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Challenging MathsContents

Contents

Contents

Introduction.................................................................................................... 001

Number........................................................................................................... 003

Number and place value .......................................................................... 003

Curriculum coverage ............................................................................ 003Teaching ideas ..................................................................................... 004Resources ............................................................................................ 006

Using all four operations .......................................................................... 016


Fractions (including decimals and percentages) ...................................... 039


Ratio and proportion ...................................................................................... 065

Curriculum coverage................................................................................. 065Teaching ideas.......................................................................................... 066Resources ................................................................................................ 068

Challenging MathsContents

Algebra .......................................................................................................... 077

Curriculum coverage................................................................................. 077Teaching ideas.......................................................................................... 078Resources................................................................................................. 080

Measurement ................................................................................................. 093


Geometry ....................................................................................................... 110

Geometry: properties of shape ................................................................ 110

Curriculum coverage ............................................................................ 110Teaching ideas ......................................................................................111Resources ............................................................................................ 113

Geometry: position and direction ............................................................. 123


Statistics ........................................................................................................ 137


Challenging MathsIntroduction

Introduction

Introduction

This pack aims to support the teaching of the year 6 maths curriculum. It is organised into the six maths areas:

Number Ratio and Proportion Algebra Measurement Geometry Statistics.

This pack is intended as a resource for the teacher to dip into as and when appropriate to support teaching and learning in the classroom, and all resources are accompanied by an answer sheet. Each area is supported by starter ideas, a selection of resources, taking it further suggestions to extend your children, and plenary ideas. Where possible, SAT style questions have also been included to help with revision. The pack is aimed at a mixed ability cohort but it is worth noting that some concepts and activities are designed to challenge your high achievers.

We hope you enjoy using this pack. If you have any questions, please get in touch: email [email protected] or call us on 01225 788851. Alternatively, you might like to give some feedback for other Teachit Primary members – you can do this by adding a comment on the Challenging Maths UKS2 page on Teachit Primary (please log in to access this).

https://www.teachitprimary.co.uk/challenging-maths

https://www.teachitprimary.co.uk/challenging-maths

Section 1: NumberSection 1a – Number and place value

Section 1: Number


Curriculum coverage This section matches the requirements of the statutory guidance in the National Curriculum for maths as follows:

Year 5: Count forwards or backwards in steps of powers of 10 for any given

number up to 1,000,000.

Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero.

Read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Year 6: Read, spell and pronounce mathematical vocabulary correctly.

Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit.

Round any whole number to a required degree of accuracy.

Use negative numbers in context, and calculate intervals across zero.

Solve number and practical problems that involve all of the above.

© www.teachitprimary.co.uk 2017 29437 Page 3 of 189


Section 1a – Number and place value

Resources: Mathematical word search (Resource 1): A fun activity to assist with

the reading, spelling and pronunciation of mathematical vocabulary. Ideal as a homework activity. Includes teacher’s notes and answers.

Starters: Reading and writing whole numbers (Resource 2): A week of

PowerPoint warm-ups to help your children achieve mastery of place value. Can also be adapted and printed off to use as a worksheet. Includes answers to allow for self-assessment.

Get in line!: Children write a whole number containing up to eight digits on their whiteboards. In small groups or whole class, the children then order themselves from the smallest to the largest number.

Choral counting: Organise the class into three groups and allocate one of the following rules to each: counting in ones, counting in tens or counting in hundreds. Pick a starting number, for example, 107, then choose a group to start counting up (indicate this by pointing up) or counting down (indicate this by pointing down) from this starting point. Keep the groups on their toes by stopping and starting different groups at random.

Mains: Rounding numbers (Resource 3): A worksheet to help children to

consolidate their skills in rounding both whole numbers and decimal numbers.

Negative numbers (Resource 4): Children calculate and consolidate differences through temperature.



Taking it further: Place value challenge: Put up the following digit cards:

1. Use five of the digits above to make a number that is bigger than fifty thousand.

2. Use the digits above to make a three-digit number which has a tens digit that is double the units digit.

3. Use the digits above to make the largest six-digit number possible.

4. Use the digits above to make the smallest six-digit number possible.

5. Use the digits above to make the largest four-digit number possible if you have a four in the thousands.

Plenary ideas: Negative of the day (Resource 5): A handy PowerPoint to aid

children’s knowledge of negative numbers and calculating intervals across zero. Includes number lines to support learning and a template to be filled in with a number of your choice.

Place value problems: Write up the following problems on the interactive whiteboard:


9 0 4 1 7 2



Look at these numbers written in Roman numerals.

MCMVII MMCD MDCCXLIII s MMDX l

Circle the largest number. What is the value of the smallest number?

What is the value of the digit 9 in the number 697432? Circle the correct answer. nine thousand nine hundred ninety thousand nine million nine hundred thousand

Section 1a – Number and place valueResource 1 – Mathematical word search

Name: ................................................ Date:...................................................

Resource 1 – Mathematical word searchFind the 47 hidden mathematical words. There will be eight unused letters left over. These can be rearranged into a different mathematical word. What is this word?

M A R G O L I K C R O T C A FS C I R C L E R E T E M A I DI P R I M E A L I T R E F D IR E W O P A N G L E O R O S AP R N O G Y L O P A A U O P GI P E V E C T O R C R S R H OM E T R E Y U H T H C A P E NO N U M B E R I A E O E P R AD D C U U G O T L G R M E E LE I A L C N R E E I O N B A QE C G T S A S A M M O R M U NQ U E I N E V E P C M I A E SU L X P T M T R A H C Y T S UA A T L N E G A R E V A S A ML R P Y R A M I D S U I D A R

ACUTE DIGIT MODE PROOFANGLE EQUAL MULTIPLY PYRAMID

ARC EVEN NET PYTHAGORASAREA FACTOR NUMBER RADIUS

AVERAGE FRACTION ODD RATIOAXIS GRAPH PARALLEL RHOMBUS

CIRCLE ISOSCELES PERIMETER SETCONE KILOGRAM PERPENDICULAR SPHERECUBE LITRE POLYGON SUM

DECIMAL MEAN POWER SYMMETRYDIAGONAL MEASURE PRIME VECTORDIAMETER METRE PRISM _ _ _ _ _ _ _ _


Section 1a – Number and place valueResource 1 – Mathematical word search

Teacher’s notes:The word search has 47 hidden words and eight unused letters which spell another mathematical word. The eight unused letters are O, I, U, Q, E, A, T, N.These can be rearranged to make the word EQUATION.

M A R G O L I K C R O T C A FS C I R C L E R E T E M A I DI P R I M E A L I T R E F D IR E W O P A N G L E O R O S AP R N O G Y L O P A A U O P GI P E V E C T O R C R S R H OM E T R E Y U H T H C A P E NO N U M B E R I A E O E P R AD D C U U G O T L G R M E E LE I A L C N R E E I O N B A QE C G T S A S A M M O R M U NQ U E I N E V E P C M I A E SU L X P T M T R A H C Y T S UA A T L N E G A R E V A S A ML R P Y R A M I D S U I D A R

ACUTE DIGIT MODE PROOFANGLE EQUAL MULTIPLY PYRAMID

ARC EVEN NET PYTHAGORASAREA FACTOR NUMBER RADIUS

AVERAGE FRACTION ODD RATIOAXIS GRAPH PARALLEL RHOMBUS

CIRCLE ISOSCELES PERIMETER SETCONE KILOGRAM PERPENDICULAR SPHERECUBE LITRE POLYGON SUM

DECIMAL MEAN POWER SYMMETRYDIAGONAL MEASURE PRIME VECTORDIAMETER METRE PRISM E Q U A T I O N


Section 1a – Number and place valueResource 2 – Reading and writing whole numbers

Name: ................................................ Date:...................................................

Resource 2 – Reading and writing whole numbers


To download this PowerPoint, go to the following page:Teachit Primary members:https://www.teachitprimary.co.uk/challenging-maths-powerpoints

https://www.teachitprimary.co.uk/challenging-maths-powerpoints


Section 1a – Number and place valueResource 3 – Rounding numbers

Name: ................................................ Date:...................................................

Resource 3 – Rounding numbers

1. Round the following whole numbers to the nearest 10, 100 and 1000.

Number Nearest 10 Nearest 100 Nearest 1000

7868

6734

89873

14325

128769

2. Round the following numbers to one decimal place:

a. 3.47 ≈ ...................................... f. 89.29 ≈ ..................................

b. 6.77 ≈ ..................................... g. 74.95 ≈ .................................

c. 9.21 ≈ ..................................... h. 88.932 ≈ ................................

d. 14.79 ≈ ................................... i. 29.96 ≈ .................................

e. 67.23 ≈ .................................. j. 30.07 ≈ ..................................

3. Round these numbers to two decimal places:

a. 14.345 ≈ ................................. f. 79.456 ≈ ................................

b. 17.443 ≈ ................................. g. 32.763 ≈ ................................

c. 89.788 ≈ ................................. h. 95.699 ≈ ................................

d. 152.567≈ ................................ i. 124.896 ≈ ............................

e. 345.783 ≈ .............................. j. 456.999 ≈ ..............................


Section 1a – Number and place valueResource 3 – Rounding numbers

Resource 3 – Answers

1. Round the following whole numbers to the nearest 10, 100 and 1000.

Number Nearest 10 Nearest 100 Nearest 1000

7868 7870 7900 8000

6734 6730 6700 7000

89873 89870 89900 90000

14325 14330 14300 14000

128769 128770 128800 129000

2. Round the following numbers to one decimal place:

a. 3.47 ≈ 3.5 f. 89.29 ≈ 89.3

b. 6.77 ≈ 6.8 g. 74.95 ≈ 75.0

c. 9.21 ≈ 9.2 h. 88.932 ≈ 88.9

d. 14.79 ≈ 14.8 i. 29.96 ≈ 30.0

e. 67.23 ≈ 67.2 j. 30.07 ≈ 30.1

3. Round these numbers to two decimal places:

a. 14.345 ≈ 14.35 f. 79.456 ≈ 79.46

b. 17.443 ≈ 17.44 g. 32.763 ≈ 32.76

c. 89.788 ≈ 89.79 h. 95.699 ≈ 95.70

d. 152.567≈ 152.57 i. 124.896 ≈ 124.90

e. 345.783 ≈ 345.78 j. 456.999 ≈ 457.00


Section 1a – Number and place valueResource 4 – Negative numbers

Name: ................................................ Date:...................................................

Resource 4 – Negative numbers 4. Calculate the difference in temperature.

Starting temperature

Finishing temperature Difference

4℃ 6℃7℃ 2℃0℃ 4℃-1℃ 3℃-7℃ 1℃-3℃ 2℃-1℃ -3℃-2℃ 2℃4℃ -3℃-5℃ -4℃-6℃ 3℃-9℃ 2℃

-12℃ 1℃-9℃ 15℃

5. Complete the table.

Starting temperature Rise Finishing

temperature3℃ 2℃5℃ 8℃-1℃ 4℃-2℃ 2℃-4℃ 1℃-5℃ 3℃-3℃ 1℃-4℃ 3℃-3℃ 5℃-2℃ 8℃-3℃ 0℃4℃ 9℃-7℃ -4℃-2℃ 6℃



Name: ................................................ Date:...................................................

6. Complete the table.

Starting temperature Fall Finishing

temperature2℃ 3℃6℃ 5℃-3℃ 1℃-2℃ 4℃3℃ 5℃-4℃ 3℃-1℃ 2℃6℃ 8℃4℃ 9℃-4℃ -7℃0℃ -5℃-2℃ -5℃6℃ -3℃

7. Describe the change in temperature.

Starting temperature Rise or fall? Finishing

temperature1℃ Fall 5℃ -4℃3℃ 7℃-1℃ 0℃2℃ 9℃-3℃ -4℃-5℃ -2℃3℃ 0℃0℃ -2℃-3℃ -7℃-1℃ -9℃-6℃ -4℃5℃ -1℃-2℃ 2℃



Resource 4 – Answers1. Calculate the difference in

temperature. 2. Calculate the finishing

temperature.Starting

Temperature

Finishing Temperatur

eDifference

Starting Temperatur

eRise


e4℃ 6℃ 2℃ 3℃ 2 5℃7℃ 2℃ 5℃ 5℃ 8 13℃0℃ 4℃ 4℃ -1℃ 4 3℃-1℃ 3℃ 4℃ -2℃ 2 0℃-7℃ 1℃ 8℃ -4℃ 1 -3℃-3℃ 2℃ 5℃ -5℃ 3 -2℃-1℃ -3℃ 2℃ -3℃ 1 -2℃-2℃ 2℃ 4℃ -4℃ 3 -1℃4℃ -3℃ 7℃ -3℃ 5 2℃-5℃ -4℃ 1℃ -2℃ 8 6℃-6℃ 3℃ 9℃ -3℃ 3 0℃-9℃ 2℃ 11℃ 4℃ 5 9℃

-12℃ 1℃ 13℃ -7℃ 3 -4℃-9℃ 15℃ 24℃ -2℃ 8 6℃

3. Complete the table. 4. Describe the change in temperature.

Starting Temperatur

eFall


e

Starting Temperatur

eRise or Fall


e2℃ 3 -1℃ 1℃ Fall 5 -4℃6℃ 5 1℃ 3℃ Rise 4 7℃-3℃ 1 -4℃ -1℃ Rise 1 0℃-2℃ 4 -6℃ 2℃ Rise 7 9℃3℃ 5 -2℃ -3℃ Fall 1 -4℃-4℃ 3 -7℃ -5℃ Rise 3 -2℃-1℃ 2 -3℃ 3℃ Fall 3 0℃6℃ 8 -2℃ 0℃ Fall 2 -2℃4℃ 9 -5℃ -3℃ Fall 4 -7℃-4℃ 3 -7℃ -1℃ Fall 8 -9℃0℃ 5 -5℃ -6℃ Rise 2 -4℃-2℃ 3 -5℃ 5℃ Fall 6 -1℃6℃ 9 -3℃ -2℃ Rise 4 2℃


Section 1a – Number and place valueResource 5 – Negative of the day

Name: ................................................ Date:...................................................

Resource 5 – Negative of the day





Section 1a – Number and place valueResource 5 – Negative of the day


Section 1: NumberSection 1b – Using all four operations

Section 1b – Using all four operations


Year 6: Multiply multi-digit numbers up to 4 digits by a two-digit whole number

using the formal written method of long multiplication.

Divide whole numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context.

Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context.

Perform mental calculations, including with mixed operations and large numbers.

Identify common factors, common multiples and prime numbers.

Solve problems involving addition, subtraction, multiplication and division.

Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places.



Section 1b – Using all four operations

Resources: Slider for multiplying and dividing by powers of ten (Resource 6):

A practical resource to help children multiply and divide by powers of ten.

Starters: Properties of number (Resource 7): A series of ten PowerPoint warm-

ups to help children revise factors, multiples, prime numbers, square and cube numbers. Can also be printed off to use as a worksheet. Includes answers to allow for self-assessment.

Fizz buzz: A great way to revise multiples and square numbers. Count normally around the group but use the word ‘fizz’ for a given multiple, for example 3, and ‘buzz’ for a different multiple, for example 5. The children then say ‘fizz buzz’ for multiples of both 3 and 5.

For example: 1, 2, fizz, 4, buzz, fizz, 7, 8, fizz, buzz, 11, fizz, 13, 14, fizz buzz and so on.

Mains: Multiplication circuit (Resource 8): A set of three fun board games to

help children to practise and consolidate their skills in multiplying by whole numbers and decimals using both formal and mental methods.

Multiplying and dividing by 10, 100 and 1000 (Resource 9): A worksheet to help children consolidate the skills of multiplying and dividing by powers of ten, including decimals and money.

Understanding division (Resource 10): A pick n’ mix worksheet to help children become fluent in their understanding of division.



Taking it further: Solve this! (Resource 11): Organise the class into six differentiated

groups and hand out one of the word problems for each group to solve. They then present problems and their workings out to the class.

What’s my function?: Write up the following problem on the interactive whiteboard:

Here are six cards.

x 10 x 100 x 1000

÷ 10 ÷ 100 ÷1000

Use a card to complete each calculation.

5.3 = 0.53 5.3 = 5300

5.3 = 0.053

Answers: 5.3 ÷ 10 = 0.535.3 ÷ 100= 0.0535.3 x 1000 = 5300

Plenary ideas: Misconceptions: There is at least one error in each of the following

division sums. Write up the sums on the board and ask the children to work in pairs to find the error/s and make the correction/s.


31103 9531

2186.14 8745

001115 3258

1105.28 9842

Answers:

3177 2186.25

651.6


Mental maths: A problem to read aloud and solve with the class:


Lara chooses a number less than 100.

She divides it by 3 and then subtracts 11.

She then divides this result by 2.

Her answer is 10.

What was the number she started with?

Answer: 93

Section 1b – Using all four operationsResource 6 - Slider for multiplying and dividing by powers of ten

Resource 6 – Slider for multiplying and dividing by powers of ten




BACK

GLUE ALONG HERE

GLUE ALONG HERE

FRONT

CUTOUT

CUTOUT

CUTOUT

CUTOUT

CUTOUT

CUTOUT

CUTOUT

CUTOUT

CUTOUT

11000

1100

110UTHTHTTHHT

H


1. Print both pages.2. Cut out and laminate the front, back and slider.3. Cut the windows out of the front of the slider. 4. Glue/sellotape the front to the back, making sure you leave a gap for the slider to go through 5. Insert the slider. Children can now write numbers and move up/down when multiplying and dividing by powers of ten.

If laminated, the slider can be wiped and reused.


SLIDER

Section 1b – Using all four operationsResource 7 – Properties of number

Name: ................................................ Date:...................................................

Resource 7 – Properties of number





Section 1b – Using all four operationsResource 7 – Properties of number


Section 1b – Using all four operationsResource 8 – Multiplication circuit

Resource 8 – Multiplication circuit

Teacher’s notesThere are three different board games to choose from:

Multiplying one digit by two, three and four digit numbers Multiplying by decimals Multiplying TU x TU and HTU x TU

This is a two player game. You will need two different coloured counters for each player and a dice for each pair.

1. Each player places one counter on ‘start’. The youngest player rolls the dice first and moves clockwise around the board to land on a calculation.

2. The player performs the calculation either mentally or by showing workings on paper. They then place their chosen coloured counter on the correct answer in the middle of the board.

3. If they answer incorrectly, their partner can attempt to ‘steal’ the square by correcting their work.

4. This player then takes their go.

5. Continue to take turns and move around the board until all answers have been covered with counters.

6. If a player lands directly on ‘start’, they can roll again.

7. The winner is the player with the most counters in the middle when no answers are left uncovered.



Multiplying by decimalsUse a mental method or paper and pencil method to calculate the answers to thefollowing sums.

8 × 3.6 2 × 32.1 4 × 11.7 6 × 10.7 7 × 3.5 9 × 5.2

3 × 18.2 46.8 54.6 16.8 46.8 3 × 9.6

8 × 2.1 28.8 16.8 64.2 28.8 6 × 4.8

5 × 4.9 54.6 28.8 46.8 16.8 6 × 2.8

2 × 27.3 24.5 64.2 54.6 24.5 3 × 21.4

6 × 7.8 16.8 54.6 64.2 28.8 2 × 8.4

Start 7 x 7.8 7 × 2.4 6 × 9.1 4 × 7.2



Multiplying TU x TU and HTU x TU

Use a mental method or paper and pencil method to calculate the answers to thefollowing sums.

39 × 341 36 × 741 46 × 19 63 × 88 34 × 825 27 × 12

25 × 721 13299 224 874 18025 34 × 921

14 × 213 3608 26676 31314 20272 28 × 724

32 × 57 5544 28050 324 12208 88 × 41

28 × 33 924 2982 20564 5244 53 × 388

16 × 14 1584 35910 1260 1824 54 × 665

Start 36 × 44 23 × 228 28 × 45 16 × 763



Multiplying one digit by two, three and four digit numbers

Use a mental method or paper and pencil method to calculate the answers to thefollowing sums.

9 × 64 6 × 741 6 × 19 3 × 8888 4 × 825 7 × 12

5 × 721 576 11664 3605 114 4 × 9214

4 × 213 84 264 852 3300 8 × 724

2 × 57 4446 114 5792 26664 8 × 41

8 × 33 36856 84 2660 360 3 × 3888

6 × 14 328 5778 264 84 4 × 665

Start 6 × 44 3 × 28 8 × 45 6 × 963



Resource 8 – AnswersMultiplying by decimals – possible answers

8 × 3.6 2 × 32.1 4 × 11.7 6 × 10.7 7 × 3.5 9 × 5.2

3 × 18.2 4 x 11.7 = 46.8

3 x 18.2 = 54.6

8 x 2.1 = 16.8

6 x 7.8 = 46.8 3 × 9.6

8 × 2.1 8 x 3.6 = 28.8

7 x 2.4 = 16.8

2 x 32.1 = 64.2

3 x 9.6 = 28.8 6 × 4.8

5 × 4.9 2 x 27.3 = 54.6

6 x 4.8 = 28.8

9 x 5.2 = 46.8

6 x 2.8 = 16.8 6 × 2.8

2 × 27.3 7 x 3.5 = 24.5

6 x 10.7 = 64.2

7 x 7.8 = 54.6

5 x 4.9 = 24.5 3 × 21.4

6 × 7.8 2 x 8.4 = 16.8

6 x 9.1 = 54.6

3 x 21.4 = 64.2

4 x 7.2 = 28.8 2 × 8.4

Start 7 × 7.8 7 × 2.4 6 × 9.1 4 × 7.2



Multiplying TU x TU and HTU x TU – answers

39 × 341 36 × 741 46 × 19 63 × 88 34 × 825 27 × 12

25 × 721 39 x 341 = 13299

16 x 14 = 224

46 x 19 = 874

25 x 721 = 18025 34 × 921

14 × 213 88 x 41 = 3608

36 x 741 = 26676

34 x 921 = 31314

28 x 724 = 20272 28 × 724

32 × 57 63 x 88 = 5544

34 x 825 = 28050

27 x 12 = 324

16 x 763 = 12208 88 × 41

28 × 33 28 x 33 = 924

14 x 213 = 2982

53 x 388 = 20564

23 x 228 = 5244 53 × 388

16 × 14 36 x 44 = 1584

54 x 665 = 35910

28 x 45 = 1260

32 x 57 = 1824 54 × 665

Start 36 × 44 23 × 228 28 × 45 16 × 763



Multiplying one digit by two, three and four digit numbers – possible answers

9 × 64 6 × 741 6 × 19 3 × 8888 4 × 825 7 × 12

5 × 721 9 x 64 = 576

3 x 3888 = 11664

5 x 721 = 3605

6 x 19 = 114 4 × 9214

4 × 213 7 x 12 = 84

6 x 44 = 264

4 x 213 = 852

4 x 825 = 3300 8 × 724

2 × 57 6 x 741 = 4446

2 x 57 = 114

8 x 724 = 5792

3 x 8888 = 26664 8 × 41

8 × 33 4 x 9214 = 36856

6 x 14 = 84

4 x 665 = 2660

8 x 45 = 360 3 × 3888

6 × 14 8 x 41 = 328

6 x 963 = 5778

8 x 33 = 264

3 x 28 = 84 4 × 665

Start 6 × 44 3 × 28 8 × 45 6 × 963


Section 1b – Using all four operationsResource 9 – Multiplying and dividing by 10, 100 and 1000

Name: ................................................ Date:...................................................

Resource 9 – Multiplying and dividing by 10, 100 and 1000

10 000 1000 100 10 1 1

101100

11000

MultiplyingX 10 digits move left 1 spaceX 100 digits move left 2 spacesX 1000 digits move left 3 spaces

Dividing÷ 10 digits move right 1 space÷ 100 digits moves right 2 spaces÷ 1000 digits move right 3 spaces

..

Multiply the following numbers by 10, 100 or 1000. Remember to write amounts of money carefully using the £ sign.

Exercise A

1. 6 x 10 = ............... 6. 0.2 x 10 = ............. 11. £9 x 10 = ...............

2. 23 x 10 = ............. 7. 2.9 x 10 = ............. 12. £5.30 x 10 = ..........

3. 40 x 10 = ............. 8. 5.6 x 10 = ............. 13. £7.06 x 10 = ..........

4. 271 x 10 = ............ 9. 0.03 x 10 = ........... 14. £36.20 x 10 = ........



5. 6.3 x 10 = ............. 10. 0.16 x 10 = ........ 15. £0.04 x 10 = ..........



Exercise B

1. 5 x 100 = ............ 6. 0.4 x 100 = ........... 11. 0.07 x 100 = ..........

2. 36 x 100 = ........... 7. 0.62 x 100 = ......... 12. 16.3 x 100 = ..........

3. 40 x 100 = ........... 8. 3.75 x 100 = ......... 13. £5.64 x 100 = ........

4. 2.8 x 100 = ........... 9. 0.1 x 100 = ........... 14. £0.80 x 100 = ........

5. 22.5 x 100 = ......... 10. 17.03 x 100 = .... 15. £0.02 x 100 = ........

Exercise C

1. 5 x 1000 = ........... 6. 250 x 1000 = ....... 11. 0.61 x 1000 = .......

2. 17 x 1000 = ......... 7. 1.35 x 1000 = ...... 12. 0.92 x 1000 = .......

3. 20 x 1000 = ......... 8. 249 x 1000 = ...... 13. 0.7 x 1000 = .........

4. 3.6 x 1000 = ......... 9. 3.8 x 1000 = ........ 14. 0.89 x 1000 = ......

5. 8.47 x 1000 = ....... 10. 0.294 x 1000 = . . 15. 0.006 x 1000 = .....

Exercise D

1. 2.3 x 100 = .......... 6. £3.70 x 10 = ......... 11. 56.47 x 100 = ........

2. 0.8 x 10 = ............ 7. 4.84 x 1000 = ....... 12. £1.63 x 10 = ..........

3. 3.81 x 1000 = ...... 8. 0.23 x 10 = ........... 13. 3.66 x 100 = ..........

4. 9.42 x 10 = ........... 9. 0.579 x 100 = ....... 14. 20.08 x 10 = ..........

5. 6.38 x 100 = ......... 10. 0.15 x 1000 = .... 15. 0.26 x 1000 = ........



Resource 9 – AnswersExercise A

1. 6 x 10 = 60 6. 0.2 x 10 = 2 11. £9 x 10 = £90

2. 23 x 10 = 230 7. 2.9 x 10 = 29 12. £5.30 x 10 = £53

3. 40 x 10 = 400 8. 5.6 x 10 = 56 13. £7.06 x 10 = £70.60

4. 271 x 10 = 2710 9. 0.03 x 10 = 0.3 14. £36.20 x 10 = £362

5. 6.3 x 10 = 63 10. 0.16 x 10 = 1.6 15. £0.04 x 10 = £0.40

Exercise B

1. 5 x 100 = 500 6. 0.4 x 100 = 40 11. 0.07 x 100 = 7

2. 36 x 100 = 3600 7. 0.62 x 100 = 62 12. 16.3 x 100 = 1630

3. 40 x 100 = 4000 8. 3.75 x 100 = 375 13. £5.64 x 100 = £564

4. 2.8 x 100 = 280 9. 0.1 x 100 = 10 14. £0.80 x 100 = £80

5. 22.5 x 100 = 2250 10. 17.03 x 100 = 1703 15. £0.02 x 100 = £2

Exercise C© www.teachitprimary.co.uk 2017 29437 Page 36 of 189


1. 5 x 1000 = 5000 6. 250 x 1000 = 250000 11. 0.61 x 1000 = 610

2. 17 x 1000 = 17000 7. 1.35 x 1000 = 1350 12. 0.92 x 1000 = 920

3. 20 x 1000 = 20000 8. 249 x 1000 = 249000 13. 0.7 x 1000 = 700

4. 3.6 x 1000 = 3600 9. 3.8 x 1000 = 3800 14. 0.89 x 1000 = 890

5. 8.47 x 1000 = 8470

10. 0.294 x 1000 = 294 15. 0.006 x 1000 = 6

Exercise D

1. 2.3 x 100 = 230 6. £3.70 x 10 = £37 11. 56.47 x 100 = 5647

2. 0.8 x 10 = 8 7. 4.84 x 1000 = 4840

12. £1.63 x 10 = £16.30

3. 3.81 x 1000 = 3810 8. 0.23 x 10 = 2.3 13. 3.66 x 100 = 366

4. 9.42 x 10 = 94.2 9. 0.579 x 100 = 57.9 14. 20.08 x 10 = 200.8

5. 6.38 x 100 = 638 10. 0.15 x 1000 = 150 15. 0.26 x 1000 = 260


Section 1b – Using all four operationsResource 10 – Understanding division

Resource 10 – Understanding divisionBuilding fluency

Work out the following division sums using a written method.

1) 892 ÷ 4 = 2) 9530 ÷ 5 =

3) 81252 ÷ 6 = 4) 627 ÷ 3 =

5) 7476 ÷ 7 = 6) 76012 ÷ 4 =

7) 984 ÷ 4 = 8) 9981÷ 9 =

9) 8472 ÷ 12 = 10) 72048 ÷ 12 =

Problem solving



Find the missing values.

11) 12)

13) 14)

Reasoning

Read the following problems carefully and show any workings to help explain your answer.

15) Tom says 58740 ÷ 5 has no remainder. Do you agree with Tom? Explain your answer.






6_261 0 7

2 051 6 4

0 232 3 4 1

5 071 3 5 8


Name: ................................................ Date:...................................................

Resource 10 – AnswersBuilding fluency

1) 892 ÷ 4 = 223 2) 9530 ÷ 5 = 19063) 81252 ÷ 6 = 13542 4) 627 ÷ 3 = 2095) 7476 ÷ 7 =1068 6) 76012 ÷ 4 = 190037) 984 ÷ 4 = 246 8) 9981÷ 9 = 11099) 8472 ÷ 12 = 706 10) 72048 ÷ 12 = 6004

Problem solving

11) 12)

13) 14)

Reasoning

15) Yes, because it ends in a multiple of five.

16) Yes, because the digit total of 621 is nine and this is a multiple of three.

17) Yes, because it is an even number and its digits add up to a multiple of three.

18) Yes, because it is an even number and you can halve the final two digits twice.

19) Yes, because the digit total of 2133 is a multiple of nine.


6 4 261 0 7

8 2 051 6 4

7 0 2 332 3 4 1

9 5 0 671 3 5 8

Section 1b – Using all four operationsResource 11 – Solve this!

Resource 11 – Solve this!

Mr Jones is having a party. Bottles of cola are 45p each. He has £9.50How many can he buy?............................................How much change will he get back?............................................

Mrs Sweetham is arranging a school trip for 978 students. For every 15 students they need one adult. How many adults must go on the school trip?.............................................

Mr Angell wants to take everyone on a school trip. There are 900 people and each coach has 42 seats. How many coaches should he hire? ............................................How many seats are free? ............................................

Pencils cost 27p each. I have £8.50. How many pencils can I buy?............................................How much change do I have left?............................................

A train has 15 carriages, each carrying 52 people. Bristol City want to take 870 fans to an away game. Will there be enough room on the train? ............................................Calculate the number of extra seats required.

A florist sells tulips for 26p each. A customer asks for £4 worth.How many tulips will she get?............................................How much change will he get?



............................................ ............................................




Mr Jones is having a party. Bottles of cola are 45p each. He has £9.50How many can he buy?21 bottles

How much change will he get back?5p

Mrs Sweetham is arranging a school trip for 978 students. For every 15 students they need one adult. How many adults must go on the school trip?66 adults

Mr Angell wants to take everyone on a school trip. There are 900 people and each coach has 42 seats. How many coaches should he hire? 22 coaches

How many seats are free? 24 seats

Pencils cost 27p each. I have £8.50. How many pencils can I buy?31 pencils

How much change do I have left?13p

A train has 15 carriages, each carrying 52 people. Bristol City want to take 870 fans to an away game. Will there be enough room on the train? No

Calculate the number of extra seats required.

A florist sells tulips for 26p each. A customer asks for £4 worth.How many tulips will she get?15

How much change will he



90get? 10p


Section 1: NumberSection 1c – Fractions (including decimals and percentages)

Section 1c – Fractions (including decimals and percentages)


Year 5: Recognise mixed numbers and improper fractions and convert from one

form to the other.

Solve problems which require knowing percentage and decimal equivalents of 12,

1415 , 25 , 45 and those fractions with a denominator of a

multiple of 10 or 25.

Year 6: Use common factors to simplify fractions; use common multiples to

express fractions in the same denomination.

Add and subtraction fractions with different denominators and mixed numbers, using the concept of equivalent fractions.

Multiply simple pairs of proper fractions, writing the answer in its simplest form.

Divide proper fractions by whole numbers.

Multiply one-digit numbers with up to two decimal places by whole numbers.

Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.



Section 1c – Fractions (including decimals and percentages)

Resources: Place value grid (Resource 12): A useful grid which extends to

thousandths to help children with their understanding of decimals. Can be laminated and reused.

Starters: Beat the teacher!: A great game to develop both place value

knowledge and logical thinking. Display the Place value grid (Resource 12) and take it in turns with the class to roll a dice to decide where each number rolled should go on the grid in order to generate the largest number. The class will soon realise that they need to place the smaller numbers in the decimal place holders and the larger numbers in the thousands, hundreds and tens.

Teachit interactives: If you are a member of Teachit Primary there are lots of snappy starter ideas to kickstart your lesson. Two useful ones are Equivalent percentage snap and Equivalent fraction snap.

Mains: Four in a row (Resource 13): Two differentiated game boards to allow

children to practise finding fractions of whole numbers.

Finding fractions, decimals and percentages (Resource 14): Two differentiated sheets to help children use and apply their knowledge of finding fractions, decimals and percentages. Includes teacher’s notes.

Equivalent fractions, decimals and percentages (Resource 15): Two differentiated worksheets to consolidate finding equivalent fractions, decimals and percentages.

All fraction calculations domino set (Resource 16): A set of domino cards involving all four operations for children to match answers to. Can be used as follow-me cards with a confident class.


http://www.teachitprimary.co.uk/resources/y5/fractions-including-decimals/number/equivalent-fractions-snap/18464

http://www.teachitprimary.co.uk/attachments/13705/percentage-snap-10-of.html


Multiplying fractions circuit (Resource 17): A board game to help children to practise and consolidate their skills of multiplying fractions by whole numbers.

Taking it further: Code breaker – simplifying fractions (Resource 18): A fun way to

engage children in simplifying fractions in order to crack a code!

Plenary ideas: Converting between mixed numbers and improper fractions

(Resource 19): A task which can be completed in pairs to allow children to consolidate their understanding of mixed numbers and improper fractions.

Mental maths: Keep skills ticking over with these examples to be shared on the interactive whiteboard:


3.005 + 6.12 =Answer: 9.125 125.48 – 72.3 =

Answer: 53.18

20% of 1800 =Answer: 360

1.52 x 6 =Answer: 9.12

23.8 divided by 1000 =Answer: 0.0238

x =Answer:



30% = Answer:

+ =Answer:

Section 1c – Fractions (including decimals and percentages)Resource 12 – Place value grid

Resource 12 – Place value grid

Place value grid

Hundreds100s

Tens10s

Ones1s

Tenths0.1s

Hundredths0.01s

Thousandths

0.001s


Section 1c – Fractions (including decimals and percentages)Resource 12 – Place value grid

Place value grid

Hundreds100s

Tens10s

Ones1s

Tenths0.1s

Hundredths0.01s

Thousandths

0.001s


Section 1c – Fractions (including decimals and percentages)Resource 13 – Four in a row

Resource 13 – Four in a row

Teacher’s notes:Print on A3 paper.

Play in pairs – choose a question and work out the answer. Find the solution in the grid (sometimes there is more that one position so some level of strategy can be involved). Aim to get four in a line to win.

OR

Play independently – print on A4 paper. Work out answers until you get a complete row/column/ diagonal. This can be suitable as a plenary/starter.

Two different versions with an increasing level of difficulty.



Name: ..................................................................................... Date:...............................................................................

Game board A

12 of 16 4

5 of 45 67 of 35 5

9 of 54 512 of 72 30 36 16 8 12

13 of 15 1

6 of 24 18 of 16 7

9 of 27 712 of 60 35 21 18 72 5

23 of 12 5

6 of 12 38 of 48 8

9 of 81 1112 of 60 8 55 63 10 21

14 of 28 1

7 of 14 58 of 40 1

10 of 50 12 of 8 2 6 5 10 30

34 of 28 2

7 of 21 78 of 72 3

10 of 40 23 of 9 18 12 3 7 16

15 of 30 3

7 of 28 19 of 27 7

10 of 90 34 of 40 4 30 8 72 9

25 of 25 4

7 of 28 29 of 90 9

10 of 80 25 of 20 18 63 20 25 4

35 of 30 5

7 of 14 49 of 36 1

12 of 108 35 of 30 6 10 6 2 30

© www.teachitmaths.co.uk 2017 29437 Page 52 of 189


Game board A – answers

12 of 16 = 8 4

5 of 45 = 36 67 of 35 = 30 5

9 of 54 = 30512 of 72 = 30

30 36 16 8 12

13 of 15 = 5 1

6 of 24 = 4 18 of 16 = 2 7

9 of 27 = 21712 of 60 = 35

35 21 18 72 5

23 of 12 = 8

56 of 12 = 10

38 of 48 = 18 8

9 of 81 = 721112 of 60 = 55

8 55 63 10 21

14 of 28 = 7 1

7 of 14 = 258 of 40 = 25

110 of 50 = 5

12 of 8 = 4 2 6 5 10 30

34 of 28 = 21 2

7 of 21 = 6 78 of 72 = 63

310 of 40 = 12

23 of 9 = 6 18 12 3 7 16

15 of 30 = 6 3

7 of 28 = 12 19 of 27 = 3

710 of 90 = 63

34 of 40 = 30

4 30 8 72 9

25 of 25 = 10 4

7 of 28= 16 29 of 90 = 20

910 of 80 = 72

25 of 20 = 8 18 63 20 25 4

35 of 30 = 18 5

7 of 14 = 10 49 of 36 = 16

112 of 108 = 9

35 of 30 = 18

6 10 6 2 30



Name: ..................................................................................... Date:...............................................................................

Game board B

12 of 160 4

5 of 475 67 of 490 5

9 of 270 512 of 300 150 380 300 80 240

13 of 225 1

6 of 210 18 of 560 7

9 of 855 712 of 900 525 210 90 180 45

23 of 45 5

6 of 180 38 of 360 8

9 of 630 1112 of 240 90 220 490 225 665

14 of 140 1

7 of 140 58 of 760 1

10 of 450 12 of 120 70 80 75 40 420

34 of 280 2

7 of 280 78 of 560 3

10 of 650 23 of 300 135 195 15 35 360

15 of 225 3

7 of 560 19 of 135 7

10 of 700 34 of 280 35 210 30 560 60

25 of 100 4

7 of 630 29 of 585 9

10 of 200 25 of 225 135 490 130 475 60

35 of 30 5

7 of 315 49 of 675 1

12 of 720 35 of 225 200 150 45 20 125



Name: ..................................................................................... Date:...............................................................................

Game board B - answers

12 of 160 = 80

45 of 475 = 380

67 of 490 = 420

59 of 270 = 150

512 of 300 = 125

150 380 300 80 240

13 of 225 = 75

16 of 210 = 35

18 of 560 = 70

79 of 855 = 665

712 of 900 = 525

525 210 90 180 45

23 of 45 = 30

56 of 180 = 150

38 of 360 = 135

89 of 630 = 560

1112 of 240 = 220

90 220 490 225 665

14 of 140 = 35

17 of 140 = 20

58 of 760 = 475

110 of 450 = 45

12 of 120 = 60 70 80 75 40 420

34 of 280 = 210

27 of 280 = 80

78 of 560 = 490

310 of 650 = 195

23 of 300 = 200

135 195 15 35 360

15 of 225 = 45

37 of 560 = 240

19 of 135 = 15

710 of 700 = 490

34 of 280 = 210

35 210 30 560 60

25 of 100 = 40

47 of 630 = 360

29 of 585 = 130

910 of 200 = 180

25 of 225 = 90

135 490 130 475 60

35 of 30 = 18

57 of 315 = 225

49 of 675 = 300

112 of 720 = 60

35 of 225 = 135

200 150 45 20 125


Section 1c – Fractions (including decimals and percentages)Resource 14 – Finding fractions, decimals and percentages

Resource 14 – Finding fractions, decimals and percentagesTeachers notes:These grids can be used in several ways. In all cases it is a good idea to laminate all question and answer grids, and then the answers grid can be cut up to give a set of answer cards.

1. Individually: A child is given a question grid and only the answer cards (top left 3 x 5) or all the answer cards to match with the questions. They then place the correct answer card on top the question until they have found all of the answers.

2. In pairs/groups:

a) Only use the correct answer cards in the 3 x 5 top left-hand section of each answer grid. Children take an answer card from the top of the pile and place it on the corresponding question. If they are correct, they then put their coloured counter on top. The next child takes a card and if correct they put their coloured counter on top. This continues until all questions are answered correctly and the winner is the one with most counters.

b) The same as for a) but the answer cards are all visible. Children take it in turns to match the answers but try to get 3 correct answers in a row (vertically, horizontally or diagonally).

Answers:The answers are in the 3 x 5 top left-hand section of each answer grid, additional wrong answers are included to increase the level of difficulty of each task.



Grid 1

12 of £20 1

4 of £16 20% of £30 0.5 x £54 110 x £82

10% of £4.50

34 of £40 25% x £7.20 0.1 x £16 1

3 of £6.60

5% x £32 0.5 of £38 0.75 of £200 15 x £45 50% of £19

Grid 2

12 of £48 14 of £1.60 20% of £300 0.6 x £50 1

10 x £82.50

10% of £983.40

34 of £92 25% x £7.20 0.1 x £17 13 of £7.50

30% x £66 0.5 of £58 0.75 of £364 15 x £450 50% of £189



Grid 1 - answers

£10 £4 £6 £27 £8.20 £26£0.45 £30 £1.80 £1.60 £2.20 £95£1.60 £19 £150 £9 £9.50 £3.20£33 £28 £1.25 £7 £12.25 £50

Grid 2 - answers

£24 £0.40 £60 £30 £8.25 £26£98.34 £69 £1.80 £1.70 £2.50 £95.60£19.80 £29 £273 £90 £94.50 £3.20£18.90 £256 £1.60 £32 £12.25 £50


Section 1c – Fractions (including decimals and percentages)Resource 15 – Equivalent fractions, decimals and percentages: Set A

Name: ..................................................................................... Date:...............................................................................

Resource 15 – Equivalent fractions, decimals and percentages: Set AUse your knowledge of fractions, decimals and percentages to complete the table below. Remember to express fractions in their simplest form.

Percentage Decimal Fraction Percentage Decimal Fraction

1 50% 0.5 or 0.50 50100

=12 11 0.75

2 32% 0.32 32100

=1650

= 825 12 0.08

3 7% 7100 13 0.45

4 25% 14 17%

5 49% 15 4%

6 3% 16 39100

7 10% 17 0.6

8 9100 18 2%

9 21100 19 9

10


Section 1c – Fractions (including decimals and percentages)Resource 15 – Equivalent fractions, decimals and percentages: Set A

10 0.2 20 925


Section 1c – Fractions (including decimals and percentages)Resource 15 – Equivalent fractions, decimals and percentages: Set B

Name: ..................................................................................... Date:...............................................................................

Resource 15 – Equivalent fractions, decimals and percentages: Set BUse your knowledge of fractions, decimals and percentages to complete the table below. Remember to express fractions in their simplest form.


1 120 11 0.15

2 60% 12 0.5%

3 1% 13 3640

4 3450 14 24

30

5 0.9 15 85%

6 0.06 16 120%

7 1640 17 3

4

8 2025 18 250%

9 1420 19 12.5%



10 45 20 1

3



Set A – answersUse your knowledge of fractions, decimals and percentages to complete the table below. Remember to express fractions in their simplest form.


1 50% 0.5 or 0.50 50100

=12

11 75% 0.75 75

100=34

2 32% 0.32 32100

=1650

= 825

12 8% 0.08 8

100= 450

= 225

3 7% 0.07 7100

13 45% 0.45 45

100= 920

4 25% 0.25 25100

=14

14 17% 0.17 17

100

5 49% 0.49 49100

15 4% 0.04 4

100= 250

= 125

6 3% 0.03 3100

16 39% 0.39 39

100

7 10% 0.1 or 0.10 10100

= 110

17 60% 0.6 60

100= 610

=35

8 9% 0.09 9100

18 2% 0.02 2

100= 150

9 21% 0.21 21100

19 30% 0.3 3

10= 30100



10 20% 0.2 20100

=15

20 36% 0.36 9

25= 36100



Set B – answersUse your knowledge of fractions, decimals and percentages to complete the table below. Remember to express fractions in their simplest form.


1 5% 0.05 120

= 5100 11 15% 0.15 15

100= 320

2 60% 0.6 60100

=35 12 0.5% 0.005 0.5

100= 1200

3 1% 0.01 1100 13 90% 0.9 36

40=360400

= 90100

4 68% 0.68 3450

= 68100 14 80% 0.8 24

30=240300

= 80100

5 90% 0.9 910 15 85% 0.85 85

100=1720

6 6% 0.06 6100

= 350 16 120% 1.2 1 2

10=1 15

7 40% 0.4 1640

= 410

= 40100 17 75% 0.75 3

4= 75100

8 80% 0.8 2025

= 80100 18 250% 2.5 2 1

2

9 70% 0.7 1420

= 710

= 70100 19 12.5% 0.125 12.5

100= 25200

=18

10 80% 0.8 45= 810

= 80100 20 33.3% 0.33.. 1

3


Section 1c – Fractions (including decimals and percentages)Resource 16 – All fraction calculations domino set

Resource 16 – All fraction calculations domino setTeaching notesCut along the thick dashed lines to create 28 dominoes. You can use these dominoes as a whole-class or small group activity:

a. In small groups, match the questions with the answers to create a chain of dominoes.

b. Give one card to each student in the class and choose one student to start. They read out the question on their card, then the student who thinks they have the correct answer on their card stands up, reads the answer, then gives the next question in the chain. Repeat until all cards have been read.

Answers (reading down the page)

6 1100

÷10 75 18+ 14

16

12 of 32

11000

23×4 3

8 234 + 114 16 58 of 16

22356 of 24 4 1−¿ 18 10 1

2÷4

20 13×2 7

812× 12

18

15× 15

23

12 of 50 1

435of 20 1

251 16×5

25 12+ 12 12 7

8−14 556 214 + 114

1 12+ 14

58

34+ 12 312

211 of 44

34

14× 14 114

34 × 4 22 1

6 of 36

116

14 of 20 3 10

12÷2

5 34 of 100 5

1213÷2



Dominoes

25What is12+ 12 ?

116

What is14 of 20?

75What is18+ 14 ?

34

What is14× 14 ?

4What is1−18 ?

1What is12+ 14 ?

78

What is12× 12 ?

11000

What is23×4?

10What is12÷4 ? 20

What is13×2 ?

125

What is1 16×5 ? 5

What is34 of 100?

22What is16 of 36? 556

What is2 14+1 14 ?



38

What is2 34+1 14 ?

12What is78−14 ?

58

What is34+ 12 ?

23

What is12 of 50?

512

What is13÷2 ? 1 1

4

What is34×4 ?

312What is211 of 44? 3

What is1012÷2 ?

16

What is12 of 32?

18

What is15× 15 ?

2 23

What is56 of 24? 6

What is1100

÷10 ?

14

What is35 of 20? 16

What is58 of 16?


Section 1c – Fractions (including decimals and percentages)Resource 17 – Multiplying fractions circuit

Resource 17 – Multiplying fractions circuitTeacher’s notes:This is a two player game. You will need about 15 red counters, 15 blue counters and a dice for each pair.

1. Each player places one counter on ‘start’. The red player rolls the dice first and moves clockwise around the board to land on a calculation.

2. The red player performs the calculation either mentally or by showing workings on paper. They then place a red counter on the correct answer in the middle of the board.

3. If they answer incorrectly, the blue player can attempt to ‘steal’ the square by correcting their work.

4. The blue player then takes their go.

5. Continue to take turns and move around the board until all answers have been covered with counters.

6. If a player lands directly on ‘start’, they can throw the dice again.

7. The winner is the player with the most counters in the middle when no answers are left uncovered.



Multiplying fractions by whole numbers

18 × 4⁄9 5 × 3⁄5 10 × 3⁄5 15 × 1⁄6 5 × 4⁄5 9 × 2⁄3

10 × 2⁄5 3 21⁄2 8 4 5 × 1⁄2

4 × 3⁄4 51⁄3 3 6 21⁄2 8 × 2⁄3

12 × 2⁄3 4 21⁄2 51⁄3 4 12 × 1⁄3

6 × 8⁄9 6 3 4 8 4 × 5⁄8

6 × 1⁄2 21⁄2 8 51⁄3 6 32 × 1⁄6

Start 6 × 2⁄3 10 × 4⁄5 10 × 1⁄4 8 × 3⁄4



Multiplying fractions by whole numbers – answers

18 × 4⁄9 5 × 3⁄5 10 × 3⁄5 15 × 1⁄6 5 × 4⁄5 9 × 2⁄3

10 × 2⁄5 4 × 3⁄4 = 3 4 × 5⁄8 = 21⁄2 12 × 2⁄3 = 8 5 × 4⁄5 = 4 5 × 1⁄2

4 × 3⁄4 6 × 8⁄9 = 51⁄3 5 × 3⁄5 = 3 10 × 3⁄5 = 6 10 × 1⁄4 = 21⁄2 8 × 2⁄3

12 × 2⁄3 6 × 2⁄3 = 4 5 × 1⁄2 = 21⁄2 8 × 2⁄3 = 51⁄3 12 × 1⁄3 = 4 12 × 1⁄3

6 × 8⁄9 9 × 2⁄3 = 6 6 × 1⁄2 = 3 10 × 2⁄5 = 4 18 × 4⁄9 = 8 4 × 5⁄8

6 × 1⁄2 15 × 1⁄6 = 21⁄2 10 × 4⁄5 = 8 32 × 1⁄6 = 51⁄3 8 × 3⁄4 = 6 32 × 1⁄6

Start 6 × 2⁄3 10 × 4⁄5 10 × 1⁄4 8 × 3⁄4


Section 1c – Fractions (including decimals and percentages)Resource 18 – Code breaker – simplifying fractions

Name: ................................................ Date:...................................................

Resource 18 – Code breaker – simplifying fractionsFind each fraction below in its simplest form.

Fraction Simplified Fraction Simplified

A 48 N 20

28

B 410 O 42

60

C 312 P 24

32

D 2240 Q 2

198

E 1821 R 5

15

F 1045 S 14

22

G 818 T 14

21

H 30100 U 9

15

I 321 V 10

65

J 810 W 27

33

K 1244 X 2

12

L 1280 Y 10

12

M 2545 Z 6

38

Use your fractions above to substitute the correct letters into the code below, to reveal a terrible joke!

9⁄11 3⁄10 5⁄6

11⁄20 1⁄7

11⁄20 2⁄3 3⁄10 6⁄7 2⁄5 1⁄7 3⁄11 6⁄7

2⁄9 1⁄2 3⁄20 3⁄20 7⁄10 2⁄13 6⁄7 1⁄3 ? 2⁄5 6⁄7 1⁄4 1⁄2 3⁄5 7⁄11 6⁄7

1⁄7 2⁄3 9⁄11 1⁄2 7⁄11 2⁄3 9⁄11 7⁄10 2⁄3 5⁄6 1⁄3 6⁄7

11⁄20


Section 1c – Fractions (including decimals and percentages)Resource 18 – Code breaker – simplifying fractions

Resource 18 – AnswersFraction Simplified Fraction Simplified

A 48

12 N 20

2857

B 410

25 O 42

60710

C 312

14 P 24

3234

D 2240

1120 Q 2

198199

E 1821

67 R 5

1513

F 1045

29 S 14

22711

G 818

49 T 14

2123

H 30100

310 U 9

1535

I 321

17 V 10

65213

J 810

45 W 27

33911

K 1244

311 X 2

1216

L 1280

320 Y 10

1256

M 2545

59 Z 6

38319

Use your fractions above to substitute the correct letters into the code below, to reveal a terrible joke!

W9⁄11

H3⁄10

Y5⁄6

D1

1⁄20

I1⁄7

D1

1⁄20

T2⁄3

H3⁄10

E6⁄7

B2⁄5

I1⁄7

K3⁄11

E6⁄7

F2⁄9

A1⁄2

L3⁄20

L3⁄20

O7⁄10

V2⁄13

E6⁄7

R1⁄3

? B2⁄5

E6⁄7

C1⁄4

A1⁄2

U3⁄5

S7⁄11

E6⁄7

I1⁄7

T2⁄3

W9⁄11

A1⁄2

S7⁄11

T2⁄3

W9⁄11

O7⁄10

T2⁄3

Y5⁄6

R1⁄3

E6⁄7

D1

1⁄20


Section 1c – Fractions (including decimals and percentages)Resource 19 – Converting between mixed numbers and improper

fractionsName: ................................................ Date:...................................................

Resource 19 – Converting between mixed numbers and improper fractionsTeaching notes

This resource contains 16 equivalent pairs of fractions, covering simplifying fractions and converting between mixed and improper fractions. Children must decide if the statements are true or false to find the correct order of cards.

You can decide whether to cut out the cards or not – the activity works well either way. You can even decide to use this activity as a treasure hunt, by photocopying the cards onto A3, cutting each out and hanging it around the room.

The cards form a loop, so students will have to work out the starting card to decipher the final fraction.

You could extend the activity by asking students to correct the cards which are false.

AnswersThe starting card is 13. The fraction is ‘Twelve twentieths’.

13 2 7 16 9 4T W E L V E

11 5 14 15 8 10 3 1 12 6T W E N T I E T H S

Examples

1220

=35

1220

= 610

1220

=2440

1220

=3660

More complicated examples:



fractions1220

= 915

1220

=1525

1220

=1830

1220

=2135



fractions

Choosing any starting card, decide if the statement is true or false to create a path through the cards, noting down the letters as you go. Identify the starting letter to spell out a word – your final task is to give five equivalent values.

168=34

True?Go to 12. 2

94=2 34

True?Go to 4.

T False?Go to 11. W False?

Go to 7.

31518

=57

True?Go to 4. 4

1 38=118

True?Go to 11.

E False?Go to 1. E False?

Go to 12.

547=2442

True?Go to 14. 6

3 27=237

True?Go to 13.

W False?Go to 7. S False?

Go to 9.

7195

=4 15

True?Go to 11. 8

1734

=13

True?Go to 2.

E False?Go to 16. T False?

Go to 10.

93648

=34

True?Go to 4. 10

174

=4 34

True?Go to 16.

V False?Go to 6. I False?

Go to 3.

11915

=35

True?Go to 5. 12

2 611

= 1128

True?Go to 7.

T False?Go to 11. H False?

Go to 6.

131830

=35

True?Go to 2. 14

323

=10 23

True?Go to 15.

T False?Go to 8. E False?

Go to 11.

15 2836

=79

True?Go to 8. 16 3 2

9=239

True?Go to 3.



fractions

N False?Go to 6. L False?

Go to 9.


Section 2: Ratio and proportionSection 2: Ratio and proportion

Section 2: Ratio and proportionSection 2: Ratio and proportion


Year 6:Pupils should be taught to:

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.

Solve problems involving the calculation of percentage (for example, of measures, such as 15% of 360) and the use of percentages for comparison.

Solve problems involving similar shapes where the scale factor is known or can be found.

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.


Section 2: Ratio and proportion


Starters: Sort the class!: Your class makes the perfect visual introduction to ratio

and proportion. Ask the children to group themselves according to a category, for example: boys and girls, skirts and trousers, siblings and no siblings, ways of travelling to school etc., and express as a ratio.

For example, if exploring the ratio of boys and girls, you could generate the ratio14:16 which can then be simplified to 7:8.

Using ratio to compare quantities (Resource 1): A fantastic PowerPoint which can be used as a starter or plenary. Questions are presented over two slides and follow a mastery approach. Can also be used as individual worksheets. Answers are displayed to allow for self-assessment.

Mains: Understanding scale factors (Resource 2): A helpful introduction to

both finding the scale factor and enlarging a shape. Includes a detailed example of how to find each and opportunities for children to apply their skills and knowledge to new examples.

Ratio code breaker (Resource 3): A fun resource to allow children to apply their knowledge of factors to simplify the ratios and crack the code!

Taking it further: Ice cream problem: Write up the following problem for the children to

discuss and solve. Encourage them to show all workings out.

Here are the ingredients for strawberry ice cream.


Strawberry ice cream recipe:

cream - 400ml milk - 500ml egg yolks - 4 strawberries -120g sugar - 100g

Question: George only has 300ml of cream to make strawberry ice cream. What weight of strawberries should he use?

Answer: 90g, as he uses one quarter less of cream, so needs one quarter less of strawberries.


You can encourage more confident children to scale down all of the ingredients so that the new recipe will be:

Plenary ideas: Mental maths: Strengthen mental maths skills by setting some 15

second type questions for children to respond to on their whiteboards. For example:


Strawberry ice cream recipe:

cream - 300ml milk - 375ml egg yolks - 3 strawberries - 90g sugar - 75g

F. 70% of 80.

Answer: 56

E. 5% of 4200

Answer: 210

D. 15% of £250

Answer: £37.50

C. 35% of 60

Answer: 21

B. 17 = ❑21

Answer: 321

A. The scale on a map is one centimetre to five kilometres.

The distance between two houses is twenty kilometres. What is the distance between these two houses on the map?

Answer: 4cm

Section 2: Ratio and proportionResource 1 – Using ratio to compare quantities

Resource 1 – Using ratio to compare quantities





Section 2: Ratio and proportionResource 1 – Using ratio to compare quantities


Section 2: Ratio and proportionResource 2 – Finding a scale factor and centre of enlargement

Name: ................................................ Date:...................................................

Resource 2 – Finding a scale factor and centre of enlargementWhen looking at enlargements you need a scale factor and a centre of enlargement.

Be clear which is the original shape (object) and which is the enlarged shape (image) – don’t confuse the two!

Points to consider: For it to be an enlargement, the shapes must look the same. Find the scale factor by comparing the lengths of the same sides. Find the centre of enlargement by drawing straight lines through

similar points and seeing where they cross. Try with at least three different lengths and points to check for errors.

Example 1

Shape P has been enlarged to give shape Q.

Find the scale factor and centre of enlargement.

You should notice:

The base and height of shape Q are twice that of shape P.

The lines through three sets of similar points cross at (0, 2)

Answer:

P has been enlarged by scale factor 2, centre of enlargement (0,


P

Q


2)



Name: ................................................ Date:...................................................

Resource 2 – Finding a scale factor and centre of enlargementIn each diagram, shape P has been enlarged to give shape Q. Find the scale factor and centre of enlargement for each.

a. scale factor ..............centre of ...............enlargement

b. scale factor ..............centre of ...............enlargement

c. scale factor ..............centre of ...............enlargement

d. scale factor ..............centre of ...............enlargement

e. scale factor ..............centre of ...............enlargement

f. scale factor ..............centre of ...............enlargement


P Q P

QP Q

P

Q P

Q

P

Q


Name: ................................................ Date:...................................................

Resource 2 – Enlarging a shape by a given scale factor and centre of enlargementWhen looking at enlargements you need a scale factor and a centre of enlargement.

Be clear which is the original shape (object) and which is the enlarged shape (image) – don’t confuse the two!

Points to consider: Diagrams must always be drawn with a sharp

pencil, and straight lines must be drawn with a ruler.

Leave your construction lines visible as part of your answer. Some questions will tell you how to label your image:

‘Enlarge shape P and label the image Q.’

If you are not told how to label your image, use the same letter(s) as the object followed by an apostrophe:

the image of A is labelled A’ the image of triangle ABC is labelled A’B’C’.

Example 1Enlarge shape A by scale factor 2, centre of enlargement (0, 0).

You should:1. Plot the centre of enlargement.2. Draw a line from the centre of

enlargement to one corner of the shape. Extend this line beyond the shape until it is twice as long (as we are using scale factor 2).

3. Repeat for two other corners on the shape.

4. Join up the corners to create the image and label

Answer:


A


it as A’.5. Check your work by comparing the

lengths of the sides. Is the height of the new shape twice the height of the original? Are the angles unchanged?


AA’


Name: ............................................... Date:...................................................

Resource 2 – Enlarging a shape by a given scale factor and centre of enlargement

a. Use centre of enlargement (0, 0) and scale factor 2 to enlarge square ABCD.

b. Enlarge shape H using centre of enlargement (0, 5) and scale factor 2.

c. Use centre of enlargement (0, 2) to enlarge the letter M by a scale factor of 3. Label the image as P.

d. Use centre of enlargement (2, 0) and scale factor 3 to enlarge arrow Q, to give image R.

e. Use centre of enlargement (0, 4) and scale factor 3 to enlarge triangle ABC.

f. Use centre of enlargement (2, 2) to enlarge hexagon T by a scale factor ½.


A

D C

B

Q

A

C B

T


Resource 2 – AnswersFinding a scale factor and centre of enlargement:

a. scale factor: 3 b. scale factor: 2

centre of enlargement: (0, 1) centre of enlargement: (1, 0)

c. scale factor: 3 d. scale factor: 2


e. scale factor: 2 f. scale factor: ½


Enlarging a shape by a given scale factor and centre of enlargement:

a. b.

c. d.


AD C

B

A’D’ C

’

B’

P Q

R


e. f.


A

C B

A’

C’

B’

T

T’

Section 2: Ratio and proportionResource 3 – Ratio code breaker

Name: ................................................ Date:...................................................

Resource 3 – Ratio code breaker Find the highest common factor of the numbers in each ratio to find the ratio in its simplest form.

A 8 : 10 M 21 : 15

B 24 : 3 N 5 : 15C 21 : 9 O 6 : 12

D 6 : 16 P 12 : 28

E 12 : 20 R 18 : 3

I 4 : 6 S 40 : 24

J 14 : 7 T 8 : 6

K 30 : 3 U 15 : 10

L 4 : 36 Y 25 : 35

Swap each simplified ratio in the code for its corresponding number to give the names of four singers.

..... ..... ..... ..... ..... ..... ..... ..... ..... .....2 : 1 3 : 2 5 : 3 4 : 3 2 : 3 1 : 3 4 : 3 2 : 3 7 : 5 8 : 1

..... ..... ..... ..... ..... ..... ..... ..... ..... .....3 : 5 6 : 1 1 : 9 4 : 5 10 : 1 3 : 5 7 : 5 4 : 5 3 : 8 1 : 2

..... ..... ..... ..... ..... ..... ..... ..... ..... .....1 : 3 1 : 3 4 : 5 8 : 1 1 : 2 8 : 1 7 : 5 4 : 5 6 : 1 1 : 9

..... ..... ..... ..... ..... ..... ..... .....3 : 5 5 : 7 3 : 7 6 : 1 2 : 3 1 : 3 7 : 3 3 : 5




Who are the four singers?



A 8 : 10 4 : 5 M 21 : 15 7 : 5

B 24 : 3 8 : 1 N 5 : 15 1 : 3

C 21 : 9 7 : 3 O 6 : 12 1 : 2

D 6 : 16 3 : 8 P 12 : 28 3 : 7

E 12 : 20 3 : 5 R 18 : 3 6 : 1

I 4 : 6 2 : 3 S 40 : 24 5 : 3

J 14 : 7 2 : 1 T 8 : 6 4 : 3

K 30 : 3 10 : 1 U 15 : 10 3 : 2

L 4 : 36 1 : 9 Y 25 : 35 5 : 7

J U S T I N T I M B

2 : 1 3 : 2 5 : 3 4 : 3 2 : 3 1 : 3 4 : 3 2 : 3 7 : 5 8 : 1

E R L A K E M A D O

3 : 5 6 : 1 1 : 9 4 : 5 10 : 1 3 : 5 7 : 5 4 : 5 3 : 8 1 : 2

N N A B O B M A R L

1 : 3 1 : 3 4 : 5 8 : 1 1 : 2 8 : 1 7 : 5 4 : 5 6 : 1 1 : 9

E Y P R I N C E

3 : 5 5 : 7 3 : 7 6 : 1 2 : 3 1 : 3 7 : 3 3 : 5




Justin TimberlakeMadonna

Bob MarleyPrince

Section 3: AlgebraSection 3: Algebra

Section 3: AlgebraSection 3 – Algebra


Year 6:

Pupils should be taught to:

Use simple formulae.

Generate and describe linear number sequences.

Express missing number problems algebraically.

Find pairs of numbers that satisfy an equation with two unknowns,

Enumerate all possibilities of combinations of two variables.


Section 3: Algebra

Section 3 - Algebra

Starters: Sequence of the day (Resource 1): A PowerPoint resource to help

children to ‘dip’ into the skills of generating and describing linear number sequences.

Mains: Missing numbers (Resource 2): A worksheet where children need to

find pairs of numbers that balance an equation with two unknowns.

Substitution code breaker (Resource 3): A fun way for children to use their algebraic skills to crack a code. Includes an extension idea.

Snakes and Ladders (Resource 4): An engaging way to help children to solve a range of algebraic problems. For support, organise children into mixed ability pairs to play the game.

Taking it further: Solve this!: Write up the following problem on the interactive whiteboard

to solve and discuss with the class:

One is done for you.

1 2 3 4 5 6 7 8


a stands for a number on a grey card.

b stands for a number on a white card.

Join all pairs of numbers that match this rule:

2a + b = 10

Section 3: Algebra

1 2 3 4 5 6 7 8

Plenary ideas Mental maths: Here are some examples from past papers to share with

your class:


n = 22

What is 2n + 9?

Answer: 53

2q + 4 = 100

Work out the value of q

Answer: 48

Section 3: AlgebraResource 1 – Sequence of the day

Resource 1 – Sequence of the day





Section 3: AlgebraResource 2 – Missing numbers

Name:................................................. Date:...........................................................

Resource 2 – Missing numbersFor each of these calculations, the same number from the scale

(-9 to 9) must go into both boxes.

Complete the calculations.

-9

-8

-7

-6

-5

-4

-3

-2

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



Over to you!

Now create five of your own

examples for a partner to solve.

................

................

................

................

................


1. a + 8 = 2 x a

2. b + 10 = 3 x b3. c + 16 = 5 x c4. 20 + d = 6 x d

5. 18 - e = 5 x e

6. f + 12 = 4 x f

7. 36 + g = 5 x g

8. 14 + h = 3 x h9. 48 + i = 7 x i

10. 21 + j = 4 x j

11. k + 40 = 9 x k

12. 28 + l = 8 x l

13. 72 + m = 9 x m

14. n + 15 = 6 x n

15. 4 + o = 5 x o

16. 40 - p = 4 x p




1. 8 + 8 = 2 x 8

2. 5 + 10 = 3 x 5

3. 4 + 16 = 5 x 4

4. 20 + 4 = 6 x 4

5. 18 - 3 = 5 x 3

6. 4 + 12 = 4 x 4

7. 36 + 9 = 5 x 9

8. 14 + 7 = 3 x 7

9. 48 + 8 = 7 x 8

10. 21 + 7 = 4 x 7

11. 5 + 40 = 9 x 5

12. 28 + 4 = 8 x 4

13. 72 + 9 = 9 x 9

14. 3 + 15 = 6 x 3

15. 4 + 1 = 5 x 1

16. 40 - 8 = 4 x 8

Section 3: AlgebraResource 3 – Substitution code breaker

Name:...................................................................................... Date:................................................................................................

Resource 3 – Substitution code breakerFind the hidden phrase. Substitute the correct values into the expressions below then use your answers to replace the numbers in the code with the corresponding letters.

A 4a =..........................................=...... N 5a + b – 2c =...........................................=.......

B 3b =..........................................=.................................................. O 12c + 4a =...........................................=.......

C 5c =..........................................=...... P 5b + c – 2d =...........................................=......

D a + d =..........................................=...... R 10c + 5d – a =...........................................=......

E 4c + 2a =..........................................=...... S 9d + 8c – 2a =...........................................=......

F 5b + c + a =..........................................=...... T 6b – 3a =...........................................=.......

H 4b – a =..........................................=...... V 8c + a – 2b =...........................................=......


a = 3

b = 5

c = 1

d = 0

e.g. 2b + 3c = (2 x 5) + (3 x 1) = 13


I 7c – a =..........................................=...... W 6b + c – a =...........................................=......

L 7a – 3b =..........................................=...... Y a + b + c + d =...........................................=......



........

........

........

........

........

........

........

........

........

........

........

........

........

........

........ .

18 24 15 24 3 9 4 2 26 10 7 29 10 5 21

........

........

........

........ ‘ ......

..........

........

........

........

........

........

........

........

........

........

21 17 12 21 2 28 17 9 26 10 18 5 4 6 2

........

........

........

........

........

........

........

........

........

........

........ .

17 12 1 10 10 7 12 2 10 7 2

Extension:

Using the same substitution values, create your own code breaker and ask a partner to solve it.

................................................................................................................................................................................................................

................................................................................................................................................................................................................



................................................................................................................................................................................................................

Resource 3 – AnswersA 4a = 4 x 3 = 12 N 5a + b – 2c = 5 x 3 + 5 – 2 x 1 = 18

B 3b = 3 x 5 = 15 O 12c + 4a = 12 x 1 + 4 x 3 = 24

C 5c = 5 x 1 = 5 P 5b + c – 2d = 5 x 5 + 1 – 2 x 0 = 26

D a + d = 3 + 0 = 3 R 10c + 5d – a = 10 x 1 + 5 x 0 – 3 = 7

E 4c + 2a = 4 x 1 + 2 x 3 = 10 S 9d + 8c – 2a

= 9 x 0 + 8 x 1 – 2 x 3 =2

F 5b + c + a = 5 x 5 + 1 + 3 = 29 T 6b – 3a = 6 x 5 – 3 x 3 = 21

H 4b – a = 4 x 5 – 3 = 17 V 8c + a – 2b = 8 x 1 + 3 – 2 x 5 = 1

I 7c – a = 7 x 1 – 3 = 4 W 6b + c – a = 6 x 5 + 1 – 3 = 28

L 7a – 3b = 7 x 3 – 3 x 5 = 6 Y a + b + c + d = 3 + 5 + 1 + 0 = 9

N O B O D Y I S P E R F E C T .18 24 15 24 3 9 4 2 26 10 7 29 10 5 21

T H A T ‘ S W H Y P E N C I L S21 17 12 21 2 28 17 9 26 10 18 5 4 6 2



H A V E E R A S E R S .17 12 1 10 10 7 12 2 10 7 2


Section 3: AlgebraResource 4 – Snakes and ladders

Resource 4 – Snakes and Ladders

Preparation

1. Laminate the board and cards.

2. Cut out the 39 equation cards.

3. Shuffle them and place them face down on the table.

4. Cut out one counter for each player and place it at the start of the game board.

How to play

1. In turns, each player takes a card from the pack and solves the equation for x.

2. The rest of the players check the answer.

3. If correct, the player moves their counter forward x number of squares.

4. If incorrect, the player misses their turn.

5. If you land on top of a snake head, you must slide all the way down to the snake’s tail. If you land at the bottom of a ladder, you can climb all the way to the square at the top of the ladder.

6. The winner is the first person to reach or pass 100.





Equation Cards

8x + 8 = 24x =

4x + 5 = 33x =

6x – 1 = 53x =

4 x + 16 = 7x + 10x =

7x + 2 = 9x =

11x – 9 = 57x =

10x – 14 = 5x + 11x =

2(4x + 10) = 76x =

3(2x – 3) = 33x =

4x + 1 = 17x =

4x – 1 = 11x =

5x + 8 = 6x + 4x =

11x + 9 = 42x =

4x – 5 = 3x =

10x – 44 = 4x + 10x =

11x – 6 = 7x + 6x =

8x + 3 = 7x + 10x =

9(3x + 8) = 261x =

9(10x – 6) = 216x =

7x – 9 = 26x =

8x + 15 = 12x + 3x =

9x – 40 = 4x + 5x =



10x + 4 = 64x =

9x – 8 = 10x =

3x + 9 = 8x – 1X=

11x – 16 = 8x + 5x =

2(7x + 3) = 118x =

8(x – 9) = -72x =

6x + 8 = 62x =

10x – 1 = 59x =

12x + 8 = 11x +10x =

9x – 7 = 5x + 1x =

4x + 5 = 29x =

2x – 3 = 13x =

6x + 34 = 11x + 4x =

9x + 7 = 7x =

5(8x + 7) = 35x =

3(2x – 5) = 33x =

Counters



Resource 4 -– Answers

8x + 8 = 24x = 2

4x + 5 = 33x = 7

6x – 1 = 53x = 9

4 x + 16 = 7x + 10x = 2

7x + 2 = 9x = 1

11x – 9 = 57x = 6

10x – 14 = 5x + 11x = 5

2(4x + 10) = 76x = 7

3(2x – 3) = 33x = 7

4x + 1 = 17x = 4

4x – 1 = 11x = 3

5x + 8 = 6x + 4x = 4

11x + 9 = 42x = 3

4x – 5 = 3x = 2

10x – 44 = 4x + 10x = 9

11x – 6 = 7x + 6x = 3

8x + 3 = 7x + 10x = 7

9(3x + 8) = 261x = 7

9(10x – 6) = 216x = 3

7x – 9 = 26x = 5

8x + 15 = 12x + 3x = 3

9x – 40 = 4x + 5x = 9



10x + 4 = 64x = 6

9x – 8 = 10x = 2

3x + 9 = 8x – 1x = 2

11x – 16 = 8x + 5x = 7

2(7x + 3) = 118x = 8

8(x – 9) = -72x = 0

6x + 8 = 62x = 9

10x – 1 = 59x = 6

12x + 8 = 11x +10x = 2

9x – 7 = 5x + 1x = 2

4x + 5 = 29x = 6

2x – 3 = 13x = 8

6x + 34 = 11x + 4x = 6

9x + 7 = 7x = 0

5(8x + 7) = 35x = 0

3(2x – 5) = 33x = 8


Section 4: MeasurementSection 4: Measurement

Section 4: MeasurementSection 4 – Measurement


Year 5:

Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre).

Year 6:

Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate.

Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places.

Convert between miles and kilometres.

Recognise that shapes with the same areas can have different perimeters and vice versa.

Recognise where it is possible to use formulae for area and volume of shapes.

Calculate the area of parallelograms and triangles.

Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units (for example, mm³ and km³).


Section 4: Measurement




Resources: Clock face (Resource 1): A handy visual resource. Print off and

laminate both the clock face and hands. Cut out and attach the hands to the centre of the clock using a split pin.

Starters: Metric Bingo (Resource 2): A fun and interactive way to revise metric

unit conversions. Includes teacher’s notes with variations and bingo boards.

Time Bingo (Resource 3): A further interactive resource to help children to mentally calculate differences in time.

Adding intervals of time: A quick fire game to sharpen children’s mental maths! Sit in a circle and specify a start time such as 9.30. Each subsequent child in the circle adds a specified number of minutes, for example 20, and expresses the new time. Play continues until one child hesitates or offers an incorrect answer. Support can be provided by grouping the children into pairs or providing a clock face (see Resource 1).

Variations: subtract a given number of minutes rather than add make use of both 12-hour and 24-hour times increase difficulty by starting at a time such as 10.57.

Mains: From sentences to formulae (Resource 4): A comprehensive

PowerPoint to introduce children to the use of formulae to calculate area, volume, perimeter and even speed.

Kilometres to miles – drawing a conversion graph (Resource 5) : A fantastic resource to help children to both convert between kilometres and miles, and to present data in a line graph.


Section 4: Measurement Perimeter problems (Resource 6): A PowerPoint to develop children’s

problem solving skills, and includes decimal calculations. Can be adapted to make a worksheet.

Taking it further: Cuboid problem: Use the following problem to extend children’s

understanding of finding the volume:

Cleo has 24 centimetre cubes.

She uses all 24 cubes to make a cuboid with the dimensions 6cm, 2cm and 2cm.

Write the dimensions of a different cuboid she can make using all 24 cubes.

__________ cm, _________ cm and __________ cm.

Answers: 1 x 1 x 24, 1 x 2 x 12, 1 x 4 x 6, 1 x 8 x 3 and 2 x 3 x 4.

Plenary ideas: Mental maths: Stengthen mental maths skills by setting some 15

second type questions for children to respond to on their whiteboards. For example:




d) A train journey began at ten thirty-five am and ended at eleven fifteen am. How long was the journey in minutes?Answer: 40 minutes

c) A spoon holds five millilitres. How many spoonfuls do you get from a two hundred and fifty millilitres?Answer: 50 spoonfuls

e) How many centimetres are there in 2.5m?Answer: 250cm

b) A car travels at an average speed of fifty miles per hour. How far does it travel in two and a half hours?Answer: 125 miles

a) I started a journey at three twenty pm. The journey lasted for forty-five minutes. At what time did I arrive? Answer: 4.05pm or Five minutes past four

f) At sunrise the temperature was minus three degrees celsius. By midday, the temperature had increased by twelve degrees.What was the temperature at midday?Answer: 9 degrees celsius

Section 4: MeasurementResource 1 – Clock face

Resource 1 – Clock facePrint off and laminate both the clock face and hands. Cut out and attach the hands to the centre of the clock using a split pin.


Section 4: MeasurementResource 1 – Clock face


Section 4: MeasurementResource 2 – Metric bingo

Name: ................................................ Date:...................................................

Resource 2 – Metric bingoSetting upCut out all 16 bingo cards, shuffle them, and place them face down on the table. Each player should create their own bingo card by choosing nine of these numbers to place onto the 3 × 3 grid:

1 5 10 20 25 40 50 75100 200 250 500 750 1000 2000 2500

How to playTake turns to pick a card and read the question card aloud. For each question, cross off the answer if it appears on your grid. Keep the cards to one side so you can check answers later.

Once you have crossed off three numbers in a row (horizontal, vertical or diagonal), shout BINGO!

Bingo cards

How many grams are in a

kilogram?

How many centimetres are in one metre?

How many centilitres are in half a litre?

What is 0.001m in millimetres?

How many metres are in

half a kilometre?

What is 2½cm in millimetres?

How many grams are in a

quarter of a kilogram?

How many centimetres are

in three-quarters of a

metre?

How many metres are in

two kilometres?

0.2kg is equal to how many

grams?


equal to 50 millimetres?

How many grams are equal to 0.04kg?


How many grams are in

three-quarters of a kilogram?

How many centimetres are equal to 0.2m?

How many millilitres are there in 2½

litres?





Teaching notesPlay in small groups by giving one sheet to each group, or play as a class by asking one student to act as the caller (the answers are not given on the cards so the caller can still play). Alternatively, the teacher could act as the caller using the answer cards below.

Make the game longer by playing for a Full House instead, where students need to cross off all nine of their numbers.

Ask students to create their own collection of bingo revision by inventing questions on different topics. You could ask that the answers match this game, so students can use the same grid every time.

Answer cards

How many grams are in a kilogram?

1000

How many centimetres are in

one metre?100

How many centilitres are in

half a litre?50


1

How many metres are in half a kilometre?

500

What is 2½cm in millimetres?

25

How many grams are in a quarter of

a kilogram?250

How many centimetres are in three-quarters of

a metre?75

How many metres are in two

kilometres?2000

0.2kg is equal to how many grams?

200


equal to 50 millimetres?

5

How many grams are equal to

0.04kg?40


10

How many grams are in three-quarters of a

kilogram?750

How many centimetres are equal to 0.2m?

20

How many millilitres are

there in 2½ litres?2500


Section 4: MeasurementResource 3 – Time bingo

Name: ................................................ Date:...................................................

Resource 3 – Time bingoSetting upCut out all 16 bingo cards, shuffle them, and place them face down on the table. Each player should create their own bingo card by choosing nine of these numbers to place into a 3 × 3 grid:

0 1 5 10 15 20 25 3035 40 45 50 55 60 90 120

How to playTake turns to pick a card and read the question card aloud. For each question, cross off the answer if it appears in your grid. Keep the cards to one side so you can check answers later.

Once you have crossed off three numbers in a row (horizontal, vertical or diagonal), shout BINGO!

Bingo cards

Three-quarters of an hour

earlier than 8.10 is how

many minutes past 7 o’clock?

What is the first digit on a

digital clock at midnight?

How many minutes are

there between 3.20 to 4 o’clock?


there between 16.40 and

17.40?

How many minutes are in a quarter of an

hour?

Forty minutes earlier than

midnight is 11. ?


between 6.25 and 7 o’clock?

How many minutes are there from

11.10 to 13.10?

How many minutes are in one and a half

hours?

Half an hour earlier than 4.25 is how

many minutes past 3 o’clock?

How many minutes are in three-quarters

of an hour?

How many minutes are there from 11.55am to 12.05pm?




between quarter to four

and 3.50?

How many minutes are in half an hour?

How many minutes are there from 9.35pm to 10.25pm?

What is the first digit on a

digital clock at midday?



Teaching notes

Play in small groups by giving one sheet to each group, or play as a class by asking one student to act as the caller (the answers are not given on the cards so the caller can still play). Alternatively, the teacher could act as the caller using the answer cards below.

Make the game longer by playing for a Full House instead, where students need to cross off all nine of their numbers.

Ask students to create their own collection of bingo revision by inventing questions on different topics. You could ask that the answers match this game, so students can use the same grid every time.

Answer cardsThree-quarters of

an hour earlier than 8.10 is how many minutes past 7 o’clock?

25

What is the first digit on a digital

clock at midnight?0

How many minutes are there between 3.20 and

4 o’clock?40

How many minutes are there

between 16.40 and 17.40?

60

How many minutes are in quarter of an

hour?15

Forty minutes earlier than midnight is

11. ... ?20


between 6.25 and 7 o’clock?

35

How many minutes are there

from 11.10 to 13.10?120

How many minutes are in one and a half

hours?90

Half an hour earlier than 4.25

is how many minutes past 3

o’clock?55

How many minutes are in

three-quarters of an hour?

45

How many minutes are there from 11.55am to

12.05pm?10


between quarter to four and 3.50?

5

How many minutes are in half an hour?

30

How many minutes are there from 9.35pm to

10.25pm?50

What is the first digit on a digital clock at midday?

1



Bingo cards


Section 4: MeasurementResource 4 – From sentences to formulae

Resource 4 - From sentences to formulae









Section 4: MeasurementResource 5 – Kilometres to miles – drawing a conversion graph

Name: ................................................ Date:...................................................

Resource 5 – Kilometres to miles – drawing a conversion graphTask oneUse the given conversion fact to fill in all of the missing values in the diagram. Think about how you can use the known fact to help you find the other facts.

There are three blank boxes for you to decide on your own conversion facts to add.

10 miles = .............. km 20 miles = .............. km 0.5 miles = ............ km

12.5 miles = ........... km 5 miles = 8km ................. miles = 1km

1 mile = ............... km ................. miles = 24km

................. miles = 2km

........... miles = ....... km

............miles = ......... km

............ miles = ........ km

Task two1. Plot the facts you have found on a set of

axes and draw the resulting line to produce a conversion graph.

2. Explain why the graph goes through point (0,0)

................................................................................................................



................................................................................................................

................................................................................................................

3. Use your graph to complete the following conversions:

a. 11km = miles b. 16km = miles

c. 6 miles = ................ km d. 9 miles = ................. km.



Name: ..................................................................................... Date:...............................................................................

Title:

Units

:

20

18

16

14

12

10

8

6

4

2

0 2 4 6 8 1 1 1 1 1 2 2 2 2 2 3 3



0 2 4 6 8 0 2 4 6 8 0 2Units:



Teaching notes:A separate sheet with pre-drawn axes is provided, but you could ask students to draw their own to extend the task. The activity works equally well if the graph is produced using software.

The pre-drawn axes and answer is given with km on the horizontal axes, although some students may draw their graph with miles on the horizontal axes. This can make an interesting discussion to compare the two different ways of drawing the graph.

Sample graph

Resource 5 - Answers

10 miles = 16km 20 miles = 32km 0.5 miles = 4km

12.5 miles = 20km 5 miles = 8km 5/8 miles = 1km

1 mile = 1.6km 15 miles = 24km 1.25 miles = 2km




Section 4: MeasurementResource 6 – Perimeter problems

Resource 6 - Perimeter problems





Section 4: MeasurementResource 6 – Perimeter problems


Section 5: GeometrySection 5a – Geometry: properties of shape

Section 5: Geometry

Section 5: Geometry

Section 5a – Geometry: properties of shape

Curriculum coverageThis section matches the requirements of the statutory guidance in the National Curriculum for maths as follows:

Year 5:


Identify 3D shapes, including cubes and other cuboids, from 2D representations.

Distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Year 6:


Recognise, describe and build simple 3D shapes, including making nets.

Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons.

Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius.

Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.



Section 5a – Properties of Shape

Resources: Circle poster (Resource 1): A handy poster to help children recall the

properties of circles.

Starters: Noughts and crosses (Resource 2) : A fun and interactive PowerPoint

to revise the properties of 2D and 3D shapes.

2D shape of the day (Resource 3): A fantastic PowerPoint to quickly consolidate children’s knowledge of 2D shapes, their properties and how to find their area.

Mains: Angles treasure hunt (Resource 4): An interactive activity to help

children revise how to calculate the missing angles.

3D shape properties (Resource 5): A sorting activity to help children revise the properties of 3D shapes.

Find the nets: Using practical equipment such as Polydron, challenge the children to make and name common 3D shapes, for example: cube, cuboid, pyramid, prism, tetrahedron, they can then carefully unfold them and draw the net.

Finding all possibilities: Challenge the children to work in pairs or small groups to find all of the possible 11 nets for making a cube. Answers are shown below.



Taking it further: Shape puzzle: Hand out dotty paper for the children to solve the

following shape puzzle.

Look at the cuboid below.

Draw two more faces to complete the net of the cuboid.

One possible solution

Plenary ideas: Shape problems: Write the following problems on the interactive

whiteboard to discuss and answer with the class.

ABCD is a rectangle. What are the values of the missing angles x

and y?

Answer: x = 90˚ and y = 270˚

Here is a rectangle. Calculate the size of angles a and b.Do not measure the angles.

Answer: a = 56˚ and b = 34˚


Section 5a – Geometry: properties of shapeResource 1 – The circle

Resource 1 – The circle

Circumference: the distance around the outside of the circle (perimeter).

Radius: the distance from the centre to the circumference.

Diameter: a line which passes through the centre of the circle splitting it into two semicircles.Formulae:


d = 2 x r or r = d is double r

r is half of d

Diameter = double radiusRadius = half diameter

Section 5a – Geometry: properties of shapeResource 1 – The circle


Section 5a – Geometry: properties of shapeResource 2 – Properties of 2D and 3D shapes – noughts and crosses

Resource 2 – Properties of 2D and 3D shapes - noughts and crosses





Section 5a – Geometry: properties of shapeResource 3 – 2D shape of the day

Resource 3 - 2D shape of the day





Section 5a – Geometry: properties of shapeResource 3 – 2D shape of the day


Section 5a – Geometry: properties of shapeResource 4 – Angles treasure hunt

Resource 4 – Angles treasure huntTeaching NotesThis activity can be used for individual or group work. Each child or group should be given a set of cards and a worksheet. Alternatively, the cards can be enlarged and hung around the room.Each card in the set shows an angle problem. The answer to each problem is given as the heading on another card. Children need to work out how the cards fit into a loop, recording the letter of each answer on the worksheet.Children can start on any card. The cards are labelled alphabetically for discussion/answer purposes only; the letters do not indicate the order of answers.Diagrams are not drawn to scale.

AnswersCard order:

A E H F K B I D G J C L



Name: ................................................ Date:...................................................



37° 9° 24°

Card A Card B Card C

51° 49° 28°

Card D Card E Card F


63°

68° ?

63°

? 89°?

? 55°

85°

??

74°

100°

20°


60° 40° 63°

Card G Card H Card I

72° 76° 91°

Card J Card K Card L


63°

?

45°

?

31°

31°

87° 24

°

142°56°

?

156° ??

81°?

53°

Section 5a – Geometry: properties of shapeResource 5 – 3D shape properties

Name: ................................................ Date:...................................................

Resource 5 – 3D shape propertiesPut these cards into groups of three to give each solid’s name, diagram and properties.

sphere 3 pairs of identical faces

cuboid no flat faces

tetrahedron only 2 flat faces

cube 5 faces6 vertices

cylinder 6 identical faces

cone 4 faces4 vertices

square based pyramid only 1 flat face

triangular prism 5 faces5 vertices


Section 5a – Geometry: properties of shapeResource 5 – 3D shape properties


cube 6 identical faces

square based pyramid5 faces

5 vertices

cuboid 3 pairs of identical faces

cone only 1 flat face

triangular prism5 faces

6 vertices

sphere no flat faces

cylinder only 2 flat faces

tetrahedron4 faces

4 vertices


Section 5: GeometrySection 5b – Geometry: position and direction

Name: ................................................ Date:...................................................

Section 5b – Geometry: position and direction


Year 6:


Describe positions on the full coordinate grid (all quadrants).

Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.



Section 5b – Position and direction

Starter: Treasure hunt: An ideal game to play outside on the playground. Draw

and label all four quadrants with both the x and y-axes labelled -3 to +3, and intersecting at 0. Place 36 identical cards in each position, 35 of them blank and one with a drawing of a treasure chest on its reverse. Children play in teams to nominate points on the grid, for example, (-3,1). Who will discover the treasure first?

Variations:

Make the grid larger to increase the challenge. Use a pack of playing cards with the Joker being the card to hunt.

Mains: Coordinate battleships (Resource 6): A PowerPoint to help children

describe positions in all four quadrants. Includes a drawn grid to provide support for less confident children.

Translating shapes (Resource 7): A worksheet to help children to consolidate their skills in translating shapes in all four quadrants.

Reflection jigsaw (Resource 8): Children reflect the shapes in horizontal, vertical and diagonal mirror lines.

Taking it further: Missing coordinates (Resource 9): Children use their problem solving

skills to find the missing coordinates of a variety of shapes.

Plenary ideas: What are the coordinates?: Write the following problem on the board

and tackle whole class.



The shaded triangle is a reflection of the white triangle in the mirror line.

Write the co-ordinates of point A and point B.

Answers: Point A (11,9) Point B (15,3)

Make it symmetrical: Write up the following problem for children to solve.

Shade two squares and one triangle to make this design symmetrical about the mirror line.


Answer drawn in green

Section 5b – Geometry: position and directionResource 6 – Coordinate battleships

Resource 6 - Coordinate battleship





Section 5b – Geometry: position and directionResource 7 – Translating shapes

Name: ................................................ Date:...................................................

Resource 7 – Translating shapesTranslate each shape by the number of squares described.

a) Translate 5 right and 1 up.

y

0

b) Translate 3 left and 5 down.

y

0

c) Translate 5 right and 3 down.

y

0

d) Translate 6 left and 2 down.

y

0

e) Translate 7 right and 1 up.

y

0

f) Translate 3 down.

y

0

g) Translate 2 right and 3 down.

y

h) Translate 4 right.

y

i) Translate 3 left and 2 down.

y



0 x 0 x 0 x

j) Translate 1 right and 4 down.

y

0 x

k) Describe the transformation A to B.

y

A

0 x

B

It is ____________________________________________

l) Describe the transformation A to B.

y

BA 0 x

It is ______________________________________________

Resource 7 – Answersy

0 x

b) c)


y

0 x


a)

y

0 x

d)

e) y

0 x

f)

g)

y

0 x

h)

y

0 x

i)

y

0 x

j)

y

k)

y

l)

y


y

0 x

y

0 x


0 x

A

0 x

B

It is translated 5 down.

BA 0 x

It is translated 5 right and 1 up.


Section 5b – Geometry: position and directionResource 8 – Reflection jigsaw

Name:................................................. Date:.................................................

Resource 8 – Reflection jigsawReflect each labelled shape in its respective line of reflection.

Do not shade in, only copy the outline.

ab

ef

a b e

gh g c f

cd

gh

d cd

gh k kl

gh

gh h kl

i l kl

ij j

m n

mn mn




ab

ef

a b e

gh g c f

cd

gh

d cd

gh k kl

gh

gh h kl

i l kl

ij j

m n

mn mn



Teaching notes

Children should reflect each shape in the appropriate line of reflection.

The finished picture is Super Mario which if they recognise, they can colour in straight away.

Some may need the solution as a clue!

For lower ability students, consider providing them with a part already complete, such as the moustache.


Section 5b – Geometry: position and directionResource 9 – Missing coordinates

Name: ................................................ Date:.................................................

Resource 9 – Missing coordinates1. Find the missing coordinates in each shape. Draw in the axis

to help you.

2. Complete each shape and label its coordinates.


A (3, 4)

B

D

C

H G

FE (0, 5)

N

M L

K

P J (-1, 5)

Q (0, 0)

S

RT (-2,-1)U

WV

A (4, -2)

Square

E (-1,-1)

Parallelogram

J (-2, 1)Kite


Draw and find the missing coordinates in the shapes below.

Rhombus A (0,0 B (5,3) C (3,0) D (…… , ……)

Parallelogram E (-3,-1) F(-2,1) G (3,1) H (…… , ……)

Square J(0,-1) K (-2,0) L (-1,2) M (…… , ……)

5

4

3

2

1

-5 -4 -3 -2 -1 0

-1

1 2 3 4 5

-2

-3

-4

-5© www.teachitprimary.co.uk 2017 29437 Page 164 of 189




Resource 9 - Answers1.

B (3,8)

C (6,8)

D (6,4)

F (3,5)

G (5,1)

H (2,1)

K (-1,4) N (-5,4)

L (-2,1) P (-5,5)

M (-4,1)

R (4,-2)

S (-1,-4)

U (-3,-1)

V (-4,1)

W (-1,2)

2. (Coordinates lettered clockwise alphabetically)

B (5,-5) F (3,-2) K (-4,4)

C (2,-6) G (4,-5) L (-2,6)

D (1,-3) H (0,-4) M (0,4)

3.

Rhombus D (2,3)

Parallelogram H (2,-1)

Square M (1,1)


A (4, -2)

Square

E (-1, -1)

Parallelogram

J (-2, 1)Kite

Section 6: StatisticsSection 6: Statistics

Section 6: StatisticsSection 6 – Statistics


Year 5:


Solve comparison, sim and difference problems using information presented in a line graph.

Complete, read and interpret information in tables. including timetables.

Year 6:


Interpret and construct pie charts and line graphs and use these to solve problems.

Calculate and interpret the mean as an average.


Section 6: Statistics


Starters: Roll a dice: With a partner, roll a dice 5 times and keep a rolling total.

Find the mean by dividing the total by 5. Challenge pairs to roll dice more than 5 times and calculate the mean, or differentiate by using a multi-sided dice.

What’s the story?: Draw an unlabelled line graph on the interactive whiteboard and ask pairs of children to decide what the graph shows. They then need to look at the line and ‘tell the story’ of the graph. For example, it could show the daily temperature of a city or the number of cookies a shop sells in a week. Children can then decide on the title of the line graph and what information each axis shows. Ask for pairs to share their stories with the class to compare and contrast examples.

Mains: Finding the mean (Resource 1): The perfect resource for introducing

the mean with a step-by-step guide to finding it.

Constructing pie charts (Resource 2): A range of frequency tables showing data for children to construct a variety of pie charts from.

Let’s investigate! (Resource 3): A fun and interactive investigation to help children to use and apply their knowledge of frequency tables and pie charts.

Taking it further: Asking questions: Take one of the pie charts created in Constructing

pie charts (Resource 2) and ask children to write up to five questions about it. They can then swap pie charts and questions with a partner who then has to answer them.



Plenary ideas: Guess the pie chart: Display a pie chart with five different coloured

segments and explain it shows the favourite colours of 30 children. Ask the class to work backwards to generate the degrees for each segment based on the size of each of the segments, and then work out the corresponding numbers for the frequency table.

Problem solving: Write up the following question on the interactive whiteboard:

Seven children measured their heights.

Children Stefan Lara Olivia Chen Maria Dev SarahHeight (cm) 144 136 142 143 152 148 150

What is the mean height of the children?

Answer: 145cm


Section 6: StatisticsResource 1 – Finding the mean

Name: ................................................ Date:...................................................

Resource 1 – Finding the mean

The mean is the average. To find the mean of a set of numbers, add up all of the values and then divide by the number of values.

Work through the following step-by-step sums to help you to find the mean.

Section A

1. Find the mean of these numbers: 4 8 3

Workings: Total = ............. Amount to share by = ..........

Mean = ........... ÷ .......... = .............

2. Find the mean of these numbers: 6 4 7 3


Mean = ........... ÷ .......... = .............

3. Find the mean of these numbers: 23 17 20


Mean = ........... ÷ .......... = .............

4. Find the mean of these numbers: 21 52 17 30


Mean = ........... ÷ .......... = .............



Name: ................................................ Date: ..................................................

The mean is the average. To find the mean of a set of numbers, add up all of the values and then divide by the number of values.

Work through the following step-by-step sums to help you to find the mean.

Section B

1. Find the mean of these numbers: 7 4 11 15 3


Mean = ........... ÷ .......... = .............

2. Find the mean of these numbers: 4.3 5.2 6.4 8.1


Mean = ........... ÷ .......... = .............

3. Find the mean of these numbers: 22 12 26 14 28


Mean = ........... ÷ .......... = .............

4. Find the mean of these numbers: 5 7 8 2 8 9


Mean = ........... ÷ .......... = .............




Section A1. Find the mean of these numbers: 4 8 3

Workings: Total = 15 Amount to share by = 3Mean = 15 ÷ 3 = 5

2. Find the mean of these numbers: 6 4 7 3 Workings: Total = 20 Amount to share by = 4Mean = 20 ÷ 4 = 5

3. Find the mean of these numbers: 23 17 20 Workings: Total = 60 Amount to share by = 3Mean = 60 ÷ 3 = 20

4. Find the mean of these numbers: 21 52 17 30Workings: Total = 120 Amount to share by = 4Mean = 120 ÷ 4 = 30

Section B1. Find the mean of these numbers: 7 4 11 15 3

Workings: Total = 40 Amount to share by = 5Mean = 40 ÷ 5 = 8

2. Find the mean of these numbers: 4.3 5.2 6.4 8.1 Workings: Total = 24 Amount to share by = 4Mean = 24 ÷ 4 = 6

3. Find the mean of these numbers: 22 12 26 14 28 Workings: Total = 102 Amount to share by = 5Mean = 102 ÷ 5 = 202/5 or 20.4

4. Find the mean of these numbers: 5 7 8 2 8 9Workings: Total = 39 Amount to share by = 6Mean = 39 ÷ 6 = 6½ or 6.5


Section 6: StatisticsResource 2 – Constructing pie charts

Name: ................................................ Date:...................................................

Resource 2 – Constructing pie charts

A pie chart is a useful visual way to present information. To calculate the number of degrees a section takes up we use the following formula:

( 360totalnumber of people

× frequency)

This is because there are 360 degrees in a circle, so 360 ÷ total gives the number of degrees for each person, and then multiplying it by the frequency gives the degrees for each section.

The frequency table below shows the results of a recent survey of people’s favourite takeaway meals.

Favourite Takeaway

Frequency (number of people

who said it)

Degrees

( 360totalnumber of people

× frequency)Fish & Chips 8

Burger 7

Pizza 6

Chinese 6

Indian 5

None 4



Total



Name: ................................................ Date:...................................................

Now use the information to construct a pie chart. Remember to use a sharp pencil and measure with a protractor accurately.

A pie chart to represent people’s favourite takeaway meals



Name: ................................................ Date:...................................................

The frequency table below shows the results of a recent survey into dream holiday destinations.

Dream Holiday Destination Frequency Degrees

Spain 9

USA 7

Australia 5

Italy 8

Caribbean 5

Other 2

Total

Now use a pair of compasses to draw a circle for your pie chart first. Remember to use a sharp pencil and measure with a protractor accurately.





Name: ................................................ Date:...................................................

Challenge! Look at the bar chart below showing pets owned by a class of year 6 children.

Dog Cat Guinea pig Hamster Fish0

5

10

15

20

25

Look at the data carefully and fill out the frequency table below.

Pet owned Frequency Degrees

Total

Use the data to create a pie chart.



Resource 2 – AnswersFavourite Takeaway Frequency Degrees

Fish & Chips 8 80Burger 7 70Pizza 6 60

Chinese 6 60Indian 5 50None 4 40Total 36 360

Dream Holiday Destination Frequency Degrees

Spain 9 90USA 7 70

Australia 5 50Italy 8 80

Caribbean 5 50Other 2 20Total 36 360

Pet owned Frequency DegreesDog 23 138Cat 16 96

Guinea pig 12 72Hamster 3 18

Fish 6 36Total 60 360


Section 6: StatisticsResource 3 – Let’s investigate!

Name: ................................................ Date:...................................................

Resource 3 – Let’s investigate!

Use your data handling skills to investigate whether it is the first names or surnames of the members of our class which are longer. Collect your data using a frequency table and display your results on two pie charts so that they are easy to compare.

HypothesisDo you think first names or surnames are longer in general? Explain your answer.

..............................................................................................................................

..............................................................................................................................

..............................................................................................................................

Frequency tablesUse the tables below to find the frequency of name lengths in your class. Use each frequency and the total frequency to calculate the angle you need to draw an accurate pie chart.

Class data: letters in our first namesNumber of

letters Tally Frequency FrequencyTotal frequency

×360

≤ 3456789

10



≥ 11



Class data: letters in our first surnamesNumber of

letters Tally Frequency FrequencyTotal frequency

×360

≤ 3456789

10≥ 11

Use the data you have collected to draw two pie charts. Remember to use a pencil and use your protractor to be as accurate as you can. Colour in the segments in different colours and use the key to make your findings clearer.

A pie chart to show the frequency of letters in our first names



Frequency≤ 345678910

≥ 11



A pie chart to show the frequency of letters in our surnames

Frequency≤ 345678910

≥ 11

Now use the information shown on your pie charts to draw your conclusion.

ConclusionUse your pie charts to compare the lengths of first names and surnames in your class. Which are longer – the surnames or the first names?

...........................................................................................

...........................................................................................

...........................................................................................

...........................................................................................

What is the most frequently occurring first name length?

..............................................................................................................................

..............................................................................................................................

..............................................................................................................................



What is the most frequently occurring surname length?

..................................................................................

..................................................................................

..................................................................................

..................................................................................

..................................................................................

Do the pie charts support your hypothesis? Why do you think this is?

..............................................................................................................................

..............................................................................................................................

..............................................................................................................................

..............................................................................................................................

..............................................................................................................................

Can you think of your own question to investigate and collect data for?

..............................................................................................................................

..............................................................................................................................

..............................................................................................................................


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