ' < ' or ' > '.

(a)

(e))

2 6 5 5 5 8

3 6 4 5 3 8

(b) (d) (f)

2 7 1 7 2 3

4 7 2 7 1 3

249

At Home Fill in the blanks.

Re ga le du ca tio n

(a)

The denominator of each fraction is is greater than

(b)

f The denominatorr of each fr fraction is is smaller maller ller than

(c)

denominator of each fraction is The denom de is greater than

250

Write the unit fraction. Check the greater fraction

Re ga le du ca tio n

(a)

(b)

Compare the fractions ac actio by writing writ ' < ' or ' > '.

(a) (c)

(e)

((g) (i)

1 5 1 5 1 7 3 5 6 8

1 8 1 3 1 8 1 5 4 8

(b) (d) (f)

(h) (j)

1 3 1 4 1 7 2 7 3 3

1 2 1 5 1 6 3 7 2 3

251

Anchor Task

252

Equivalent Fractions

Let’s Learn

Re ga le du ca tio n

Jordan, Blake and Dominic each have a paper strip of the e same size. Jordan divides his paper strip into 2 equal parts. He colors 1 part. 1 of the p paper 2 strip is co colored.

ts. Blake divides his paper strip into 4 equal parts. He colors 2 parts.

2 of the paper 4

strip is colored.

ip into nto 8 equal parts. Dominic divides his paper strip He colors 4 parts.

4 of the paper 8

strip is colored.

Let’s compare each ch strip of o paper.

1 2

2 4

4 8

4 are equal. The e fractions 21 , 42 and a 8 are called equivalent fractions. Equal fraction fractions ar

1 2 4 = = 2 4 8

253

Re ga le du ca tio n

What fraction of each shape is shaded?

1 3

1 2 3, 6

and

2 6

3 9

1 3

are equivalent fractions.

2 6

3 9

6 9

What fraction of each shape is shaded? ded?

2 3

2 4 3, 6

and

4 6

6 9

2 3

are equivalent uivale fractions.

4 6

What fraction n of each ach shape shap is shaded?

3 4

3, 6 4 8

254

and

6 8

9 12

are equivalent fractions.

9 12

3 4

6 8

9 12

Let’s Practice What fraction of each shape is colored? Find the equivalent fractions.

Re ga le du ca tio n

(a)

and

are e equivalent quivalent fr fractions.

and an

are equivalent fractions.

(b)

255

Fill in the blanks to label the equivalent fractions.

Re ga le du ca tio n

(a)

1 2

1 3

3 4

(b)

(c)

(d)

256

(a) Circle the equivalent fraction of 1 . 2

2 3

2 4

2 5

Re ga le du ca tio n

(b) Circle the equivalent fraction of 1 . 4

1 2

3 6

2 8

2 10

3 8

1 2

(d) Circle the equivalent ent fraction of 2 . 3

6 9

1 3

3 6

(e) Circle the equivalent of 3 . equivalen fraction fra 4

1 2

3 8

9 12

fraction of 1 . (f) Circle Circle the equivalent equ 2

4 6

4 8

4 12

257

Solve It!

Re ga le du ca tio n

Use the fraction tiles to find 4 different pairs of equivalent ent fractio fractions. Color the fraction pairs and write them below. 1 2

1 2

1 3

1 4

1 3

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 0 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 1 12 12 12 12 12 12 2 2 1

(a)

1 4

1 5

1 6

1 7

1 9

1 11

1 6

(b)

(d)

1 5

1 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

258

1 4

At Home Find the equivalent fractions.

Re ga le du ca tio n

(a) A B C D

Fractions

and

are equivalent. uivalent lent..

and

are equivalent. equi equ

and

are equivalent.

and

are equivalent.

(b) P Q R S

Fractions

X Y Z

Fractions ns

(d) L M

N O

Fractions Frac

259

Fill in the blanks to label the equivalent fractions.

Re ga le du ca tio n

(a)

(b)

(c)

(d)

260

Circle the equivalent fractions. (a)

1 4

2 5

2 6

2 4

3 4

1 2

4 5

3 9

6 9

2 12

1 6

2 5

1 2

4 10

4 7

Re ga le du ca tio n

1 3

(b)

(c)

(d)

Write an equivalent fraction. ction. (a)

(c)

(e)

(g)

1 3 1 3

3 4

4 12

(b) (b

(d)

(f)

(h)

1 2

2 3

1 4

6 9

261

Looking Back Color and write the unit fraction. (a)

ed uc ati on

(b)

(c)

Check the shapes that show 1 .

Write the fractions tions ns for each e shape.

Re ga

(a)

is blue.

is orange.

is yellow.

is green.

(b)

262

Fill in the blanks. (a) 2 is represented by point

Re ga le du ca tio n

(b) 4 is represented by point

Compare the fractions by writing ' < ' or ' > '.

1 2 4 7

(a) (c)

1 5 6 7

(b)

(d) d)

1 6 1 3

1 3 2 3

Circle the equivalent fractions. quivalent valent frac fraction (a)

2 3

2 4

4 5

4 6

1 2

5 10

6 12

5 6

(b))

263

Data and Graphs

Picture Graphs With Scales

du ca i

Anchor Task

Re ga l

Creatures in Springfield Nature Park Spiders Ants Beetles Butterflies

264

Let’s Learn

Re ga le du ca tio n

The children in class 3A made a picture graph of theirr favorite fruits. Favorite Fruits

Apple

Orange Pear

Mango

stands for 2 children.

ure graph raph shows. show Let’s look at what the picture There are 4 2

for apple. ple. 1 6

st stan stands for 2 children.

4x2=8

In class 3A, 8 children like ap apples. There are re 8 2

mango. for ma mang 6

8 x 2 = 116 In classs 3A 3A, 16 children like mangoes.

2 65

Re ga le du ca tio n

Chelsea, Sophie, Halle and Riley made a picture graph to compare the number of movies they watched in a year. Movies Watched This Year

Chelsea

Sophie

Halle

Riley y

stands for 3 movies.

There are 3 3

for Sophie. e. 1

stands stan for 3 movies. stand

3x3=9 Sophie watched 9 movies. There are 5 3

for Chelse Chelsea. 9

How many more movies did Chelsea watch than Sophie?

5 x 3 = 15 Chelsea helsea watch watched 15 movies.

15 – 9 = 6 Chelsea watched 6 more movies than Sophie. w watc

26 6

Let’s Practice The picture graph shows the number and color off Blake’s ake’s toy cars.

Re ga le du ca tio n

Toy Cars at Home

Blue Red

Yellow Green

stands for 2 toy cars.

(a) How many red cars does es Blake ake have? have x

Blake has

red ed cars. s

w cars does doe Blake have? (b) How many yellow x

Blake has as

yellow c cars.

w many any more red r cars than green cars does Blake have? (c) How –

Blake ake has

more red cars than green cars.

(d) Ho (d H w many ma fewer blue cars than red cars does Blake have? How –

Blake lake has

fewer blue cars than red cars.

2 67

The picture graph shows the animals Keira spotted during a field trip to the wetlands.

Re ga le du ca tio n

Wetland Animals

Fish

Birds

Crabs

Frogs

Lizards

stands for 3 animals.

(a) Which animal did Keira ra spot the most? mo

(b) How many fish and d crabs bs did Keira Ke spot in all? x

ed d Keira spotted

fish sh and a crabs in all.

Keira eira spotted

more fish than lizards.

Ho ow many animals anim (d) How did Keira spot that were not birds? x

spotted K i spo Keira

268

animals that were not birds.

The picture graph shows the money Riley saved in 5 weeks.

Re ga le du ca tio n

Money Saved Week 1

Week 2

Week 3 Week 4

Week 5

stands for $5.

d Riley ey save $15? $15 $1 (a) In which week did

(b) How much money ey did Riley save in Week 4? x

Riley saved ved d$

in We Week 4.

w much uch more money mon m (c) How did Riley save in Week 3 than Week 5?

–

Riley ley saved $