1

Introduction for teachers and parents

In this book there are single-page exercises covering most of the mathematics work that children will meet in Year 6.

On each page there are some examples/hints along with a set of questions for children to answer. There is space for answers to be written in the book.

Each exercise ends with a challenging question for the more able children.

At the end of each page, children are invited to answer a self-assessment question.

Using this book

The exercises in the Maths Practice Questions books are not intended to be used in the initial teaching of new mathematics topics.

However, they can be used as:

Homework activities - to consolidate work done in class.

End of topic class activities - to give children the opportunity to check their understanding of a particular topic.

Assessment tasks - allowing teachers to establish whether or not children are secure in their understanding of a topic.

Year 6Maths Practice Questions

2

ContentsContents

Number and Place Value 3 - 7

Addition, Subtraction, Multiplication and Division 8 - 16

Fractions, Decimals and Percentages 17 - 27

Ratio and Proportion 28 - 31

Algebra 32 - 36

Measurement 37 - 42

Statistics 51 - 54

Appendix - Information for Parents 55 - 57

Notes 58 - 60

Geometry 43 - 50

Are you ready for

this?

3

Number and Place Value

A Place valueYou should know the values of all the digits in any number up to 10 million (10,000,000).

What is the value of these digits? Write your answers in words.1

6 in 1,640,225

5 in 1,249,560

8 in 8,745,645

Nine million, six hundred and forty-one thousand, eight hundred and twelve

Eight million, two hundred and ten

Can you write these numbers in digits?2

What is 10 million take away 1? Write your answer in digits.3

I’m confi dent I’m nearly thereI can read, write, order and compare numbers up to 10,000,000.

Can you put these numbers in order of size, smallest to largest?4

9,482,169 9,284,169 9,248,169 9,248,196 9,284,196

If you started with 3,445,841 and doubled it, what digit would be in the millions column?

What digit would be in the 1000s column?

5Brain

training!

ix d

e

t

9,641,812

8,000,210

9,999,999

9,248,169 9,248,196 9,284,169 9,284,196 9,482,169

6

1

4

I’m confi dent I’m nearly thereI can round numbers to the nearest

10, 100, 1000, 10,000, 100,000 or million.

Rounding numbersB

You should be able to round any whole number to the nearest 10, 100, 1000, 10,000, 100,000 or million.

E.g. 2,845,565 rounded to the nearest 1000 is 2,846,000

A city has a population of 3,684,266. Can you round this number to:1

the nearest 10?

the nearest 1000?

the nearest 100,000?

Which of these numbers would be rounded to 60,000 if they were rounded to the nearest 1000? Circle your answers.

2

60,584 59,842 60,499 59,444 60,010

John said that his home town had 30,000 people to the nearest 1000 living in it. What is the biggest number of people who could live there?

3

What is 3,999,999 rounded to the nearest 10?

What is 3,999,999 rounded to the nearest 100?

4

In a quiz Ali was asked to round this number so that it had one 6 in it: 4,445,525.

What answer would have been correct?

(You are only allowed to round to the nearest 10, 100, 1000, 10,000, 100,000 or million.)

5 Phew!

3,684,270

3,700,000

3,684,000

4,000,000

4,000,000

30,499

4,446,000

5

I’m confi dent I’m nearly thereI can do calculations containing negative numbers.

C Using negative numbers

Sometimes we need to think about numbers less than zero. This number line may help with some questions.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

In the daytime, the temperature reached a maximum of 8 oC in Suzie’s garden. At night it fell to -4 oC. By how many degrees did the temperature fall?

1

oC

In a quiz Jon got 2 points for each correct answer, but he lost 2 points for each wrong answer.

In round 1 he got 2 questions correct and 4 wrong. How many points did he have?

2

Try these calculations:3

2 – 6 =

6 – 8 =

0 – 4 =

-1 + 4 =

-2 – 3 =

-4 + 4 =

The weather forecast said that it was 20 oC hotter in Madrid than in London. If it was -3 oC in London, what was the temperature in Madrid?

4

oC

Is 3661 rounded to the nearest 100 bigger or smaller than 3711 rounded to the nearest 10?5

(bigger or smaller)Help!

12

-4

-4

-2

-4

3

-5

0

17

r

6

I’m confi dent I’m nearly thereI can solve some number problems.

Solving problemsD

What is the temperature measured by this thermometer?

If the temperature fell by 18 oC what would it be?

1

-10 0 10 20 30 (oC)

oC

oC

Jason’s bank statement said that he had -£87.00 and that he must immediately bring his balance back to zero. For his birthday he received £90.

After paying back the bank, how much did he have left to spend?

2

£

Sara played a party game where she had to wear a blindfold. The others gave her these instructions:

“Take 6 steps back, three steps forward, two steps back, fi ve steps forward, three steps back.”

At the end she had to fi nd her way back to where she started. What did she need to do?

4

Are you serious?!

Would you rather win prize : £1501 rounded to the nearest £1000

or prize : £1890 rounded to the nearest £100?

3 A

B(A or B)

What were the prizes actually worth?

£1501 to the nearest £1000 =

£1890 to the nearest £100 =

£

£

13

-5

3.00

A

2000

1900

Take steps3 d

7

I’m confi dent I’m nearly thereI can answer word questions about number and place value.

Word problemsE

1 Blake was asked to fi nd the second largest number in this list: 1,236,544, 1,236,545, 1,236,455, 1,236,561 and 1,236,456.

What should his answer be?

3 Which is more, £84,865 rounded to the nearest 100 or £84,891 rounded to the nearest 10? Show how you worked this out.

4 In Alaska it is -21 oC. If the temperature increases by four degrees, what temperature will it be?

5 Rounded to the nearest 100, Zac has 62,500 stamps in his collection. What is the largest number of stamps he could have?

6 What is the answer to twenty-eight minus thirty-three?

7 What number do you need to add to minus two thousand eight hundred and twelve to get an answer of 50?

OK!

2 Yousef went to a football match where there were thirty-three thousand, eight hundred and sixty two people in the crowd.

What is this number rounded to the nearest hundred?

Answer (in digits):

1,236,456

33,900

£84,865

-17oC

62,549

-5

2862

3 3 8 6 2,

28 − 33 = -5

2 8 1 2

5 0

2 8 6 2

+

84865 o t 100

= 84900

84891 o t 10

= 84890

rounded to the nearest: 100

8

I’m confi dent I’m nearly thereI can do mental maths with bigger and bigger numbers.

Addition, Subtraction, Multiplication and Division

A Mental maths You will need to know your times tables and know how to simplify calculations.

E.g. 31 x 8 = 30 x 8 + 1 x 8 = 240 + 8 = 248

Try these calculations in your head:1

Now you are warmed up, try these:2

Hint: Start with 48 x 10

What about some division?3

x 220

+ 24 ÷ 8 – 10

Try this:4

If that was too easy, try this:

x 319

– 21 x 4 ÷ 12

Answer:

5 If 6372 ÷ 6 =

=

6000 ÷ 6 360 ÷ 6 12 ÷ 6+ +

1000 60 2+ + 1062=

What is 8256 ÷ 8?

Not now!

244 + 143 =

251 + 29 =

728 – 513 =

498 – 19 =

a)

c)

b)

d)

28 x 3 =

121 x 4 =

32 x 6 =

48 x 9 =

a)

c)

b)

d)

640 ÷ 8 =

132 ÷ 12 =

a)

c)

490 ÷ 7 =

1320 ÷ 12 =

b)

d)

387

280

215

479

192

432

84

484

80

11

70

110

40 64 8 -2

57 36 144 12

1032

+

+

+

+

8000 ÷ 8

1000

240 ÷ 8

30

16 ÷ 8

2

9

B Written addition and subtractionNow it’s time to try some bigger numbers!

I’m confi dent I’m nearly thereI can do written addition and subtraction.

Wow!

Let’s start with some addition.1

Now for a take-away!2

2 1 4

+ 1 3 5

6

2

4 4

+ 1 0 6

4

6

42 6

+ 1 3 2

8

4

3

5 9 9

+ 1 1 1

9

1

9 9

+

9

3

90 0

+ 9 9

2

9

4

3 2 4

– 1 1 3

6

4

1 4

– 6

0

4

42 2

– 1 1 1

0

6

4

6 8 2

– 2 9 1

4

4

0 0

– 5 4

0

3

40 0

– 0 0

0

2

7

1

Can you fi nd the missing numbers in this calculation?

3 4

– 6 4

9

2 9 91

3 4 9 8 4 5 9 21

5 5 1 011

7 1 1 01 1 1

5 0 0 11 1 1

0 0 0 21 1 1

1

2 1 1 2 3 1 0 4

1 1

4 0 7 6

0 13 1

3 9 1 0

5 1

5 9 9 8

6 9 9 1

3 4 5 7

3 9 9 1

8 32 9

8 94

9−

3

4

1

6

9 92 1

187

10

I’m confi dent I’m nearly thereI can multiply numbers with up to 4 digits

by 2-digit whole numbers.

Remember long multiplication?

1

2 4 2 1

x 1 4

6 8 494 2 1 023 8 9 43

C Written multiplication

Can you fi nd the missing numbers?4 1

x

4 5

4 5 63

2

9 4 00

3 9 63

I need a sleep!

Ready to try some?1

Now with 4-digit numbers.2

4 3

x 1

8

2

5 4

x 3

3

8

6 3

x 2

4

4

3 8

x

4

6

5 6

x 2

7

3

2 4

x 1

5

4

1 1 1

1

3 A bottle of water costs 56 p.

How much would it cost for 1250 bottles?Convert your answer from pence to £s.

£

8 7 1 6

3 8 04

2 5 651 1

3 1 6

6 8 02

2 1 65

5 1

1

1

2

1 1

42 4

2 9 06

6 3 40

33

1

2

4

11

1

4023582 82 0

4 5 02

4 3 07

9 1

1

1

4

1 1

02 1

3 4 01

0 4 16

7 2

3

3

4

1

1

111

700.00

2 3

2

3

1 2 5 0

5 6

7 1 53 0 0

22 5 0 06 1

0 0 0 07

x

11

1

11

I’m confi dent I’m nearly thereI can use short and long division to divide by 1 and 2-digit numbers.

D Written division22

5411

12

2 1

9

9277

3

321

6 r 1

or 216 1

12Short Division

2 2

1 3615

r 3Long Division

4 The town mayor wants to send out 3259 invitations to a special party in the town hall.

The invitations are in packs of 12.

How many packs will the mayor need?

How many invitations will be left over?

Tricky!

Try these using short division.1

Try these using long division. (They have remainders.)2

1 97 6 2 73 41 3 4 94 42 4

4 62 93 9 9 51 14 5

1 97 8

Use short division and write the remainders as fractions.3

2 58 7 4 69 7

272

5

82 112 6025 1 1 1 14

r 274 61 r 33 22

23

41 9

21 8

9

91 2

2 7

1120

28

1 1

21 3

5

8 2

3

8

32 1

82 23 1527

18

89

15 1

1 2 3 2 5 9

2 4

8 5

8 4

1 9

2 7 1 r 7

−

−

12

E Multiples, factors and prime numbers

2, 3, 5, 7, 11, 13, 17, 19, etc. are prime numbers. Their only factors are 1 and themselves.

1, 3 and 9 are factors of 9

The lowest common multiple of 3 and 4 is 12

2 is a common factor of 4 and 6

I’m confi dent I’m nearly thereI can fi nd multiples and factors and

I can recognise prime numbers.

Look at these pairs of numbers. Can you circle the common factors?1

(8, 12) 2 3 4 5 6

(36, 24) 2 3 4 5 6 7 8 9 10 11 12

Which of these numbers are prime numbers?3

3 16 23 27 31 39 43 77 83

Can you fi nd three common factors of 16 and 8 (not including 1)?2

Now we are going to fi nd some lowest common multiples for the following pairs of numbers. 4

The lowest common multiple of 6 and 9 is The lowest common multiple of 8 and 6 is

The lowest common multiple of 8 and 7 is

5 Multiply the lowest common multiple of 4 and 9 by the biggest common factor of 6 and 18.

What is your answer? x =

OK!

3, 6, 9, 12, etc. are multiples of 3

2 4 8

18

24

56

36 6 216

3 6x

1

6

2 63

13

I’m confi dent I’m nearly thereI know what order to do operations in.

F The order of operationsWhat is 2 + 3 x 6 – 1? Is the answer 29 or 19 or 25 or 17? Answer: 19

Why? Because we always do operations in this order: brackets, ÷ x, + –

Try these calculations:1

Now try these!2

4 + 6 ÷ 2 x 3 – 1 = 8 x 2 + 4 ÷ 2 + 6 =

Can you put the brackets into the calculations to make them correct?4

2 + 8 x 4 – 1 = 266 + 3 x 2 = 18

Can you add brackets to make this true?5

3 x 8 ÷ 2 + 4 = 4

Bring it on!

16 ÷ 4 + 2 =

12 + 8 ÷ 4 =

a)

c)

18 + 2 x 6 =

20 ÷ 2 + 3 =

b)

d)

To make things easier we can use brackets. Operations in brackets must be done fi rst.

Try these (the fi rst one is done for you).

3

88 x (3 – 2) =

12 ÷ (2 + 2) =

a)

c)

11 x (4 + 3) =

30 ÷ (11 – 5) =

b)

d)

8

6

14

30

13

12 24

3 5

77

( ) ( )

)( )(

14

G Estimating to check answersIt is always best to check your answers. One way you can do this is by estimating.

For example, Jon worked out that 6 x 199 = 1004. We can check this out by working out 6 x 200 which is 1200 and we see that Jon’s calculation must be wrong.

I’m confi dent I’m nearly thereI can make estimates to check my answers.

Mark these calculations by estimating. The fi rst is done for you.1

x8 99 = 792

x8 100 = 800

or x6 51 = 306

x6 =

or

Use your mental maths skills to estimate the answers to these calculations ( ≈ means “is approximately equal to”).

2

Estimate the answer to this calculation.4

89.9 + 2 x 5 – 50.006 =

Use a calculator for these. Sometimes a calculator gives answers to lots of decimal places. We have to decide how accurate the answer needs to be.

Example: 2 ÷ 3 = 0.66666666666. In most cases it would be good enough to write the answer as 0.67.

Try these:

3

800 cm ÷ 3 =

122 mm ÷ 5 =

4 litres ÷ 7 = Hint: Convert to ml before dividing.ml

Give me a break!

mm

cm

90.1 x 4 ≈

199.85 x 6 ≈

89.9 x 5 ≈

204.99 + 163.03 ≈

a)

c)

b)

d)

50 300

+999 399 = 1498

+ =

or +69 69 = 227

+ =

+ 69

+

or

70 70 70 210

360 450

1200 368

266.67

24.4

571.43

50

14001000 400

15

I’m confi dent I’m nearly thereI can solve problems involving addition, subtraction, multiplication and division.

Solving problemsH

1 Zak is 4 years older than Jody and Jody is 2 years younger than Mike. Zak is 10 years old.

How old is Mike? years old

2 In a game there are 3 sets of cards. Each set has 16 cards. The cards are mixed together and shared equally between 4 players.

How many cards does each player get? cards

3 Billy bought four boxes of cakes for his birthday party. Each box contained eight cakes. He carefully put fi ve cakes on each of six plates.

How many cakes were left over?

Sarah had £3 to spend on her lunch.4

drinks 40 p

sandwiches £1.60

fruit 50 p

biscuits 15 p

How many biscuits did she buy?

How much money did she have left?

She bought a drink, a sandwich and a piece of fruit.

She then bought as many biscuits as she could.

In a quiz, you get 3 points for a correct answer but you lose 2 points for a wrong answer. If you answer a ‘bonus’ question correctly your score is doubled, but if you get it wrong your score goes back to zero. Below is Jayne’s score card.

5

bonusbonusbonus

Question

Answers

1 2 3 4 5 6 7 8 9 10What is her score?

Help!

8

12

2

3

5 p

10

3 x 16 = 48

48 ÷ 4 = 12

4 x 8 = 32

5 x 6 = 30

6

5

5

1

0

2

+0

0

0

40 0.

.

.

.

£3 £2.50 = 50 p t

r u

3 x 15 p = 45 p

Z JM

(10) (6)(8)4

2

16

Word questionsI

I’m confi dent I’m nearly thereI can answer word questions using addition, subtraction,

multiplication and division.

1 What is three hundred and sixty-three minus one hundred and seventy-four?

2 How many would three more than 899,899 be?

3 8,420 spectators each spent £28 on a ticket for the match.

How much was spent on tickets in total? £

4 Susie said that 494 bananas could be shared equally between twenty-nine monkeys with no bananas spare. Do a calculation to fi nd out if this is correct.

Circle your answer: Correct or Incorrect

5 Use long division to work out the answer to 2473 divided by 12.

Write down any remainder as a fraction.

6 Counting up in ones, what is the next prime number you get after twenty-nine?

7 Which number is the lowest common multiple of twenty-seven and eighteen?

8 Write this in numbers so that it is correct: Eight times fi ve minus two equals twenty-four.

Let’sgo!

189

899,902

235,760

31

54

8 x (5 − 2) = 24

112206

6

7

1

− 4

8 9

1

15 3132

8 4 2 0

2 8

6 03 17 36

0 04861

6 07532

x

r 11 7

4 9 492

2 9

2 0 4

2 0 31

62 0

2 4 721 3

2 4

0 7 3

7 21

1 1

17

Fractions, Decimals and Percentages

I’m confi dent I’m nearly thereI can simplify fractions.

Simplifying fractionsA

We can simplify using what we know about equivalent fractions.

6

36

636

212

= 16

=

Can you simplify these fractions?1

816

= 936

=

1284

= 354

=

46

65

79

812

1015

1213

2030

Which of these fractions are equivalent to ? Circle your answers.22

3

Can you change all these fractions so that their denominator is 6?3

23

=6

318

=6

1012

=6

How many fractions can you fi nd that are equivalent to with a denominator less than 24?4 18

24

49168

= 147168

=

5 Try to simplify these fractions.

24

=6

a)

c)

b)

d)

OK!

1827

= =654

515

=3

=6

12

17

14

118

4 1 5

3 1 2 36 4

34

1520

1216

912

68

724

78

741

861

94

65

7

8==

18

I’m confi dent I’m nearly thereI can compare fractions by changing them so that

they have the same denominator.

B Comparing fractions

Is bigger or smaller than ? Answer: = so is smaller than .6

18

4

9

6

18

3

9

6

18

4

9

Now try doing the same with these, but you will need to choose the ‘common denominator.’2

23

35

715

smallest largest

Can you put these in order from largest to smallest?3

16

2 146

56

1 186

largest smallest

Now try putting these in order - no hints!4

34

812

1924

smallest largest

Stop it!

Can you put these fractions in size order from smallest to largest? Hint: Convert them all to twelfths.1

12

512

26

23

712

12 12 12 12 12

smallest largest

75

26

512

12

712

23

6 4 8

1015

915

715

715

23

35

812

1924

34

162

561

146

186

19

I’m confi dent I’m nearly thereI can add and subtract some fractions.

C Adding and subtracting fractions

We can use what we know about equivalent fractions.

For example:1

3 +2

9 =3

9 +2

9 =5

9

Try these:1

Now have a go with mixed numbers. The fi rst is done for you.3

13

1 +56

1 =43

+116

=86

+116

=196

=16

3

14

1 +18

=

+13

=

Now try these:2

16

4 − =12

2

4 What is the missing number in this calculation?

12

+ 18

=8

18 8

=

27

– 314

=14

314 14

=

16

+ 312

=

59

– 318

=

=

=

+

–

+

–

++ = = =

++ = = =36

2

2

1

Phew!

212

312

1018

318

512

718

54

156

178

43

108

156

178

86

278

236

38

56

3

3

26

4

4

5

1

25

6−

1

6

50

12=4

?

12−

50

12

24

12=

? = 26

20

I’m confi dent I’m nearly thereI can multiply two proper fractions together

and simplify my answer.

D Multiplying two fractions together

4 Which is bigger : a half of a quarter of a half or : a third of a third?

AB

Answer:

Tough!

To multiply fractions multiply the top numbers together then multiply the bottom numbers together.

23

x23

=491

4

1

4

1

2x = 1

8

2

3

2

3

1

2x = 2

6= 1

3

Use the diagrams to multiply fractions.2

14

x13

14

= 25

x23

25

=

One of the fractions could be a whole number such as = 2. Try these, the fi rst is done.1 2

1

13

x = x =2 13

21

23

a)

27

x = x =5c)

14

x = x =3b)

49

x = x =9 =d)

Now try these.3

23

x 34

= =

(simplify)

a)

29

x 37

= =

(simplify)

21c)

16

x 34

= =

(simplify)

b)

211

x 211

=d)

27

107

51

49

369

91

14

34

31

4

112

415

612

12

324

18

4121

663

2

B

1

2x

1

4

1

16=x

1

2

1

3x

1

3

1

9=

3 x 3

2 x 2

21

I’m confi dent I’m nearly thereI can divide proper fractions by whole numbers.

E Dividing fractions by whole numbers

Remember: Dividing by 2 is the same as multiplying by1

2

and dividing by 3 is the same as multiplying by .1

3

Let’s start with these.1

14

÷ 2 We know this is the same as:14

x 12

= 18

Now it’s your turn!

15

÷ 2 15

x ==

16

÷ 3 16

x ==

311

÷ 4 311

x ==

Now try these and remember to simplify your answers.2

911

÷ 3

1016

÷ 4

26

÷ 12

=

=

=

=

=

=

=

=

=

3 Luke ate of his birthday cake and shared the rest equally between himself and 6 friends.

How much cake did each of his friends get?

1

15

Try this...

x

x

x

12

13

14

110

118

344

911

1016

26

13

14

112

933

1064

272

311

532

136

215

÷14

15=7 x

14

15

1

7

= =14

105

2

15

22

F Changing fractions to decimals

is the same as 1 ÷ 2 = 0.51

2

I’m confi dent I’m nearly thereI can change fractions to decimals using division.

Tenths, hundredths and thousandths can easily be changed to decimals. Try these:1

110

= 0.1210

= 510

=

4100

= 14100

= 61000

=0.04 0.14 0.006

0.2 0.5

With some fractions we need to divide the top part (numerator) by the bottom part (denominator) to change them to decimals. Try these - the fi rst is done.

2

= 1 ÷ 41

4

1 04 0.0 2 5.

0 8.0 2 0.0 2 0.

3 04 0. = 3 ÷ 4 3

4

3 020 0. 9 020 0. = 3 ÷ 203

20 = 9 ÷ 209

20

Ready for some more? Try these if you dare!3

Woah!

0.625

0 7 5.2

0 4 5.10

0 1 5.10

0 3 7. 5

3 0 0. 086 4

0 6 2. 5

5 0 0. 082 4 = 3 ÷ 83

8 = 5 ÷ 85

8

23

I’m confi dent I’m nearly thereI can multiply decimals by whole numbers.

G Multiplying with decimals Remember: Keep your eye on the decimal point!

Let’s start by multiplying by 10, 100 and 1000.1

1.2 x 10 =

34.5 x 10 =

0.12 x 100 =

1.23 x 100 =

0.4 x 100 =

1.24 x 1000 =

Write down the value of the digit 2 in these numbers in words.2

24

1.264

4.812

8.020

Now let’s try some mental multiplication using decimals.3

0.6 x 7 =

0.03 x 8 =

0.002 x 4 =

0.5 x 9 =

0.08 x 6 =

0.006 x 12 =

Are you ready for some written multiplication? The fi rst is done for you.4

8 7

6 2 4.x 3

2.11

1 2 4.x 3

2 3 5.x 5

4 7 6.x 6

5 A boy bought 4 magazines at £1.34 each and 3 birthday cards at £1.65 each.

How much did he spend? £

No!

a)

c)

e)

b)

d)

f)

a)

c)

e)

b)

d)

f)

12

345

12

123

40

1240

4.2

0.24

0.008

4.5

0.48

0.072

o

o

o

o

10.31

3 7 1 2 1 1 1 7 2 5 2 84 53 6. . .

3x 4

6

41

5 1

6x 3

5

51

3 1 4 1 9 1

.

.

.

.

24

I’m confi dent I’m nearly thereI can do division calculations and write my answers as decimals.

H More written division - writing your answers as decimals

Look at the calculation 16 ÷ 5

Try this using short division.1

18 ÷ 5

1 85 0

91 ÷ 2

9 12 0

26 ÷ 4

2 64 0

Now have a go at these using long division. The answers will have 2 decimal places.2

66 ÷ 8 3.14 ÷ 278 ÷ 8

3 Jackie paid £2.88 for 6 cupcakes.

How much did each cake cost?

£

Ok let’s go!

1

1

0

0

0

5

3 2

6

5

1

1

.

.

.

or we can write the answer as

the decimal 3.2(3 x 5)

(0.2 x 5)

Remember that 1.0 is 10 tenths and 10 tenths ÷ 5 = 2 tenths

.

1

1

6

5

1

5

3r1 or 31

5

6 5.2

3 6.3

5 5.1

41

8 2

6 6 08

5

0

.

.9 7

7 8 08

5

0

.

.5 7

3 1 42

.

.1

4 8

2 8 864

.

.0

0.48

6 4 .

2 0.

1 6.

0 4 0.

0 4 0.

−

−

7 2 .

6 0.

5 6.

0 4 0.

0 4 0.

−

−

2 .

1 1.

1 0.

0 1 4.

0 1 4.

−

−

... .

25

I Rounding Remember: 4.6591 is 4.66 to two decimal places.

I’m confi dent I’m nearly thereI can round numbers to a sensible number of decimal places.

Try rounding these numbers to the nearest tenth (to one decimal place).1

11.94 6.88 3.06

Can you round these numbers to two decimal places?2

15.619 21.444

If you round these numbers to 1 decimal place, which one would not be 10.5? Circle your answer.3

10.48 10.54 10.501 10.45 10.555

5 Jake measured a bar of chocolate. It was 131 mm long. He wanted to break it into 5 equal pieces.

How long would each piece be to the nearest millimetre?

4 Sally wanted to share £4 between her 3 sisters. She worked out on her calculator that they would each get £1.333333.

What should she round the answer to so that she could give them their share?

6 A number with 3 decimal places is rounded down to 4.76. The original number didn’t have a 1, 2 or 3 in it.

What was the number?

Oh no!

11.9 6.9 3.10

15.62 21.44

£1.33

26 m

4.764

2 6

1 3 153

2

01.

.

26

I’m confi dent I’m nearly thereI can swap between fractions, decimals and percentages.

J Fractions, decimals and percentages

Remember: A fraction written in hundredths can easily be turned into a percentage or a decimal.

54

100= 0.54 = 54% 28

100= 0.28 = 28%

Write these fractions as percentages.1

20100

= %15100

= 80100

=% %

Now try these:2

410

= 610

= 910

=% % %

Use what you know about equivalent fractions to convert these fractions to decimals.3

14

= 25

= 1325

=

5 Zane had £120 and put 20% in the bank.

His sister Zara had £200 and put in the bank.

Who put the most money in the bank?

Show your working.

1

10 Tricky!

Can you fi ll in the spaces using your mental maths skills?4

Remember to simplify your fractions.

% DecimalFraction

40%

0.12

34

20 15 80

40 60 90

25 % 40 % 52 %

75 % 0.75

0.4

12 %

25325

Z

1 0 % of 1 2 0 = 1 2

2 0 % of 1 2 0 = 2 4

of 2 0 0 = 2 0110

=34 =75

100 0.75 = 75%

= =40100 0.440%

=40100

410 = 2

5=40%

=12100=0.12 12%

=12100

325

27

I’m confi dent I’m nearly thereI can answer word questions about fractions, decimals and percentages.

K Word questions

1 Which fraction is larger? Circle your answer.

Explain how you know.

53

or 169

2 Can you write down an equivalent fraction to that has a denominator of forty-fi ve?

5

9

3 Find a common denominator for these fractions and circle the largest.

23

= 34

= 56

=

4 Can you subtract one sixth from four ninths?

5 Work out the answer to three elevenths multiplied by four elevenths.

6 Sally and her brother have one seventh of a cake to share equally between them. What fraction of the cake will each of them get?

7 What is one fi fth as a decimal?

8 What is as a percentage?3

5

9 If you bought seven books at £3.89 each, how much would you spend?

£

Phew!

0.2

60 %

27.23

2545

812

912

1012

518

12121

114

=5

3

15

9

=5

9

25

45

−4

9

1

6= −

8

18

3

18

x3

11

4

11=

12

121

x1

7

1

2=

1

14

=1

5

20

100

=3

5

60

100 8x 7

3

93

7 6 26

.

.2 1

u t n of159

53

28

Ratio and Proportion

I’m confi dent I’m nearly thereI can scale up and down by multiplying and dividing.

A Scaling up and down

If you get a free drink with every six meals, how many meals would you need to buy to get two free drinks? Answer: 12

1 Ice creams cost 60 p each.

How much would 8 ice creams cost?

Answer:

3 In a bag of beads there were 3 red beads for every blue bead.

Altogether there were 80 blue beads. How many red beads were there? Answer:

2Serves 3 people

1 egg

50 g fl our

50 ml milk

Look at this recipe for Yorkshire puddings. How much fl our would you need to make puddings for 6 people?

g

Complete this: “for every egg you need fl our

and milk.”

g

ml

4 On a plane there were 6 airline workers and 240 passengers.

If each worker looked after the same number of passengers, how many passengers did each worker look after?

Answer:

Can you complete this chart showing the price of biscuits?5

Biscuits

Cost

1 2 3 4 5 6 7 8

£1.80

In a card game each player must have 7 red cards, 9 blue cards and 5 yellow cards. If there were 42 red cards in play, how many blue cards were in play?

6

Wow!

100

5050

£4.80

240

40

£0.30 £0.60 £0.90 £1.20 £1.50 £2.10 £2.40

54

x 6 0 = 4 8 08

x 8 0 = 2 4 03

0 ÷ 6 = 4 02 4

29

To fi nd of a number we divide it by 10.

I’m confi dent I’m nearly thereI can calculate percentages of whole numbers.

B Calculating percentages

What is 10% of 30? 10

100

1

1010% is = 1

10

So, 10% of 30 is: 30 ÷ 10 = 3

Try these:1

of10% 40 10% is 1

10of 40 is:1

1040 ÷ 10 =

of10% 90 10% is 1

10of 90 is:1

1090 ÷ 10 =

What is 10% of 80?

What is 5% of 80?

What is 25% of 80?

3

Hint: 10% + 10% + 5%

Here goes...

On a pie chart, Charlie wanted to show that 10% of children cycled to school. The angle around a point at the centre of a circle is 360o.

How big should angle A be?

4

On the same chart he wanted to show that 35% of the children travelled by car. What angle should he measure for this slice of pie chart?

o

10%

A

o

If 10% of 20 is 2, we know that 20% of 20 will be 4 (twice as much). Try these:2

of20% 50 =So

of30% 50 =

of10% 50: 10% is 1

10of 50 is:1

1050 ÷ 10 =Find

4

9

5

10

15

8

20

4

36

126

of 80 = 80 ÷ 10110

= 8

8 + 8 + 4 = 20

35% = 10% + 10%

+ 10% + 5%

= 36 + 36 + 36 + 18

= 126o

30

I’m confi dent I’m nearly thereI know what is meant by ‘scale factor.’

C Scale factor

S

The square has been enlarged by a scale factor of 2.

S

The sides of a triangle measure 3 cm, 4 cm and 5 cm. It is enlarged so that the shortest side is 36 cm. What is the scale factor?

How long will the longest side be on the enlarged triangle?

3

cm

On a map the distance from Sam’s home town to London was 30 mm.

The scale on the map was 1 mm for every 3 kilometres.

How far was it from Sam’s town to London?

4

km

2

B

Shape B has been enlarged and part of the enlarged shape is shown.

What scale factor has been used?

Can you enlarge shape A by a scale factor of 3?

Draw your answer on the empty grid.

(Be careful where you start!)

1

A

5 This picture of a tree is 9 mm high. If it is enlarged by a scale factor of 400, how high will the new picture be in metres?

Wow!

9 mm

4

12

60

90

3.6 m

31

I’m confi dent I’m nearly thereI can answer word questions about ratio and proportion.

D Word questions

1 To make fruit punch, Zoe mixed litre of orange juice with litre of mango juice and litre of pineapple juice. This made enough punch for three people.

How much mango juice would she need if she made punch for twenty-four people?

1

2

1

41

8

2 There are 30 members of a swimming club. 40% of them can swim 1500 m. How many members can swim 1500 m?

3 Zane was supposed to share a cake with his three sisters. One sister ate 30% and the other two ate 35% each.

How much was left for Zane?

4 Can you work out fi ve percent of one hundred and thirty?

5 On a pie chart Yousef wanted to show that 30% of people in his class had blue eyes.

What angle should he use for the ‘blue eye’ section?

6 A rectangle has sides of 6 cm and 8 cm. If it was enlarged by a scale factor of 28, what will the lengths of its sides be?

and

7 Amy’s dad takes two steps for every three of hers. When they walked to town, Amy counted her steps and she needed 582.

How many did her dad need?

Phew!

2 l

12

0 %

6.5

108o

168 m 224 m

388

x 8 = = 214

84

10% of 30 = 3

40% of 30 = 4 x 3 = 12

35 + 35 + 30 = 100

10% of 130 = 13

5% = 13 ÷ 2

10% = of 360 = 36110

110

of 360 = 108310

9 4x

8

2

3 8

1

9 4

5 8 231

12

2 8x 6

1 864

2 8x 8

2 426

32

Algebra

I’m confi dent I’m nearly thereI can use some formulae.

Using a formulaA

Example: The area of a rectangle is found using the formula: Area = length x width

5 cm

3 cm

Area = length x width = 5 cm x 3 cm = 15 cm2

Use the formula Area = length x width to answer these questions.

A rectangle has a length of 12 mm and a width of 6 mm. What is the area?

A rectangle has an area of 48 cm2 and a length of 12 cm. What is its width?

1 Area = length x width = =

x

mm2

Area = length x width 48 cm2 = 12 cm x The width is cm

2

The area of a triangle is found using the formula Area = base x height.1

2height

base

Can you calculate the areas of these triangles?

5 cm

6 cm

7 cm

14 cm

Adie made up a formula to work out the cost of his shopping.

Cost = A x 40 p + B x 50 p + P x 60 p

(A is the number of apples, B is the number of bananas and P is the number of pears).

He bought 6 apples, 6 bananas and 4 pears. Complete this to fi nd out how much he spent.

3

Cost =

=

+

+

+

+

x 40 p x 50 p x 60 p

= £

Brainstrain!

12 m 6 m

72

4 m

4

15 m2 49 m2

6 6 4

240 p 300 p 240 p 7.80

x 6 x 5 x 14 x 712

12

33

I’m confi dent I’m nearly thereI can describe number sequences and fi nd missing numbers.

Number sequencesB

What is the next number in this sequence? 1, 8, 15, 22, 29 ...?

Answer: 36 Why? Because the rule is ‘add 7’ to get the next number.

What is the rule to get the next term in this sequence?1

5 14 23 32

The rule for this sequence is ‘add 12’. Can you write the next three numbers?2

8 20 32

Can you spot the rule for this sequence and fi nd the next two numbers?3

34 29 24

Now try fi lling in the missing numbers in this sequence.4

9 30-12 2

This sequence involves subtracting the same number every time to get to the next term.5

3587

Can you fi nd the missing numbers?

Complete this: The rule for this sequence is ‘subtract ’

Impossible!

d

44 6856

19 14

-5 16 23

74 61 48

13

34

I’m confi dent I’m nearly thereI can solve missing number problems.

Missing number problemsC

John is three years older than Lisa. We can write a formula for this: J = L + 3 (J is John’s age and L is Lisa’s age)

If Lisa is ten (L = 10) then J = L + 3 = 10 + 3 = 13 John is 13

Try these:

Josh is six years older than Amy. If Josh is twelve, use this formula to work out Amy’s age.

1

J

12

=

=

+

+

6

6

A

So Amy is years old.

Michael is eleven years younger than Fran. If Michael is 8, how old is Fran?

M

8

=

=

–

–

11

11

F

So Fran is years old.

If4 –3 13 =x 44 What is the missing number?

2 The length of a box can be found using this formula.

4 x l = 64 cm

How long is the box? cmlength (l)

Harder!

The perimeter (P) of a rectangle can be found using this formula.

P = 2a + 2b

If a is 8 cm and b = 12 cm, what is the perimeter (P)?

3

P =

=

+

+

2 2 x

= cm

x

a

b

6

19

6

19

16

8

16

12

24 40

19

35

I’m confi dent I’m nearly thereI can fi nd pairs of numbers that work in equations

with two missing numbers.

Two missing numbersD

If A + B = 6, what values could the numbers A and B have?

0

6

6

1

5

6

2

4

6

3

3

6

4

2

6

5

1

6

6

0

6

A

B

A + B

A can be any whole number less than 7. B can be any whole number less than 9.

If A x B = 48 what are the values of A and B?

3

A = B =

Try this: If P x Q = 8 what values could the numbers P and Q have?1

P

Q

P x Q 8 8 8 8

If C + 2D is 12 can you list some possible whole number values for C and D? How many can you fi nd?

2

C

D

C + 2D 12 12 12 12 12 12 12

6

0

In a card game is worth 8 points.

Zac has these cards and a total of 28 points.

If is worth three times as many points as , how many

points is worth?

4 Help!

2 814

4 182

2

5

4

4

6

3

8

2

10

1

12

0

6 8

3

+ = 12

= 3 x

= 3

36

I’m confi dent I’m nearly thereI can answer word questions about algebra.

E Word questions

1 Lucy had a £1 coin and she spent 47 p. Which formula shows how much change (C) she got? Circle your answer.

C = £1 + 47 p C = 47 p – £1 C = £1 – 47 p

2 If you have £5 and you spend £2.64 can you write a formula to show how much change (C) you would get?

C =

3 What is the next number in this sequence?

Three, eleven, nineteen, twenty-seven,

Complete this: The rule for this sequence is .

4 Look at this equation: A + B = 29

If A is thirteen what is the value of B?

5 Ali is fi ve years older than Yogi. Using A for Ali’s age and Y for Yogi’s age, can you complete this formula?

= +

6 If P x Q = 12 what are the possible values of P and Q?

7 If A x B – 9 = 33 and if A is equal to six, what is the value of B?

Wow!

P

Q

P x Q 12 12 12 12 12 12

£5 − £2.64

35

d 8

16

A 5 Y

7

1

12

2

6

3

4

4

3

6

2

12

1

13 + B = 29

6 x B − 9 = 33

6 x B = 42

3, 11, 19, 27

+ 8

37

Measurement

A Units of measurement

Jake’s summer holiday lasted for 6 weeks and 3 days. How many days was this in total?

Answer: 6 weeks is 6 x 7 = 42 days. So 6 weeks and 3 days is 45 days.

I’m confi dent I’m nearly thereI can convert between different units.

Now try these.2

255 g is

6500 mm is

kg

m

2.4 m is

0.5 litres is

cm

ml

Five people shared a litre bottle of lemonade.

How much did each person get? Give your answer in millilitres.

3

ml

There are approximately 8 km in 5 miles. Can you complete this conversion chart?5

miles

kilometres

5

24

20

40

Try these to get started:1

There are

There are

There are

ml

cm

g

in a litre

in a metre and

in a kilogram

mm in a metre

6 Can you use short division to calculate approximately how many kilometres there are in 1 mile?

Phew...

4 Can you work out how many seconds are in 1 hour? (This will take 2 steps.)

seconds

Answer:

1000

100

1000

1000

0.255

6.5

240

500

200

3600

15

8 32

25

1.6 m

60 n 1

60 n 1 r

o 60 x 60 n 1 r

6.8 0

13

5

.

38

I’m confi dent I’m nearly thereI can use scales and graphs to help me do some conversions.

B Using scales and graphs to convert units

We can see from this scale that 2 cm = 20 mm.

0 10 20 30

0 1 2 3

mm

cm

Can you complete this to show how centimetres can be converted to metres?1

0

0 1 2

cm

m

Look at this diagram. It shows how inches can be converted into millimetres.

Find the values of , and in mm. (The fi rst one is done for you.)

3

0

0 1 2 30.25 0.5 0.75 1.25 1.5 2.251.75 2.5 2.75

6.35 12.7 19.0525.4 50.8 76.2

38.1BA C mm

inches

121110987654321

1 2 3 4 50

6

2Look at this graph. It shows how you can convert between miles and kilometres.

The dotted lines show that 5 miles = 8 km

Use a ruler and draw your own dotted lines to show how to do this conversion.

km

miles

1 7

5 4.+ 5

5.3

3

2

Ok!

6 .

B 1.75 inches 1 inch

mm

+

+

=

=

inch

mm = mm

C 2.5 inches +

+

=

=

inch

mm

2 inches

mm = mm

A 1.25 inches 1 inch

25.4 mm

+

+

0.25 inch

6.35 mm

=

= = 31.75 mm

BA C

1

100 200 300 400

43

2.5 miles = km4

0.75

0.5

19.0525.4 44.45

12.750.8 63.5

5 42

9 0

4 44

+

.

5

51

1 .

.

0 85

2 7

3 56

+

.

1

1 .

.

39

C Areas and perimeters

Question: Do all shapes that have the same perimeter have the same area? Soon you will know!

I’m confi dent I’m nearly thereI know that shapes can have the same areas

but different perimeters and vice versa.

Can you draw a shape with the same area as the shape below but a different perimeter?3

12 cm2Area =

Perimeter = cm

12 cm2Area =

Perimeter = cm

2

Look at these shapes. Which shapes have the same area?

Which shapes have the same perimeter?

and

and

6 cm

2 cm A

4 cm

3 cm B

2 cm

5 cm

2 cm1 cm

C

Work out the areas and perimeters of these two new shapes.1

rectangle

6 cm

2 cmsquare

4 cm

4 cm

cm2Area = cm Perimeter = cm2Area = cm Perimeter =

Complete this sentence. These shapes have the same but different .

Ouch!

16 14

16 16 12 16

A

B

B

C

40

I’m confi dent I’m nearly thereI can calculate the areas of triangles and parallelograms.

D Calculating areas of triangles and parallelograms

Area of triangle = base x height1

2

base

height

base

height

Area of parallelogram = base x height

Try calculating the areas of these triangles.1

10 cm

4 cm

12 cm

5 cm

Area x

x=

=

=cm2

height

4

base

x 10

1

2

1

2

Area x

x=

=

=cm2

base

x

1

2

1

2

height

6 cm

3 cm

8 cm

2 cm

Now try calculating the areas of these parallelograms.2

Area x

x=

=

=cm2

height

Area x

x=

=

=cm2

3 Some shapes are made up of triangles and parallelograms.

Can you fi nd the area of this shape?

Hint: Make a parallelogram and a triangle.

12 cm

4 cm

8 cm

Funtime!

Answer:

20

30512

183

base

6

162

base

8

t

40 m2

A a of a = x x t

= x 4 x 4

= 8 m2

A a of a m = x t

= 8 x 4 = 32 m2

T l a = 8 + 32 = 40 m2

1212

4 m 8 m

41

I’m confi dent I’m nearly thereI can calculate the volume of cuboids.

E Volumes Remember that the volume of a cuboid can be found using the formula:

Volume = length x width x height

1

3 cm

3 cm

2 cm

Volume =

=

=

x

x

x

x

cm3

length width height

Can you work out the volume of this cuboid?

3 A block of concrete measured 6 m by 3 m by 4 m.

What is its volume?

Think about units in your answer!

4 A sheet of steel measures 2 cm by 3 m by 3 m.

What is its volume? 3 m 3 m

2 cmAnswer:

Help!

2 Which of these cuboids A or B has the biggest volume?

Answer:

3 mm

5 mm

5 mm

4 mm

4 mm

4 mm

AB

3 2 3

18

A

72 m3

0.18 m3

V A =

5 m x 5 m x 3 m

= 75 m3

V B =

4 m x 4 m x 4 m

= 64 m3

2 m = 0.02 m

V =

0.02 m x 3 m x 3 m = 0.18 m3

V of =

6 m x 3 m x 4 m

= 72 m3

42

I’m confi dent I’m nearly thereI can answer word questions about measurement.

F Word questions

1 How would you write two thousand, six hundred and thirteen grams in kilograms?

kg

2 Eight people shared a kilogram of chocolate; how many grams of chocolate did each person get?

g

3 Zac needed some 14 cm lengths of string. His mum gave him a metre of string.

How many 14 cm pieces could he cut from it?

4 If one inch is 25.4 mm, how many millimetres are there in 12 inches?

mm

6 A rectangle has sides that measure 4 cm and 9 cm. A square has the same area as the rectangle.

How long would the square’s sides be?

5 A rectangle has sides that measure 18 mm and 9 mm.

What is the perimeter of the rectangle?

7 Can you write down the formula for the volume of a cuboid?

= x

8 The volume of a cuboid is 36 cm3. It is 3 cm long and 3 cm wide.

What is the height of the cuboid? cm OK!

= x x

2.613

125

7

54 m

6 m

304.8

h h t

4

2613 g

10 = 254.0 m

2 = 50.8 m

12 = 304.8 m

a of =

4 m x 9 m = 36 m2

36 = 3 x 3 x ?

36 = 9 x ?

r 27

1 0 041

2

1 08 02

0451

43

Geometry

A Drawing 2D shapes You will need a pencil, ruler, protractor and set square.

I’m confi dent I’m nearly thereI can draw some 2D shapes.

Draw this triangle to scale.

One line is drawn for you.

1

30 o

10 cm

Can you draw a rectangle with sides 45 mm and 85 mm in the space below?2

Try to draw a hexagon with these measurements.

One line is drawn for you.

3

120 o

3 cm

3 cm

10 cm

Not again!

44

3D shapesB

I’m confi dent I’m nearly thereI can recognise 3D shapes and make nets for them.

What 3D shape can you build using this net?

Answer: A cylinder

Can you spot which 3D shapes these nets are for?1

Jon wanted to make his own dice for a board game. 2

21

3

56

4 Can you write the numbers in their correct places on this net?

6

3Look at this square based pyramid.

Can you draw a net for it?

4 Try to draw a net for this 3D shape.

Hint: You can copy it on to a piece of paper, cut it out and try it if you want to!

Woah!

Hint: Opposite sides always add up to 7.

d r m

1 2 54

3

45

I’m confi dent I’m nearly thereI know some properties of shapes.

Properties of shapesC

The angles inside a quadrilateral

add up to 360o140o

40o

The angles inside a triangle add

up to 180o60o

30oRemember:

Which of these shapes have at least 2 pairs of parallel sides? Circle your answers.1

square pentagon hexagon rhombus trapezium

2 What quadrilateral is being described here?

It has 4 sides. Opposite sides are the same length and opposite angles are equal.

No!

This is a regular pentagon.

Can you write down the angle P and the length Q?

4

108o

PQ

o

Angle =P

cm

Length =Q

2 cm

3 Can you fi nd the missing angles?

50o

90oo

80o

120o

110o

=Ao=B

A

B

5

B

A70o

100o

15o

30o

Can you fi nd angles A and B?

o

Angle =A

o

Angle =B

m

40 50

2108

5095

70o + 15o + A = 180o

100o+ 30o + B = 180o

A of a

d p o 180o

A of a l

d p o 360o

46

I’m confi dent I’m nearly thereI can fi nd missing angles.

AnglesD

Can you fi nd angle B without measuring it?

2

oAngle =B

6 cm

6 cm

135oB

1 Without measuring it, work out the missing angle in this diagram.

A

130o

110o

90o

o

Angle =A

80o

140o140o

The angles meeting at

a point add up to 360o

Angles on a straight line add

up to 180o120o

60o

With two straight lines

vertically opposite

angles are equal

120o 120o

60o

60o

Can you write down angles C and D?3

152o

28o

C

D oAngle =C oAngle =D

4 Look at this regular hexagon. What are angles A and B?

o 60o

B

A

oAngle =A oAngle =B

What is the sum of all the interior angles in a hexagon?

Hint: B is an interior angle.

5 Look at this regular pentagon.

Can you work out angle A?

Now can you work out angle B?

Finally, what is angle C?

o

o

o

Wow!

AB

C

30

45

28 152

12060

720

72

54

108

360o = 110o + 130o + 90o + A

360o = 330o + A

120o x 6 = 720

A = 360o ÷ 5 = 72o

72o + B + B = 180o

B + B = 108o

A = 30o

B = 54o

47

E Properties of circles You will need to understand the words circumference, radius and diameter.

Draw arrows pointing to the parts of this circle.

1 circumference

diameter

radius

A circle has a diameter of 67 mm, what is the radius?2 mm

4 The diameter of this wheel with no tyre is 48 cm.

The radius of the wheel with its tyre is 30 cm.

cm

Here we go!

B

A3 In a maze Billy started at A and followed the path shown back to A.

If the radius of the maze is 6 m and the circumference is approximately 38 m, how far did Billy walk?

m

I’m confi dent I’m nearly thereI know what is meant by the radius, diameter and

circumference of a circle.

Can you work out the depth of the tyre?

depth of tyre

6

31

33.5

A o B g

= of 38 = 19 m

R h o e =48 m ÷ 2 = 24 m

D h of e =

30 m − 24 m = 6 m

12

B o A = 2 x

= 2 x 6 m = 12 m

48

I’m confi dent I’m nearly thereI can use coordinates in 4 quadrants.

1 Look at the grid to the left.

What are the coordinates of points C and D?

C has coordinates

D has coordinates

,

,

F Coordinates

3

2

1

-1

-2

-3

1 32-2-3 -1

y

x

B

A

D

C

A has coordinates (3 , 2)B has coordinates (3 , -2)

-3 2

-3 -2

Look at this shape. It is an isosceles triangle. What are the coordinates of point A?

A has coordinates:

3

,

6

5

4

3

2

1

-1

-2

-3

1 32-2-3 -1

y

x

Look at this parallelogram. What are the coordinates of corner P?

P has coordinates:

4

,

A

y

x

(-4 , 6) (8 , 6)

(6 , -5)P

Here we go...

2 -3 -6 -5

Plot these points on the grid and join them up to make an irregular hexagon.

(1 , 3) (2 , 0) (1 , -3)

(-1 , 3) (-2 , 0) (-1 , -3)

4

3

2

1

-1

-2

-3

-4

1 32 4-4 -2-3 -1

2y

x

49

I’m confi dent I’m nearly thereI can translate shapes and refl ect shapes in the axes of a grid.

G Translations and refl ections

Reminder: A translation is the same as sliding an object without rotating or refl ecting it.

1

1 32 4-4 -2-3 -1

y

x

5

4

3

2

1

-1

-2

-3

-4

-5

5-5

T

If triangle T is translated 2 units in the y direction and 1 unit in the x direction, what will its coordinates be?

, ,

,

If the triangle T in question 1 is translated -4 units in the x direction and -6 units in y direction,

what will its coordinates be?

2

, , ,

3

4

3

2

1

-1

-2

-3

-4

1 32 4-4 -2-3 -1

y

x

Refl ect this shape in the y-axis and draw the refl ection.

What are the coordinates of the vertices of the refl ected shape?

, ,

, ,

4

Describe in detail how you would get shape Z to the new position shown using refl ections and translations.

Look at shape Z on this grid.

1 32 4-4 -2-3 -1

y

x

5

4

3

2

1

-1

-2

-3

-4

-5

5-5

Is this a joke?Z

3 3 5 3

4 5

-2 -5 0 -5 -1 -3

2 0

2 4

3 2

1 2

R t n y-a

n 3 n x n

d -7 n y n.

50

I’m confi dent I’m nearly thereI can answer word questions about geometry.

H Word questions

1 Can you draw a rectangle with sides 15 mm and 85 mm in the space to the right?

2 Jack said that this is a net for a cuboid.

Can you draw it again and make it correct?

3 Two of the angles inside a triangle are 42o and 46o.

What is the third angle inside the triangle?

4 What shape is this? “It has four sides, two of them are parallel and the angles inside it are all different.”

5 Can you fi nish this sentence about quadrilaterals?

“The angles inside a quadrilateral add up to .”

6 A javelin is stuck in the ground at an angle of 62o. What would angle A be?62o A

7 Five logs were used to make a raft. The radius of each log was 27 cm.

How wide was the raft?width

OK!

92o

360o

118o

270 m

m

A of a

d p o 180o

A n a t

d p o 180o

D r of 1 g = 54 m

54 x 5 = 270 r

W h = 10 x

= 10 x 27 = 270

51

Statistics

A Pie charts

pet

nopet

90o

This pie chart shows that or 25% of the children in a class have no pets.

The angle you need to show will be = 90o

1

4

1

4

360

4

I’m confi dent I’m nearly thereI can take information from pie charts and I can make pie charts.

Hint: Think about a clock!

Let’sgo!

The eye colours in Class 6 are shown below:

Work out the angles for each sector and use a protractor to draw a pie chart.

3

Colour

Brown

Blue

Number of children

20

10

Angle

60 children were asked to name their favourite colour.

Their answers are shown in this table.

Can you fi nish the pie chart to show this information?

2 Favouritecolour

Blue

Red

Yellow

Orange

Pink

Number of children

15

5

10

20

10

The children in Class 6 were asked to choose their favourite sports. The pie chart shows the results.

What percentage of the children chose football?

What fraction of the children chose swimming?

What is the angle at the centre of the cricket and hockey sectors if they are both the same size?

1

football

swimmingcricket

hockey%

o

120o

240o

50

45

14

d

w

k

n

120o240o

52

I’m confi dent I’m nearly thereI can use line graphs.

B Line graphs

A line graph is a good way to show how something changes as time goes by.

1

140

120

100

80

60

40

20

1 2 3 4 5 6 7 8 9 100

XX

X XX X X

XX

XX

This graph shows how Sara’s height changed each year from when she was born.

How tall was she when she was 10?

Approximately how tall was she when she was 4?

By how much did Sara grow from when she was born to when she was 8?

cm

cm

cm

Age (years)

Hei

ght

(cm

)

3

Jack heated some water in a pan.

He used a thermometer to measure the temperature of the water every 15 seconds.

Can you plot a graph to show Jack’s results?

2100

90

80

70

60

50

40

30

20

10

15 30 45 60 75 90 105 1200

Time (seconds)

Tem

pera

ture

(o C

)

Time (secs)

Temp(oC)

0

20

15

25

30

40

45

55

60

70

75

80

90

90

105

95

120

100

Not again!

150

100

90

80

70

60

50

40

30

20

10

15 30 45 60 75 90 105 120 1350

XX

XX

X

XX

Time (seconds)

Tem

pera

ture

(o C

) Jill repeated Jack’s experiment in question 2, but she ran out of time and had to stop after 90 seconds.

Look at the line graph of her results.

Can you predict how long it would have taken for her water to boil at 100 oC?

secs

165

140

90

80

150

XX

X

X

X

X

XX

X

53

I’m confi dent I’m nearly thereI can calculate the mean of a set of numbers.

C Averages - the ‘mean’

The mean is a type of average. To work out the mean we add up all the numbers and then divide the total by how many numbers there are.

Four friends started collecting World Cup cards. Jon had 12, Lucy had 8, Ben had 6 and Sara had 14.

How many cards did they have between them?

Complete this to work out the mean number of cards.

1

mean =

=

÷

÷

total number of cards number of people

=

mean =

In a café Siân buys 2 cups of tea at £1.20 each, 1 cup of coffee at £1.40 and 2 cups of hot chocolate at £1.60 each.

How many drinks did she buy altogether?

How much did she spend altogether?

What was the average (mean) cost of each drink?

4

£

£

Yes!

Can you fi nd the mean of these groups of numbers?3

18 20 24 26 32 mean =

18 20 24 24 24 26 32 mean =

Can you fi nd the mean of this group of numbers?2

6 8 9 4 7 2

40

40 4 10

6

24

24

5

7.00

1.40

12 + 8 + 6 + 14 = 40

8 + 2 + 6 + 4 + 9 + 7 = 36

36 ÷ 6 = 6

120 ÷ 5 = 24

168 ÷ 7 = 24

£2.40 + £1.40 + £3.20

= £7.00

4

7 0

12

5

.

. 0

54

I’m confi dent I’m nearly thereI can answer word questions about statistics.

D Word questions

1 What fraction of children chose orange?

2 What fraction of children chose red?

3 What percentage of children chose blue?

4 If there were 28 children in the classhow many chose either blue or orange?

5 What percentage of children did not choose blue or orange?

6 What fraction of children chose yellow?

7 What percentage of children chose yellow?

orange

red

yellowblue

36o

54o

Look at this pie chart which shows the favourite colours of the children in Class 2.

Oh!

25 %

21

25 %

15 %

110

320

36o = of 360o110

= 25 %14

= 25 %14

of 28 = 2134

54360

27180

320= =

320

15100= = 15 %

12

55

Maths facts that children are expected to know by the end of Year 6

By the end of Year 6, children are expected to know the facts in this section. Parents can help by regularly asking questions to test their children's ability to recall these facts.

A little and often is often the best approach.

Appendix - Information for Parents

The times tables up to 12 x 12

Year 6 provides a good opportunity for children to consolidate their multiplication and associated division facts.

They should also try to increase their speed of recall.

A

0123456789

101112

xxxxxxxxxxxxx

1111111111111

=============

0123456789101112

1111111111111

xxxxxxxxxxxxx

0123456789101112

=============

0123456789101112

0123456789

101112

xxxxxxxxxxxxx

2222222222222

=============

024681012141618202224

2222222222222

xxxxxxxxxxxxx

0123456789101112

=============

024681012141618202224

0123456789

101112

xxxxxxxxxxxxx

3333333333333

=============

0369121518212427303336

3333333333333

xxxxxxxxxxxxx

0123456789101112

=============

0369121518212427303336

0123456789

101112

xxxxxxxxxxxxx

4444444444444

=============

04812162024283236404448

4444444444444

xxxxxxxxxxxxx

0123456789101112

=============

04812162024283236404448

56

0123456789

101112

xxxxxxxxxxxxx

5555555555555

=============

051015202530354045505560

5555555555555

xxxxxxxxxxxxx

0123456789101112

=============

051015202530354045505560

0123456789

101112

xxxxxxxxxxxxx

6666666666666

=============

061218243036424854606672

6666666666666

xxxxxxxxxxxxx

0123456789101112

=============

061218243036424854606672

0123456789

101112

xxxxxxxxxxxxx

7777777777777

=============

071421283542495663707784

7777777777777

xxxxxxxxxxxxx

0123456789101112

=============

071421283542495663707784

0123456789

101112

xxxxxxxxxxxxx

8888888888888

=============

081624324048566472808896

8888888888888

xxxxxxxxxxxxx

0123456789101112

=============

081624324048566472808896

0123456789

101112

xxxxxxxxxxxxx

9999999999999

=============

0918273645546372819099108

9999999999999

xxxxxxxxxxxxx

0123456789101112

=============

0918273645546372819099108

0123456789

101112

xxxxxxxxxxxxx

10101010101010101010101010

=============

0102030405060708090100110120

10101010101010101010101010

xxxxxxxxxxxxx

0123456789101112

=============

0102030405060708090100110120

0123456789

101112

xxxxxxxxxxxxx

11111111111111111111111111

=============

0112233445566778899110121132

11111111111111111111111111

xxxxxxxxxxxxx

0123456789101112

=============

0112233445566778899110121132

0123456789

101112

xxxxxxxxxxxxx

12121212121212121212121212

=============

01224364860728496108120132144

12121212121212121212121212

xxxxxxxxxxxxx

0123456789101112

=============

01224364860728496108120132144

57

Common factors

Children should be able to fi nd the factors of two numbers and say which factors the numbers have in common.

Example: 24 has factors 1 2 3 4 6 8 12 24

32 has factors 1 2 4 8 16 32

So the common factors of 24 and 32 are 1 2 4 and 8.

B

Decimals, fractions and percentages

By the end of Year 6 children should know these facts and be able to recall them instantly.

C

=

=

=

0.5

0.25

0.75

1

2

1

4

3

4

=

=

=

0.1

0.2

0.3

etc.

1

10

2

10

3

10

=

=

=

=

0.2

0.4

0.6

0.8

2

10

4

10

6

10

8

10

=

=

=

=

1

5

2

5

3

5

4

5

Try to use the following vocabulary:

How many tenths is 0.8?

How many hundredths is 0.12?

Write 0.75 as a fraction.

What is 75% as a fraction / as a decimal?

Change to a decimal.1

4

=

=

=

0.01

0.21

0.99

etc.

1

100

21

100

99

100

=

=

=

=

=

0.01

0.1

0.25

0.5

0.75

=

=

=

=

=

1%

10%

25%

50%

75%

1

100

10

100

25

100

50

100

75

100

=

=

=

1

4

1

2

3

4

Prime numbers and composite numbers

Children should know the prime numbers up to 50 which are:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

and know that a prime number has no factors apart from 1 and itself.

They should also know that numbers that are not prime numbers are composite numbers.

A composite number does have other factors apart from 1 and itself.

D

58

Notes

59

Notes

60

Notes