Fractions Grade 3 Student Book

GRADE 3 STUDENT BOOK

www.mathseeds.com

My Name

Fractions

My Name

Fractions

Mathseeds Fractions Grade 3 Student Book

Blake Publishing

Locked Bag 2022

Glebe NSW 2037

www.blake.com.au

Publisher: Katy Pike

Written by Megan Smith

Design and layout by the Modern Art Production Group

Fractions

•

Grade 3

• Unit fractions ...............................................................................................

/ /

• Unit fraction multiples ......................................................................

/ /

• Fractions of collections ....................................................................

/ /

• Sharing and fractions .........................................................................

/ /

• Fraction number lines .........................................................................

/ /

• Compare fractions ................................................................................

/ /

• Compare fractions of collections .......................................

/ /

• Who am I? ........................................................................................................

/ /

• Fraction bingo ...............................................................................................

/ /

iii

Topic 1: Fractions to 1

Topic 2: Fractions over 1

• Whole number fractions .................................................................

/ /

• Whole number diagrams .................................................................

/ /

• How many wholes? .................................................................................

/ /

• Making whole number fractions ............................................

/ /

• Fractions over 1 ...........................................................................................

/ /

• Recognize fractions over 1 ..........................................................

/ /

• Fraction number lines over 1 .......................................................

/ /

• Compare fractions over 1 ..............................................................

/ /

• Mixed numbers ............................................................................................

/ /

• Compare mixed numbers ...............................................................

/ /

• Party problems .........................................................................................

/ /

• Compare fractions games ...........................................................

/ /

10

11

12

13

14

15

16

17

18

19

20

21

Contents

Date Completed

1

2

3

4

5

6

7

8

9

Page

Date Completed

Resources

• 8-sided spinner

• 6 and 10-sided spinners

• Blank fractions

22

23

24

iv

Fractions

•

Grade 3

In this book

The Mathseeds program teaches children the core maths and

problem solving skills needed to be successful at school.

Each online lesson begins by introducing and modeling a

mathematical concept. The child then completes a wide range

of activities to practice the new skill. These activities present

the content in many different ways, so children learn to use

and apply each new skill in a variety of situations.

This book is designed to supplement the online program with

more exercises in the core mathematical concepts. Each unit

focuses on a topic within the main learning strand, presenting

a series of pen and paper activities, word problems, puzzles,

and games to practice their skills and understanding.

The topics in this book align with the following components of

the State Standards:

3.NF.A.1 Understand a fraction 1/b as the quantity formed

by 1 part when a whole is partitioned into b equal parts;

understand a fraction a/b as the quantity formed by a parts

of size 1/b.

3. N F. A . 2 Understand a fraction as a number on the number

line; represent fractions on a number line diagram.

3. N F. A . 3 Explain equivalence of fractions in

special cases, and compare fractions by

reasoning about their size.

3.G.A.2 Partition shapes into parts with equal

areas. Express the area of each part as a

unit fraction of the whole.

1

Fractions

•

Grade 3

•

Topic 1

Unit fractions are 1 part of an equally divided shape.

Unit fractions have a numerator of 1 for 1 part:

The denominator tells us how many parts in total:

1 Match.

Unit fractions

Fractions to 1

one sixth

one eighth

one fifth

one third

one half

one fourth

!2

!3

!4

!5

!6

!8

a

b

c

d

e

f

!2

Fractions

•

Grade 3

•

Topic 1

2

Unit fraction multiples

Fractions to 1

1 Color the fractions.

a !4 red, @4 yellow, !4 green

b @5 blue, #5 purple

c @6 yellow, @6 green, !6 pink, !6 blue

2 Write the fractions.

a b

c d

e f

= =

Fractions can refer to more than 1 part

of an equally divided shape.

The numerator tells us how many parts

in the fraction. The denominator tells us

how many parts in total.

#4

denominator

numerator

3

Fractions

•

Grade 3

•

Topic 1

Fractions of collections

Fractions to 1

Fractions can refer to a share of

a collection. The numerator tells

us how many items in the share.

The denominator tells us how

many items in total.

#8

denominator

numerator

1 a How many sea creatures are in this group? ______

b How many crabs? ______ c How many fish? ______

d How many seahorses? ______ e How many dolphins? ______

2 What fraction of the group are

a crabs? b fish? c seahorses? d dolphins?

3 What fraction of the group are

a flowers? b sticks? c leaves?

4 What fraction of the group are

a oranges? b apples? c pears?

Fractions

•

Grade 3

•

Topic 1

4

Sharing and fractions

Fractions to 1

1 Draw a diagram to share the items equally.

2 What fraction of the collection does each person get?

a 2 people sharing 8 balloons.

b 3 people sharing 9 party hats.

c 4 people sharing 12 cupcakes.

d 5 people sharing 10 cups.

5

Fractions

•

Grade 3

•

Topic 1

Fraction number lines

Fractions to 1

2 Fill in the fraction number lines.

1 Put these in order from smallest to largest.

3 Put these in order from smallest to largest.

0

!3 @8

#3

=

a

$4

=

1

0

!8 @4 #8

b

0

!5 @8 #8 $8

%5

=

1

c

0

!6 @6 #6 $6 %6 ^6

1

*8

=

d

0

!8 @8 #8 $8 %8 ^8 &8

*8

=

e

a

!5, @5, $5, #5, %5 ____________________________________

b

^6, !6, #6, %6, $6, @6 ____________________________________

c

1, #8, @8, &8, $8, !8, %8, ^8 ____________________________________

!5, !2, !6, !4, !8, !3 ____________________________________

6

Fractions

•

Grade 3

•

Topic 1

Compare fractions

Fractions to 1

1 Circle the larger fraction. Color that fraction of the food.

2 Use the correct symbol:

<

or

>

.

a

!2 !4 b #4 !4 c @3 !3

d !5 $5 e %6 !6 f !8 &8

g @8 %8 h @4 #4 i #5 $5

ba

!4 #4 !3 @3

dc

^8 @8 %8 #8

fe

$6 @6 #5 @5

Compare the numerators in fractions

with the same denominator:

$8 &8

<

7

Fractions

•

Grade 3

•

Topic 1

Compare fractions of collections

Fractions to 1

1 Color each fraction of the collection.

2 Write the correct symbol in the box:

>

or

<

.

(0 ^0

a b

#6 %6

c d

^8 @8 !4 #4

e f

%5 @5 #6 $6

g h

!8 #8 $0 @0

8

Fractions

•

Grade 3

•

Topic 1

Who am I?

Draw a diagram to find each answer.

Fractions to 1

1 Dahlia shares a bag of 20 bouncy balls between 5 people.

a How many balls does each person get? _____

b What fraction of the collection does each person get?

2 Ash has 16 cards. He gives each person 4 cards and

has none left.

a How many people does Ash share his cards with? _____

b What fraction of the collection does each person get?

3 Fox bakes 18 cupcakes. She eats 9 and Joel eats 9.

a How many people shared the cupcakes? _____

b What fraction of the cupcakes did each person eat?

9

Fractions

•

Grade 3

•

Topic 1

Fraction bingo

Play in pairs

rr

, small groups, or as a class. You need one

8-sided spinner and one 6-sided spinner (see pages 22 and 23).

Each player needs a pen and a copy of page 24.

1 On the 8-sided spinner write the numbers 1-8 for numerators.

On the 6-sided spinner write 2, 3, 4, 5, 6, 8 for denominators.

2 Each player writes 9 different fractions on their sheet.

3 Spin both spinners to make a fraction.

If you get a fraction over 1, reverse the numerator and

denominator, eg

%2



@5

.

4 All players look for the fraction on their grid.

If they have it, they cross it off.

5 Repeat steps 3 and 4, taking turns to make a fraction.

The winner is the first person to cross out all their fractions

and call out ‘Bingo!’

Harder variations:

Include whole number fractions and fractions over 1.

Add a third spinner and make mixed numbers.

Fractions to 1

6

1

5

7

4

8

3

2

6

7

10

Fractions

•

Grade 3

•

Topic 2

Whole number fractions

Fractions over 1

2 Fill in the fractions to match.

a b

c d

e f

1 Complete. Use the words numerator or denominator for

1a and 1b.

a In the fraction

^3 , 6 is the _______________________________________ .

b In the fraction

^3 , 3 is the _______________________________________ .

c Draw

^3 .

d How many thirds in

^3 ? ________

e How many thirds in one whole? ________

f How many wholes in

^3 ? ________

Fractions

•

Grade 3

•

Topic 2

11

Whole number diagrams

Fractions over 1

1 Match the fractions.

a b

c d

e f

2 Draw shapes to show these fractions.

a b

c d

18

6

20

5

18

3

12

4

8

10

2

10

5

6

2

16

4

9

3

12

Fractions

•

Grade 3

•

Topic 2

How many wholes?

Fractions over 1

1 Complete this sentence using the words numerator and

denominator.

To find the number of wholes in a fraction, divide the

________________________________ by the ________________________________ .

2 Find the number of wholes.

a

= 12 ÷ 2 = ____

12

2

c

= ____ ÷ ____ = ____

16

8

e

= ____ ÷ ____ = ____

30

5

b

= 20 ÷ 4 = ____

20

4

d

= ____ ÷ ____ = ____

21

3

f

= ____ ÷ ____ = ____

12

6

a

= ____ wholes

2

c

= ____ wholes

15

3

e

= ____ wholes

30

6

b

= ____ wholes

10

1

d

= ____ wholes

40

4

f

= ____ wholes

24

8

3 Find the number of wholes.

4 Complete.

a

= 7 wholes

2

4

c

e

= 5 wholes

= 6 wholes

25

b

= 9 wholes

1

d

f

= 5 wholes

= 8 wholes

40

48

Fractions

•

Grade 3

•

Topic 2

13

Making whole number fractions

Fractions over 1

a Write a fraction for each number of wholes.

b Divide the shapes to match.

1 3 wholes

2 6 wholes

3 4 wholes

4 10 wholes

5 5 wholes

14

Fractions

•

Grade 3

•

Topic 2

Fractions over 1

1 Color the parts to match the fractions.

a b

c d

e f

2 Circle the correct answer.

a In the fraction

%3 , the type of fraction is (thirds) (fifths).

b In the fraction

%3 , I colored in (5) (3) parts.

3 Complete these sentences using the words numerator and

denominator.

a In the fraction

%3 , 5 is the ______________________ .

b In the fraction

%3 , 3 is the ______________________ .

In a fraction over 1 …

c the ______________________ is the number of parts in one shape.

d the ______________________ is the number of colored parts.

e the ______________________ is larger than the ______________________ .

14

5

11

6

13

8

5

3

7

2

6

4

15

Fractions

•

Grade 3

•

Topic 2

Recognize fractions over 1

Fractions over 1

1 Match.

a

b

c

2 Write fractions to match.

a

b

c

%2

&3

(4

=

16

Fractions

•

Grade 3

•

Topic 2

Fraction number lines over 1

Fractions over 1

Put these fractions in order on the number lines.

0

1 !2, #2, %2, @2, $2

0

2 ^4, #4, %4, @4, $4, !4

0

3 ^5, #5, &5, @5, $5, %5, *5, !5

0

4 &3, !3, #3, (3, %3, @3, ^3, $3, *3

5 (6, !6, $6, &6, @6, *6, %6, #6, ^6

17

Fractions

•

Grade 3

•

Topic 2

Compare fractions over 1

Fractions over 1

Write each fraction. Color the fraction of the food you would

rather eat.

3 a b

1 a b

2 a b

4 a b

5 a b

18

Fractions

•

Grade 3

•

Topic 2

Mixed numbers

Fractions over 1

1 Color the fractions.

2 Fill in the fraction number lines.

0

!8 @4 #8

1 1!4

^8 &8

2

a

0

!3 @4

1

1!4

2

b

0

!5

!2

$5

2 4

1

2!2

1!5 1$5

&8

c

d

a

c

b

d

1#81#4

1#51%6

19

Fractions

•

Grade 3

•

Topic 2

Compare mixed numbers

Fractions over 1

1 Complete the number line.

3 Compare these pairs of mixed numbers using:

>

<

=

a 2!4 3!4 b 2!4 2#4 c 3!8 3$8

d 1#4 1!4 e 2!2 2#4 f 3!4 3$8

g 1@8 1!8 h 2^8 2%8 i 4$8 4$8

4 Write a fraction to complete the sum.

a #4 > b 1 = c !2 <

d 1!2 = e 1 < f 1^8 >

g 1%6 > h 1 > i 1!4 <

0

!6 #6 $6

1 21!6 1@6 1$6

a b c d

2 Order from smallest to largest:

1!2 #4 2!2 1!4 2#4 !2 2

a b c d e f g

20

Fractions

•

Grade 3

•

Topic 2

Party problems

Fractions over 1

There are 6 party bags to fill. Share these items equally.

a How many lollipops are there? _______

b How many go in each party bag? _______

c What fraction of the lollipops goes in

each bag?

a How many squares of chocolate are there? _______

b How much goes in each bag? _______ pieces

c What fraction of the bar goes in each bag?

a How many stickers? _______

b How many in each bag? _______

c What fraction of the stickers

goes in each bag?

4 What is in one party bag?

Draw the contents.

5 Share this cake between

8 people. Draw the lines to

cut along.

1

2

3

♥ ★ J ♥ ★ J

J

♥ ★ J ♥ ★

★ J ♥ ★ J ♥

Happy

Birthday

21

Fractions

•

Grade 3

•

Topic 2

Fractions over 1

Compare fractions games

Play in pairs

rr

. You each need a pen and a copy of page 24.

You also need one 8-sided spinner numbered 1-8 (see page 22).

Aim of the game:

Make the largest fraction, including fractions over 1.

1 Each person needs 3 blank fractions for each game.

Hide your sheets from each other.

2 Take turns spinning a digit on the spinner.

3 Decide which fraction to put the digit in and whether it will be a

numerator or denominator. Write the digit in a box. Once written

it can’t be changed.

4 After 6 spins you should both have 3 fractions. Compare them.

You may want to draw fraction diagrams. The winner has the

largest fraction.

Variation: Aim to make the smallest fraction.

Play as a class. You need 2 class sets of empty fractions

(see page 24) cut into separate fraction cards.

1 Make a class set of fraction cards:

a Give each person 2 cards.

b They write a fraction under 1.

c And a fraction over 1.

2 Shuffle all the cards and deal 1 card to each person.

3 Pair up and compare your fractions. Draw a diagram on the back

of the card if necessary.

4 If you have the smaller fraction, sit down.

If you have the bigger fraction, pair up with someone new.

5 Keep pairing up and comparing fractions until one person is left.

The winner has the largest fraction.

Variation: The winner has the smallest fraction.

GO LARGE

BIG, BIGGER, BIGGEST

5

1

4

8

22

Fractions

•

Grade 3

•

Resources

8-sided spinner

Resources

Materials:

• board

• paper clip

• paper fastener

(split pin)

• adhesive tape

• scissors.

1 Print or glue the spinner and the arrow

onto board. Write on the numbers.

You can laminate them after this.

2 Bend out one end of the paper clip to

make the spinning pointer.

3 Insert the split pin with the paper clip on it

through the center of the spinner.

4 Split the back of the pin and tape the ends

down. The top of the split pin should sit

about half an inch above the card to allow

the paper clip pointer to spin freely.

5 Tape the arrow onto the paper clip.

6

1

5

7

4

8

3

2

23

Fractions

•

Grade 3

•

Resources

6 and 10-sided spinners

Resources

24

Fractions

•

Grade 3

•

Resources

Blank fractions

Resources