unit and non-unit fractions...unit 9: fractions (1), lesson 1 m05 powermaths practice bk 3b 89853...

$: Unit and non-unit fractions...Unit 9: Fractions (1), Lesson 1 M05 PowerMaths Practice Bk 3B 89853 U09.indd 122 20/06/2018 12:09 3 Complete the sentences. 1 5 of the cars are . have$
1 Complete the sentences.

There are birds altogether.

The denominator is .

birds are fl ying to the right.

The numerator is .

of the birds are fl ying to the right.

Unit and non-unit fractions

2 Match each shape to the fraction that shows how much of the shape is shaded.

14

23

12

122

➜ Textbook 3B p164Unit 9: Fractions (1), Lesson 1

M05 PowerMaths Practice Bk 3B 89853 U09.indd 122 20/06/2018 12:09


15 of the cars are .

have numbers on the roof. are .

4 a) Divide the bar into 2 equal parts. Shade in 12 .

b) Divide the bar into 3 equal parts. Shade in 13 .

c) Use your answers to a) and b) to help complete the following expressions. Use the <, = or > sign for each expression.

12 1

3 13 1

2

1 3

123

Unit 9: Fractions (1), Lesson 1


Colour the hexagon so that it is 12 yellow

and 16 red.

How do you know you have coloured the shape correctly?

Refl ect

5 Shade 12 of each of the three large squares. Show 1

2 in as many different ways as possible. You may fi nd it useful to copy the large squares on to a piece of squared paper.

A B C

I know that the fraction shaded yellow is a 12 because

I know that the fraction shaded red is a 16 because

124



1 Complete the missing information.

a) out of the 6 eggs are in the box.

This is of the whole.

out of the 6 eggs have been used.


+ = 1

b) out of the parts is shaded.


out of the

parts are not shaded.


+ = 1

Making the whole

125



2 a) 35 + 25 = 1 whole

Use the bar model to show how you know this is true.

b) 14 + 34 = 1

Use the bar model to show how you know this is true.

3 Complete these number sentences.

a) 58 + = 1 d) 7

7 = 37 +

b) = 25 + 35 e) 1 = 16 +

c) + 19 = 99 f) 4

9 + = 1

4 In a group, 47 of the children are sitting down.

What fraction of the group are standing up?

of the group are standing up.

1

1

126



Refl ectWhat did you learn about making the whole in today’s lesson?

6 Write two different ways that you could share the cake between the 2 plates.

5 Explain the mistake in this calculation.

23 + 1

3 = 36

I will record each different way as a new calculation.

Can you use the words numerator and denominator in your answer?

1 whole cake = + 1 whole cake = +

Today I learnt that

127



1 What fraction of each shape is shaded?

a) 10

of the circle is shaded.

b) 10

of the cuboid is shaded.

c)

of the smiley faces are shaded.

Tenths 1

2 Colour the correct fractions.

a) Colour 410 of the triangles.

b) Colour 710 of the rectangle.

c) Colour the circles. Leave 210 of the circles white.

128



3 2 tickets have been taken off a strip of 10 tickets.

a) What fraction of the 10 tickets are left?

are left.

b) Use the number line to show the fraction of tickets that have been taken off and the fraction of tickets that are left.

10

10

10

5 Richard and Jamilla are both counting in tenths.

Richard starts at 0 and counts up. Jamilla starts at 1 and counts down.

If they both count at the same speed will they ever say the same fraction at the same time?

Explain your answer.

Richard starts at 0 and counts up. Jamilla starts at 1 and counts down.

4 Complete the calculations. Show each one on a number line.

a) 1 = 110 +

b)

+ 310 = 1010

129



Refl ectWhat will the next 2 numbers in the sequence be?

7 Lexi has been experimenting to see how many different ways she can make a whole using tenths.

+

= 1 whole

How many different possible ways can you fi nd?

6 This strip of paper is 110 of the whole.

Explain what shape the whole could have been. Is there more than one possibility?

I know the next 2 numbers in the sequence will be and

because

710, 8

10, 910,

,

130



1 Shade 110 of each bar model and complete the calculations.

a) 1 out of the 10 parts must be shaded. 1 ÷ 10 =

b) There are 2 wholes. 1 out of the 10 parts in each whole must be shaded.

Altogether tenths have been shaded. 2 ÷ 10 =

c) 3 ÷ 10 =

Tenths 2

1 whole

1 whole

1 whole 1 whole 1 whole

1 whole

2 wholes

3 wholes

131



d) 5 ÷ 10 =

2 There are 30 grapes in a bag. Each child gets 110 of the bag of grapes.

5 wholes

amount 1 child gets

110

1 whole 1 whole1 whole 1 whole 1 whole

How many grapes does each child get?

Each child gets grapes.

3 Complete the calculations.

a) 4 ÷ 10 = 10

d) 7 ÷ 10 =

b) 5 ÷ 10 = 10

e) 10 ÷ 10 =

c) = 6 ÷ 10 f) 0 ÷ 10 =

132



Prove that 2 divided by 10 is equal to 210 .

Refl ect

5 There are 10 children at a party. There are 5 pizzas.

Each child eats 110 of the 5 pizzas.

What fraction of each pizza does each child eat?

How should the pizzas be cut so that this is possible?


a) ÷ 10 = 210 c) 3 ÷ 10 =

b) 9 ÷ = 910 d) ÷ 10 =

I know 2 divided by 10 is equal to 210 because

133


I wonder if there is more than one way that this could be solved.



a) The whole has been split into parts.

Each part is

. A represents the number

.

b) 1 has been split into parts.

Each part is

. B represents the number

.

c) 1 has been split into parts.

Each part is

. C represents the number

.

Fractions as numbers 1

A 10

18

18

18

18

18

18

18

18

C 10

19

19

19

19

19

19

19

19

19

B 10

15

15

15

15

15

134

Unit 9: Fractions (1), Lesson 5➜ Textbook 3B p180


2 What fractions are shown at points A, B and C?

A = B = C =

3 Mark these fractions in the correct positions on the number lines.

a) 13

b) 48

4 Help Astrid position these fractions on the number line.

310 5

10 910

I do not think I can use the resource that I have been given to help me.

10

10

1015

15

15

15

15

A B C 10

I do not think I can use the resource that I have been given to help me.

135



Refl ectComplete these sentences.

6 Mark 18, 1

4 and 12 on the number line.

a) What size is the interval between 18 and 1

4?

b) What size is the interval between 18 and 1

2?

5 Explain the mistakes that have been made.

28

39

410

10

10

To place 15 on a number line you must fi rst

and then

To place any fraction on a number line you must fi rst

and then

136



1 Mark the lengths on the number lines.

a) 3 15 m

First, I fi nd the whole number on the number line.

Then I count on fi fth.

b) 2 35 m

First, I fi nd the whole number on the number line.

Then I count on fi fths.

c) 4 34 m

d) 1 23 m


5 m0 m 1 m 2 m 3 m 4 m

5 m0 m 1 m 2 m 3 m 4 m

5 m0 m 1 m 2 m 3 m 4 m

5 m0 m 1 m 2 m 3 m 4 m

137



2 Mark the fraction shown in each picture on the number line.

3 What fractions are marked by the letters A, B and C?

A =

B =

C =

4 Which of these numbers could be represented on the number line by X?

3 14 2 36 4 7

8 3 910

Explain your choice.

0 1 2 3

0 1 2 3

0 1 2 3

2 4

X

14

14

14

14

14

14

14

14

0 1 2 3 4

A B C

a)

b)

c)

138



Refl ect

Mark 1 25 on the number line and then complete the sentences.

5 Danny and Aki are counting at the same speed.

Danny is counting up in quarters from 2.

Aki is counting down in eighths from 4.

Will they say the same number at the same time?

Explain your answer.

0 1 2 3 4

0 1 2 3

To accurately mark 1 25 on the number line I must fi rst

and then

139



1 Identify the fractions shaded. Write the fractions in the boxes.

a)

b)

c)

d)

e) Place the 4 fractions that you have identifi ed on the number line.


0 1 2 3

18

18

16

16

16

16

16

161 whole1 whole

16

16

16

16

16

16

18

18

18

18

18

18

18

18

18

18

18

18

18

18

1 whole

1 whole

140



2 What fractions are shown by letters A, B and C on the number line?

Explain your answers.

A =

This is because

B =

This is because

C =

This is because

3 Toshi is 1 34 metres tall. His nephew, Kit, is 18 metre

shorter than 1 metre. Mark both of their heights on the number line.

2 3 4 5

CA B

0

1 m

2 m

141



Refl ect

Explain how you would place 1 58 on the number line below.

4 Starting with the section of the number line below, complete the number line up to 3 and back to 0.

1 47 1 57

5 Mark 2 78 on the number line below.

I can use the intervals given to help me fi nd 78 .

2 4

0 321

142



1 a) A school buys 36 new books.

Each class gets 16 of the books.

How many books does each class get?

36 ÷ =

16 of 36 books = books

Each class gets books.

b) The 36 books are shared between more classes.

Now each class gets 19 of

the books.

How many books does each class get?

÷ =

of 36 books = books

Each class gets books.

Fractions of a set of objects 1

?

?

143



3 Amelia cuts a chocolate cake into 5 slices. She wants to decorate the cake with 15 cherries.

How many cherries should she put on each slice so they are all the same?

Amelia should put cherries on each slice of cake.

4 Zac has 12 sweets in his hand. This is 12 of the whole bag. v

How many sweets are in a whole bag?

2 13 of 21 =

?

12

12 of = 12

There are sweets in a whole bag.

144



Refl ect

5 a) Luis has a bunch of balloons.

He bursts 8 balloons. This is 13 of the total balloons.

How many balloons did Luis have before he burst any?

Luis had balloons to start with.

b) Lee bursts 14 of the

remaining balloons.

How many balloons does Lee burst?

Lee bursts balloons.

Aki has a pack of 30 pencils.

Do you agree or disagree with Aki?

Explain your reasoning to a partner.

Total number of balloons

8

Balloons Luis bursts

I have arranged the pencils into fi fths.

15 of 30 = 5

145



1 a) Find 14 of 16 fl owers. c) Find 1

6 of 18 glasses.

16 ÷ 4 = ÷ =

14 of 16 fl owers = fl owers 1

6 of 18 glasses = glasses

b) Find 34 of 16 fl owers. d) Find 56 of 18 glasses.

16 ÷ 4 = ÷ =

× 3 = × =

34 of 16 fl owers = fl owers 5

6 of 18 glasses = glasses


16

16

18

18

146



2 13 of 18

18 ÷ 3 =

23 of 18

18 ÷ 3 =

× 2 =

3 A slice of cake has 4 candles on it. This is 18 of the total

number of candles on the cake.

How many candles are on the whole cake?

The cake has candles altogether.

4 Join each fraction to its correct answer.

23 of 12 3

4 of 20 25 of 25 7

8 of 16

10 8 15 14

147



Refl ect

I can fi nd a fraction of an amount by

6 Which would you rather have? Show your working.

34 of £16 or 35 of £20

5 Lee has used counters to show 34 of 24. Do you agree with his answer?


34 of 24 = 6

I agree / disagree because

148


1 a) Find 34 of 100 pencils.

100 ÷ 4 =

× 3 =

34 of 100 pencils = pencils

b) Find 23 of 180 g of fl our.

÷ =

× =

23 of 180g of fl our = g

c) Find 25 of 95 dog biscuits.

÷ =

× =

25 of 95 dog biscuits =

d) Find 38 of 32 km.

÷ =

× =

38 of 32 km = km


180 g

100pencils

100 pencils

180 g

95 dog biscuits

32 km

149



2 A piece of ribbon was 32 cm long.

34 of the ribbon was used to wrap a present.

What length of ribbon was used?

cm of ribbon was used.

3 Finley’s garden is 60 m long.

56 of the garden is being planted with fl owers.

How many metres of the garden will have fl owers? Show your working.

m of the garden will have fl owers.

4 Use the fact 15 of 60 = 12 to fi nd the missing numbers below.

a) 25 of 60 = b)

of 60 = 48 c) 35 of = 36

32 cm

150



Refl ect

Explain how you would work out 35 of 80.

6 34 of a race will always be a longer distance to run

than 12 of a race.

Is this always, sometimes or never true? Explain your answer.


a)

of 48 = 32

b) 23 of = 18

48

8 8 8 8 8 8

Explain how you would work out 5

First

then

?

18

151



Problem solving – fractions1 There are 24 kg of rice in a sack. A restaurant uses 23 of the rice.

How many kilograms of rice are left in the sack?

There are kg of rice left in the sack.

20

12

Apples

20

15

15

Oranges

There are 20 pieces of fruit in a bowl.

12 are apples, 25 are oranges and the rest are bananas.

a) How many apples are in the fruit bowl?

12 of 20 =

There are apples in the fruit bowl.

b) How many oranges are in the fruit bowl?

of 20 =

÷ = × = oranges

2

152



3

After the fi rst roll of a dice the counter is moved 14 of the way along

the number track.

After the second roll of the dice it is moved another 15 of the way

along the track.

What number does the counter fi nish on?

14 of 20 = 1

5 of 20 =

+ =

The counter fi nishes on number .

c) How many bananas are in the fruit bowl?

What fraction is this of the whole?

apples + oranges =

20 − =

There are bananas. This is of the whole.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

4 23 of a group of children are boys. 18 children in the group are girls.

How many children are there in the group?

There are children in the group.

153



My journal

112 of 60 = 5

What other fraction number sentences can be written from this fact?

Refl ect

5 Holly has baked some blueberry, chocolate chip and raspberry muffi ns.

18 of the muffi ns are blueberry.

38 of the muffi ns are chocolate chip.

There are 12 raspberry muffi ns.

How many muffi ns did Holly bake in total? How many muffi ns did Holly bake in total?

You could use a bar model to help.

Holly baked muffi ns.

154



End of unit check

My journal

➜ Textbook 3B p208

1 Here is a representation that has been used to solve a problem.

What question could have been asked?

What calculation would fi t this question?

155

Unit 9: Fractions (1)


Power check

How do you feel about your work in this unit?

2 Can you think of more than one possible question?

156



Power puzzle

Toshi and Jen are going on a picnic.

They want to share the following items of food between them.

Is it possible to share all these items of food?

How much of each item of food will they each get?

Write number sentences that show how each item of food will be shared.

I would give each of them half of each of the juice cartons.

They want to share the following

500 ml 500 ml500 ml 500 ml

I wonder if it is possible to share some of the food and drink out in different ways.I would give them one carton of juice each.

157



unit and non-unit fractions...unit 9: fractions (1), lesson 1 m05 powermaths practice bk 3b 89853...

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