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Audio test 2 About this workbook
Questions split into three levels of
–Challenge 1, Challenge 2 and Challenge 3 – to aid
‘How am I doing?’ checks for self-evaluation.
Starter test recaps skills covered in Years 3 to 5.
Four progress tests allow children to test how well they have remembered the information.
QR codes link to online interactive quizzes for extra practice.
Handy tips included.
Total marks boxes for each topic.
Progress test charts to record results and identify which areas need further practice.
Answers are included at the back of the book.
Audio test 2 Contents
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Published by Collins
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HarperCollins Publishers
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© HarperCollins Publishers Limited 2025
ISBN 9780008727895
First published 2025 10 9 8 7 6 5 4 3 2 1
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Collins.
British Library Cataloguing in Publication Data.
A CIP record of this book is available from the British Library.
Publisher: Fiona McGlade
Author: Katherine Pate
Contributor: Frances Naismith
Project manager and editorial: Chantal Addy
Cover design: Sarah Duxbury
Inside concept design: Ian Wrigley
Text design and layout: Rose & Thorn Creative Services Ltd
Artwork: Shutterstock and Collins
Production: Bethany Brohm
Printed in India
Starter test
1. Robbie buys a pencil. He pays with a £2 coin and gets 45p change. How much does his pencil cost? £
2. The table shows the number of laps some children ran.
laps
a) Who ran the most laps?
b) How many laps did the children run in total?
c) How many more laps did Terri run than Nikhil?
3. Write these numbers in order, starting with the smallest.
4. Write this number in words.
5. These numbers are written in Roman numerals. Write them as ordinary numbers.
a) XLVIII b) M MXIV
6. Brodie catches a bus at 7.45 am. He gets off the bus 25 minutes later. What time does Brodie get off the bus?
7. Kevin has 250 ml of water in a jug. How much more water does he need to make 1 litre?
8. Elias has 135 books. He can put 9 books on each shelf. How many shelves does he need for all his books?
9. Write 3 5 8 as an improper fraction.
10. Work out: 27 345 – 15 174 =
11. How many sides does a hexagon have? sides
12. Colour 1 5 of this shape.
13. Write the missing numbers in the boxes.
14. a) Tick (✓ ) the obtuse angles.
b) Write the letters in order of angle size.
smallest angle largest angle
15. Write this number in figures.
three hundred and seven thousand and one
16. Work out the volume of this cuboid.
17. Write 16 3 as a mixed number.
18. Write a multiple of 9 between 70 and 80.
19. A tablet costs £230. A school buys 15 of these tablets. Work out the total cost.
20. How many lines of symmetry does a regular pentagon have?
21. 120 chairs are arranged in rows. There are 8 chairs in each row.
How many rows of chairs are there?
22. Work out 1 9 of 126 kg.
23. Here is a rectangle.
a) Work out the area of this rectangle.
b) Work out the perimeter of this rectangle.
24. Write down all the factors of 32.
25. What fraction of this shape is shaded? Write your fraction in its simplest form.
26. How many minutes are there in 51 2 hours? minutes
27. Rosie pours water into a 2-litre bucket until it is 1 5 full.
How much water is in the bucket?
28. Write these fractions in order, starting with the smallest.
29. Write each fraction as a decimal. a) 74 100 b) 1 10 c) 57 1000
30. Write in the missing number.
34 8 g + g = 1 kg
31. Colour 3 4 of this shape.
32. Work out: a) 32 = b) 112 = c) 103 =
33. Circle every prime number.
34. Write the missing numbers in these calculations.
35. Work out:
9 16 + 1 16 + 7 16 = Give your answer as a mixed number.
36. Complete these conversions.
a) 36 cm = mm b) 10 60 g = kg
c) 3. 5 k m = m d) 1. 45 m = cm
37. The two thermometers show the temperature in Hull and the temperature in Cardiff.
a) Which city is warmer – Hull or Cardiff ?
b) How many degrees warmer? °C
38. Work out the size of each angle marked with a letter.
39. Here are some points on a coordinate grid.
Write the coordinates of each point.
Hull
Cardiff
40. The pictogram shows the numbers of people who went swimming on different days.
Monday Tuesday Wednesday Thursday Friday
a) How many people went swimming on Monday?
Key represents 20 people
b) How many more people went swimming on Friday than on Wednesday?
c) Which was the most popular day for swimming?
41. Draw the reflection of the shape in the mirror line.
Mirror line
42. Round 5176:
a) to the nearest 10
b) to the nearest 100
c) to the nearest 1000
Place value
Challenge 1
1 a) Write this number in words.
794 302
b) Write this number in figures. two million
c) Write this number in figures. thirty-four point zero six
2 The numbers in this sequence increase by the same amount each time. Write the missing numbers.
3 Write these decimals in order, starting with the smallest.
Challenge 2
1 a) Write this number in words.
b) Write this number in figures. eight million, four hundred and fifty-two thousand
2 In this number:
5 247 360.189
a) What is the value of the digit 4?
b) What is the value of the digit 6?
c) What is the value of the digit 9?
3 Write the missing numbers in this table.
1 995 000
Challenge 3
1 Circle the values that are equivalent to thirty-two thousand. One has been done for you.
2 Write the missing numbers in the
3 a) Write the number that is 1 hundredth greater than 2.67 b) Write the number that is 1 tenth less than 2.67 c) Write the number that is 1 thousandth less than 2.67
4 Work out:
Negative numbers
Challenge 1
1 Write these temperatures in order, starting with the coldest.
2 The temperature is −5°C and it falls by 4°C. What is the new temperature?
3 The temperature is −6°C and it rises by 5°C.
What
Challenge 2
?
1 What is the difference between −5°C and 10°C?
2 The temperature is 3°C and it falls by 11°C.
What is the new temperature?
3 9°C is warmer than −7°C.
How many degrees warmer?
4 The temperature is −6°C and it rises by 15°C.
What is the new temperature?
5 −21°C is colder than 5°C.
How many degrees colder?
6 One morning the temperature is −4°C.
During the day the temperature rises by 6°C and then falls by 12°C.
What is the new temperature?
7 Work out the calculations below. You can use this number line to help you.
Challenge 3
1 The temperatures in this sequence decrease by the same amount each time. Write the missing numbers in the sequence. −4°C 7°C
2 Write the temperature at A and the temperature at B.
35°C
3 The top of a cliff is 45 metres above sea level. The seabed at the bottom of the cliff is 6 metres below sea level.
What is the distance from the top of the cliff to the seabed?
4 Work out:
Rounding
Challenge 1
1 Round each number to the nearest 1000. The first one has been done for you.
2 Circle every number that rounds to 5.8, to 1 decimal place.
3 Round 526.37:
a) to one decimal place. b) to the nearest whole number. c) to the nearest ten.
Challenge 2
1 Round these numbers to the nearest hundred.
Use your rounded numbers to calculate an estimate for 580 × 320
=
2 Round these numbers to the nearest whole number.
Use your rounded numbers to calculate an estimate for 29.742 × 12.04
=
3 Round 5 555 555:
a) to the nearest thousand.
b) to the nearest ten thousand.
c) to the nearest million.
4 1 pen costs £1.80
Jack says that 33 of these pens cost £594
Work out this estimate for the cost. 30 × 2 =
Challenge 3
1 Maisie and Liam are playing a game.
Maisie’s score rounds to 300 00 0, to the nearest hundred thousand.
a) What is the lowest number her score could be?
Liam’s score rounds to 320 00 0, to the nearest ten thousand.
b) What is the highest number Liam’s score could be?
2 The table shows the number of bus passengers each day, for a week.
a) Round each number to the nearest thousand.
b) Use your rounded values to calculate an estimate for the total number of passengers that week.
c) Round your estimate to the nearest ten thousand.
Prime, square and cube numbers
Challenge 1
4 Circle the cube numbers from the list.
5 Write the
Challenge 3
1 Luis arranges 9 counters into a square shape.
Rani has 40 counters.
She arranges the counters into the biggest square shape possible.
Rani has some counters left over.
How many counters does she have left over?
2 Work out:
3 Write a number less than 30 in each box, to make the statement correct.
4 Write a number less than 30 in each box, to make the statement correct. square number
5 Write all the numbers from 1 to 20 in the correct places in this diagram.
Order of operations
Challenge 1
2 Work out:
Challenge 2
1 Work out:
2 Draw lines to match each calculation to the correct answer.
4 Write these four digits in the calculation below, to give the highest possible answer. 2 4 5 7 ( + ) × – =
5 Work out: a) 6 × 12 – (25 – 9) ÷ 4 = b) (3 + 5) × (9 – 2)
Challenge 3
1 Work out:
a) 32 + 4 = b) (3 + 4)2 = c) 3 + 42 = d) 32 + 42 =
2 Work out:
a) 4 + 32 – 5 = b) (7 – 3) + 4 × 2³ = c) (3 + 5) × 8 – 8² = d) 6² – 3 + 2 =
3 Lou and Jay write these calculations using the same numbers. Tick (✓ ) the calculation that has the greatest answer.
4 Write brackets in this calculation, so that the answer is 20. 2² + 4 × 5 + 7
Mental calculations
Challenge 1
1 Work out:
a) 4600 + 750 = b) 3500 − 50 + 200 =
c) 140 00 0 + 20 50 0 − 3000 =
d) 1 00 0 00 0 – 200 + 5000 =
2 Jo buys these three items.
a) How much does Jo spend in total?
b) How much change does Jo get from £10?
3 Marcus had his 19th birthday on 1st January 2014.
In which year was Marcus born?
Challenge 2
1 Work out:
a) 30 00 × 5 =
0 × 8 = c) 80 00 0 ÷ 4 =
= e) 120 × 30 =
2 Work out:
a) 227 ÷ 10 =
2500 ÷ 50 =
÷
= c) 4.08 × 1000 =
=
3 Mr S mith has 40 boxes of pens. Each box contains 10 packs of pens. Each pack contains 12 pens.
How many pens does Mr Smith have in total?
4 In this multiplication
Write the missing numbers in the wall.
5 Work out:
Challenge 3
1 Work out these calculations. Write your answers in ordinary numbers.
a) MCMIV + DCC =
b) MMLX – MCCCXX =
2 Write a number in each box to make the statement correct.
a) 0.1 is times greater than 0.001
b) 0.01 is times smaller than 0.1
3 Work out:
4 Complete these conversions.
Written addition and subtraction
Challenge 1
1 Work
2 These are the prices for hiring boats.
Neil’s family hire the speedboat and the canoe.
Ellie’s family hire the sailing boat and the rowing boat.
How much more does Ellie’s family spend than Neil’s family?
3 Work
Challenge 2
1 In this addition pyramid, add two numbers to get the number in the space above. Complete the pyramid.
2 Here are the weights of four people in a lift.
The maximum weight for the lift is 400 kg.
Another person weighs 78 kg.
Can all five people go in the lift at the same time? Show working to explain your answer.
3 Circle two numbers that add together to make 2.
4 Work out:
Challenge 3
1 A stack of 20 boxes is 3 metres tall.
Lola takes 4 boxes off the top of the stack.
How tall is the stack now? m
2 Jess is making fruit salad for a party.
Strawberries cost £4.50 per kg.
Bananas cost £2.40 per kg.
Grapes cost £1.90 per kg.
10 paper bowls cost £1.60
She uses 2 kg of strawberries, 1 kg of bananas and 0.5 kg of grapes to make 30 bowls of fruit salad.
Calculate the total cost to make 30 bowls of fruit salad.
How am I doing?
marks : / 16
Common factors and multiples
Challenge 1
1 Write the first 5 multiples of 8.
2 a) Write all the factors of 28.
b) Write all the factors of 40.
c) Write all the common factors of 28 and 40.
3 Circle all the multiples of 3 in this grid.
Challenge 2
1 Write all the common factors of 24 and 32.
2 a) Write the first ten multiples of 5.
b) Write the first ten multiples of 4.
c) Write two common multiples of 4 and 5.
3 a) Write all the common factors of 8 and 6.
b) Write the first three common multiples of 8 and 6.
4 Circle the numbers that are divisible by 9 and also by 4.
5 I think of a prime number greater than 5. The number is a factor of 39 and of 52.
Challenge 3
1 Write two common multiples of 2, 3 and 5. and
2 Write all the common factors of 8, 16 and 20.
3 I think of a number between 100 and 200. My number is a factor of 600 and a multiple of 20.
What is my number?
4 In a perfect number, the sum of the factors (excluding the number itself) equals the number itself.
For example, the factors of 6 are 1, 2 and 3.
The sum of factors = 1 + 2 + 3 = 6
So, 6 is a perfect number.
Which of these is a perfect number?
5 Tisha writes a list of common multiples of 3, 6 and 8. What is the smallest number in Tisha’s list?
Written multiplication
Challenge 1
1 Work out:
2 Write the missing numbers in this long multiplication.
3 How many hours are there in 3 weeks? hours
Challenge 2
1 £1 = 108 Indian rupees. Baldeep has £65. How many Indian rupees are equal to £65?
2 Work
Written division
Challenge 1
1 Work
2 Work
3 A box holds 8 batteries.
Challenge 2
1
2 Use
3 There are 330 children in Key Stage 2. The children are put into teams of 15 for sports day. How many teams are there?
4 Shappi uses 34 cm of wire to make a star shape. She has 5 metres of wire.
a) How many 34 cm lengths can she cut from 5 metres of wire? b) How much wire is left over? cm
5 Work out these divisions. Give the remainders as fractions.
6 393
Challenge 3
1 Four flying lessons cost £395. How much does one flying lesson cost?
2 Work out: 8 5.0 Give your answer as a decimal.
3 Write the missing numbers in the boxes to make each calculation correct.
a) 17 × = 884 b) 32 × = 7136
4 A factory makes crackers. There are 12 crackers in one box. The factory makes 10 00 0 crackers a day. How many full boxes of crackers is this?
How am I doing?
Mixed problems
Challenge 1
1 Work out:
a) 12 tens less than 12 thousand.
b) 15 tens more than 15 hundreds.
2 A full bucket of water holds 5 litres.
Ben pours 2465 ml of water out of the bucket. Then Carys pours 1130 ml of water into the bucket.
How much water is in the bucket now?
3 283 children go on a school trip.
The children are in groups of 12, and one smaller group.
There is one adult with each group of children.
How many adults are there?
4 A time capsule was buried in MCMXIV. It was dug up 108 years later.
In which year was it dug up?
Write your answer in ordinary numbers.
Challenge 2
1 Mrs Jones buys 7 packs of stickers. Each pack contains 48 stickers.
Mrs Jones shares all the stickers fairly between the 28 children in her class.
How many stickers does each child get?
2 Cherry has a box of beads. She gives 5 of her friends 75 beads each. She has 220 beads left.
How many beads were in the box to start with?
3 There are 75 g of pasta in one portion.
a) How many portions are there in a 2 kg bag of pasta?
b) How much pasta is left over? g
4 Miles is planning a tea party for 47 people.
Each person needs two scones.
Scones come in packs of 5.
How many packs of scones does Miles need?
5 Work out the total cost of: 25 drinks at £2.40 each and 22 cakes at £3.25 each
Challenge 3
1 Tristan thinks of a number. He squares his number.
Then he adds 12.
The answer is 93.
What is Tristan’s number?
2 One horse eats 8 kg of hay each day.
Work out the amount of hay needed for 6 horses for 4 weeks.
3 Is 14 a factor of 903?
Explain how you know.
4 An ice cream shop sells:
• 8 flavours of ice cream: vanilla, strawberry, chocolate, toffee, raspberry, banana, mint, lemon
• 4 sizes of cone: small, medium, large, giant
One possible combination is: vanilla with small cone.
How many possible combinations are there?
How am I doing?
Progress test 1
1. The numbers in this sequence increase by the same amount each time.
Write the missing numbers.
2. Write this number in figures. six million, four hundred and twenty-three thousand, five hundred and six
3. Complete this multiplication grid.
4. Write the number that is 100 less than 1010.
5. Write these decimals in order, starting with the smallest.
6. Write the missing numbers in these boxes on the number line.
7. a) Write down all the factors of 36. b) Write all the common factors of 36 and 48.
8. Work out:
1999 + 300 =
9. Write the value of the digit 2 in each number.
a) 32 456
b) 3765.2
c) 245 763
10. In this number pyramid, each number is the difference between the two numbers above.
Difference between 1426 and 875
Complete the pyramid.
11. Circle every prime number in this list. 32
12. Meghan puts eggs into boxes. She has 340 eggs.
Each box holds 12 eggs.
a) How many boxes can Meghan fill with eggs? boxes
b) How many eggs are left over? eggs
13. Write three common multiples of 6 and 10.
14. At 2 pm the temperature is 8°C. At 9 pm the temperature is −5°C.
Work out the difference between these two temperatures.
15. Work out:
6 + 4 × 3 – 2 =
16. Work out:
12 20 0 – 1250 =
17. Write the number 37 609 in words.
18. Work out:
275 × 34 =
19. Work out: 53 – 42 =
20. Work out: 7 2702
21. Circle every square number:
22. Work out:
18 .36 – 4.5 =
23. Write the temperature that is 15 degrees lower than 6°C.
24. Divide 132 by 5. Write the remainder as a fraction.
25. Work out: (3 × 7 + (11 – 8)) ÷ 4 =
26. Round 46 237.95:
a) to the nearest whole number.
b) to the nearest ten.
c) to the nearest thousand.
d) to the nearest ten thousand.
27. There are 792 children in a school. The children are put into classes of 24. How many classes are there?
28. 1 notepad costs £2.30
Write a calculation to estimate the cost of 82 of these notepads.
29. Tom wants to put LED lights all along the top of his bedroom walls.
Here is a plan of his bedroom.
Calculate an estimate of the length of LED lights Tom needs.
Give your answer to the nearest metre.
30. A packet of stickers costs 89p.
Work out the cost of 75 packets of stickers.
31. Mike cuts 3 metres of wood into 11 equal pieces.
Work out the length of one piece in centimetres, accurate to one decimal place. cm
Equivalent fractions
Challenge 1
1 Shade 1 4 of each shape.
2 For each shape, write the fraction shaded in its simplest form.
3 Write <, > or = between each pair of fractions to make the statements correct.
Challenge 2
1 Write
fraction in its simplest form.
2 Write the missing
3 Write three equivalent fractions for 12 18
4
a) Write a number less than 15 which is a common multiple of 2, 3 and 4.
b) Write all these fractions with your answer to part a) as the denominator (bottom number).
c) Write the fractions from part b) in order, starting with the smallest. smallest largest
Challenge 3
1 Write these fractions in order, starting with the smallest.
2 In each set, circle the fraction that is not equivalent to the others.
3 Jayesh has 24 counters.
15 of these counters are yellow. What fraction of the counters are yellow?
Write your answer in its simplest form.
Fractions of amounts
Challenge 1
1 Draw lines to match each box to the correct number. One has been done for you. 1 3 of 120 1 5 of 150 1 4 of 100 1 8 of 160
2 Work out:
3 Work out:
Challenge 2
1 Isabella had 75 beads. She gave 2 5 of these beads to Rora. How many beads did she give to Rora?
2 Write the answers as improper fractions and as mixed numbers. The first one is done for you.
3 Work out: a) 3 4 of 2000 kg = b) 2 7 of 840 km = c) 5 6 of £288 = d) 2 3 of £15.99 =
4 A book has 225 pages.
Ivy has read 3 5 of the book. How many more pages are left for Ivy to read?
5 I am thinking of a number.
2 5 of my number is 24.
What is my number?
6 Three-sevenths of a number is 15.
What is the number?
Challenge 3
1 Work out:
2 What is half of one-third of 114?
3 Leo has green marbles and blue marbles.
1 5 of the marbles are green. Leo has 24 blue marbles.
a) What fraction of the marbles are blue?
b) How many marbles does Leo have in total?
4 The length of a day on Earth is 24 hours.
What is the length of a day on Pluto?
How am I doing?
The length of a day on Pluto is 62 5 times the length of a day on Earth.
Adding and subtracting fractions
Challenge 1
1 Work out:
2 Write the answer to each calculation as an improper fraction and a mixed number.
3 Rick painted 2 5 of a wall.
Mo painted 3 10 of the same wall.
What fraction of the wall was not painted?
Challenge 2
1 Work out:
2 In this circle, 1 4 and 2 5 are coloured.
3 Write the answer to each calculation as an improper fraction and a mixed number.
4 Work out:
Challenge 3
1 In these addition walls, the number in each box is the sum of the numbers below it. Fill in the missing numbers.
2 Work out:
3 Ali, Ben and Cat share some sweets. Ali has twice as many sweets as Cat. Ben has 2 3 of the sweets.
What fraction of the sweets does Cat have?
4 This sequence grows by adding the same fraction each time.
Work out the next two terms in the sequence.
Multiplying fractions
Challenge 1
1 Work out:
2 a) Tick (✓ ) two fractions that multiply to make 1 28
b) Circle two fractions that add to make 15 56
3 For each rectangle, complete the calculation and write the fraction shaded in its simplest form.
Challenge 2
1 Work out:
2 Write in the missing fractions.
3 Work out these multiplications. Write your answers in their simplest form.
4 In this multiplication wall, you multiply two fractions to get the fraction in the box above. Fill in the missing fractions.
Challenge
3 1 ( 1 2 )2 = 1 2 × 1 2 = 1 4 Work out:
( 1 3 )2 =
( 2 5 )2 =
2 Work out the area of this rectangle.
(16)2 =
3 4 5 of the children in a class like milkshakes. 1 3 of the children who like milkshakes like banana milkshakes. What fraction of the children in the class like banana milkshakes?
3 Work out:
am I doing?
Dividing fractions
Challenge 1
1
2 Use these shapes to help you work out:
3 Use these shapes to help you work out:
Challenge 2
1 Work out:
2 Draw lines to match the calculations with the same answer. One is done for you.
3 Work out:
Challenge 3
1 Work out these calculations. Give each answer in its simplest form.
2 The area of this rectangle is 3 5 m2
Work out the width of this rectangle. m
3 The perimeter of this square is 2 3 metres. Work out the area of this square.
4 Work out: Use the order of operations.
How am I doing?
Improper fractions and mixed numbers
Challenge 1
1 Write each number as an improper fraction and a mixed number. The first one is started for you.
4 = 1 1
2 Write each mixed number as an improper fraction.
3 Write each improper fraction as a mixed number.
Challenge 2
1 1 2 3 of these shapes are shaded. Use these shapes to help you work out:
1 2 3 × 2 = Write your answer in its simplest form.
2 Work out: Use the shapes to help you. a) 1 1 4 × 3 = b) 1 1 4 × 4 =
in the correct places on this number line.
2 4 Work out:
5 Write < or > to make each statement true.
Challenge 3 1 Write these in order, from smallest to largest.
Work out:
Percentages
Challenge 1
1 Write the missing fractions and percentages in this table.
2 Work out:
Challenge 2
1 Draw lines to match each percentage to its equivalent fraction.
4 A clothes shop is having a sale. All the prices have been reduced by 30%.
How much money do you save on each item?
5 Here are Peter’s test marks: English 17 20 Maths 21 25
a) Convert these test marks to percentages.
=
b) Which subject did Peter get the best mark for?
Challenge 3
1 Kiera is buying this house. It costs £270 00 0. She needs to pay 20% of the price as a deposit. How much is the deposit?
2 There are 25 children in tennis team A.
7 of the children in tennis team A are left-handed. There are 40 children in tennis team B.
12 of the children in tennis team B are left-handed. Which team has the highest percentage of left-handed children?
Fraction, decimal and percentage problems
Challenge 1
1 40 0 children were asked which animal they like best. The table shows the results.
dogs cats rabbits hamsters
a) How many children chose each animal?
dogs children cats children
rabbits children hamsters children
b) How many more children chose cats than chose dogs? children
2 Write each decimal as a fraction in its simplest form:
0. 3 =
=
=
3 To write 3 8 as a decimal, work out: 8 3.000
4 To write 7 20 as a decimal, work out: 20 7.00
Challenge 2
1 Milo’s sticker album holds 832 stickers. Milo’s album is 75% full. How many more stickers does Milo need to fill his album?
2 Muhammad thinks of a number. 30% of his number is 18. What is Mohammad’s number?
3 Write these fractions as decimals.
4 A farmer has 140 sheep. 60% of these sheep are brown.
a) How many of the sheep are brown?
b) Half of the remaining sheep are white. What fraction of the 140 sheep are white? Write your answer in its simplest form.
5 Write < or > between each pair of values, to make the statement correct.
Challenge 3
1 Two shops are selling the same model of TV.
a) At which shop is the TV the cheapest?
b) How much cheaper is the TV at that shop?
2 Write each set of values in order, starting with the smallest.
Challenge 1
1 Rana makes samosas.
For every 1 meat samosa, she makes 2 vegetable samosas.
a) On Monday Rana makes 20 meat samosas.
How many vegetable samosas does she make?
b) On Tuesday Rana makes 28 vegetable samosas.
How many meat samosas does she make?
2 Hugo puts black and white counters in a row.
For every 1 black he puts 3 white counters.
Colour the counters to show the correct ratio.
Challenge 2
1 Here are some yellow and purple cubes.
Tick (✓ ) the correct statement for these cubes.
The ratio of yellow to purple is 2 : 3
The ratio of yellow to purple is 3 : 2
2 a) Write the ratio of blue to grey for these cubes. :
b) Write the ratio of grey to blue for these cubes.
3 The ratios show yellow to white.
Draw lines to match each ratio to a diagram.
5 : 1
1 : 2
1 : 5
2 : 3
4 The ratio of red squares to yellow squares is 4 : 3
There are 28 squares in total.
You can colour the squares to help you.
How many squares of each colour are there? red yellow
Challenge 3
1 Here is a set of shapes.
a) Write the ratio of triangles to quadrilaterals. :
b) Write the ratio of pentagons to triangles. :
c) Write the ratio of shapes with vertices to shapes without vertices. :
d) Write the ratio of circles to quadrilaterals to triangles. : :
2 Mario decorates a cake with coloured sweets. The ratio of red to yellow sweets is 3 : 5
There are 15 yellow sweets on the cake. How many red sweets are there?
How am I doing?
Scale factor
Challenge 1
1 Here is a square.
Draw a square that has sides 3 times as long.
2 Enid builds a tower 7 cm tall.
Ollie’s tower is 3 times taller than Enid’s.
How tall is Ollie’s tower? cm
3 Sam and Riki have model boats.
Sam’s model
Riki’s model is shorter than Sam’s model.
How many times shorter?
Challenge 2
1 Rectangle B is an enlargement of rectangle A. A
What is the scale factor of the enlargement?
Riki’s model
2 Here is a triangle.
Enlarge this triangle by a scale factor of 2.
Challenge 3
1 Here is a triangle.
Enlarge this triangle by a scale factor of 11 2
2 Sameera is building a model plane. Her model is 80 times smaller than the real plane.
Here are the measurements of the real plane.
Work out the measurements of Sameera’s model.
How am I doing?
Unequal sharing
Challenge 1
1 Look at this diagram and answer the questions below.
a) What is the ratio of green to white triangles in this diagram? :
b) What fraction of the triangles are white?
c) What fraction of the triangles are green?
2 A necklace has 1 blue bead for every 3 yellow beads.
a) What fraction of the beads are yellow?
b) What fraction of the beads are blue?
3 Ma x and Tilly share 24 grapes.
Ma x has 1 3 of the grapes.
Tilly has 2 3 of the grapes.
How many grapes do they each have?
Challenge 2
1 There are 4 black pens for every 1 red pen.
a) What fraction of the pens are red? There are 30 pens.
b) How many of each colour are there? red pens black pens
Max grapes
Tilly grapes
2 In a car park there are 3 silver cars for every 4 blue cars.
a) What fraction of the cars are silver?
There are 21 cars in the car park.
b) How many of each colour are there? blue cars silver cars
c) How many more blue cars than silver cars are there?
3 Here is a bowl of oranges and bananas.
The ratio of bananas to oranges is 2 : 3
a) What fraction of the fruit in the bowl is oranges?
There are 20 pieces of fruit in the bowl.
b) How many oranges are there in the bowl?
Challenge 3
1 The ratio of red balls to blue balls to yellow balls is 3 : 2 : 1
There are 12 more red balls than blue balls.
How many of each colour are there? red blue yellow
2 In a set of 28 building blocks, there are:
Twice as many green bricks as blue bricks. An equal number of blue and yellow bricks.
Five times as many red bricks as green bricks.
How many of each colour are there?
3 James makes a tropical fruit drink by mixing mango juice, orange juice and sparkling water in the ratio 2 : 3 : 5
How many millilitres of each does he need to make 1500 ml of tropical fruit drink? mango juice orange juice
Progress test 2
1. Write each fraction in its simplest form.
a) 4 20 = b) 12 18 =
2. Write each fraction as a decimal.
a) 31 100 = b) 7 10 = c) 27 50 =
3. Write 2 3 5 as an improper fraction.
4. Write each decimal as a fraction in its simplest form:
a) 0. 3 = b) 0. 48 =
5. Fabian has a box of football cards. He gives 6 of his friends 12 cards each. He has 34 cards left.
How many cards were in the box to start with? cards
6. Work out 10% of £47
7. The ratios show green to white. Draw lines to match each ratio to a diagram.
4 : 1
1 : 3
1 : 4
1 : 1
8. Round 42 714.2 to the nearest hundred.
9. Triangle B is an enlargement of triangle A.
What is the scale factor of the enlargement?
10. 9210 × 61
11. Write these three fractions with the same denominator.
12. Find 80% of 150 kg kg
13. A time capsule was buried in MDCCCXCIX. It was dug up 105 years later. In which year was it dug up?
Write your answer in ordinary numbers.
14. Work out:
16. Write in the missing numbers.
a) 72 = b) 23 = c) 3 = 27 d) 2 = 81
17. Work out: 1120 ÷ 32 =
18. Work out: 1 6 × 1 4 =
19. Write 24 7 as a mixed number.
20. In a box there are 3 red balls for every 2 blue balls.
a) What fraction of the balls are blue?
There are 20 balls in the box.
b) How many of each colour are there? red balls blue balls
c) How many more red balls than blue balls are there?
21. Ben recorded the temperature in his garden one month.
The lowest temperature was −9°C
The highest temperature was 11°C
What is the difference between the highest and lowest temperatures?
22. Work out: 13 20 –3 5 =
23. Write these numbers in order, from smallest to largest.
24. Write 3 8 as a decimal.
25. Grace puts 3 blue marbles, then 5 green marbles, like this:
a) Grace uses 45 green marbles in her pattern. How many blue marbles does she use? blue marbles
b) Grace uses 40 marbles in total. How many of each colour does she use?
blue green
26. I am thinking of a number.
3 5 of my number is 12. What is 1 10 of my number?
27. Luca had 54 toy cars. He gave 4 9 of these cars to Archie.
How many cars did Luca have left?
28. A smoothie recipe uses: mangoes : bananas in the ratio 2 : 3
a) Ava makes smoothies using 8 mangoes. How many bananas does she need? bananas
b) Theo makes smoothies using 9 bananas. How many mangoes does he need? mangoes
29. Draw lines to match the equivalent fractions. One has been done for you.
Equations
1
2 Write the
3 a and b are positive whole numbers. Neither a or b is zero.
a + b = 9
One possible pair of values for a and b is a = 4, b = 5
a) List all the possible pairs of values for a and b.
b) How many possible pairs of values are there?
Challenge 3
1 Work out the
2 a and b are
a × b = 12
How many possible pairs of values are there for a and b?
3 Solve each equation.
Formulae
Challenge 1
1 A bike hire company uses this formula:
Hire cost = £6 × number of hours
a) Work out the hire cost for: 1 hour £ 3 hours £
b) Daisy pays £24 to hire a bike. How many hours does she hire it for? hours
2 An online shop uses this formula to work out the total price:
Total price = price of item + £2.95 delivery charge
a) Work out the total price for these trainers.
£99.99
b) Balvinder buys this T-shirt.
The total price is £27.45
Work out the price of the T-shirt.
Challenge 2
1 Here is a formula: y = 4x + 3
Work out the value of y when x = 5
2 Here is a formula: s = t 3 − 7
Work out the value of s when t = 24
3 Jacob sells hats online.
He uses this formula to work out the total price:
Total price = £9 × number of hats + £3.50 delivery charge
a) Work out the total price for: 2 hats £ 5 hats £
b) Seren pays £30.50 to buy hats online. How many hats does she buy? hats
4 Complete this table.
The first one has been done for you.
Challenge 3
1 Bella’s rule for making green paint is: use twice as much yellow (y) as blue (b)
Tick (✓ ) the formula that represents this.
y = 2b b = 2y b = y – 2 y = b 2
2 The formula for the area of a triangle with base b and height h is: A = b × h 2
Use the formula to work out the area of this triangle.
Sequences
Challenge 1
1 The numbers in this sequence increase by equal amounts each time. Write in the next three numbers.
51 59
2 The numbers in this sequence decrease by equal amounts each time. Write in the next three numbers.
10 4 97 76
3 Here is a sequence of patterns made from matchsticks.
Pattern 1
Pattern 2 Pattern 3
a) Draw the next pattern in the sequence.
b) The table shows the numbers of matchsticks in each pattern.
6 11
Write in the missing numbers.
c) Joe wants to make Pattern 5. How many matchsticks does he need?
Challenge 2
1 Here is part of a number sequence.
The numbers increase by the same amount each time.
The sequence continues.
Circle all the numbers below that would appear in the sequence.
475 580 700 830
2 The first number in a sequence is 2000.
The rule to get from one term to the next is: subtract 150. Write the next 4 terms in this sequence.
3 Here is a sequence of patterns made from counters.
a) Complete this rule to get from one pattern to the next: Add counters.
b) How many counters will there be in pattern 6 in this sequence? counters
Challenge 3
1 The numbers in this sequence increase by 20 each time.
The sequence continues in the same way. Write two consecutive numbers from the sequence that add to make a total of 228.
3 Ruby makes a sequence of numbers. She chooses a starting number and then subtracts equal amounts each time. The 3rd number in her sequence is 26. The 10th number is −16.
Units of measurement
Challenge 1
1 Convert these measures.
a) 10 0 cm = m
c) 3 cm = mm
e) 18 0 seconds = minutes
2 Tess pours 350 ml of water into a jug.
How much more does she need to pour in to fill the jug to the 2 litre mark?
3 Hakan is 1.85 m tall.
Noah is 94 cm tall.
How much taller is Hakan than Noah?
Challenge 2
50 00 g = kg
2 litres = ml
40 k m = m
1 Write these times in order, starting with the shortest.
2 Convert these measures: a) 750 m = km
485 g = kg c) 1670 mm = m
3.6 litres = ml e) 2. 3 m = cm
3 8 identical parcels weigh 1 kg.
What is the weight of 1 parcel?
4 A row of 28 tiles is 2.072 m long. How long is a row of 17 of these tiles?
10 090 g = kg
Challenge 3
1 Here is a train timetable.
Sopley Bridge 08:45 12:27 17:25
Dramford Lane 09:25 13:25 18:00
Calshott 10:02 14:06 18:24
Inkley Town 10:56 14:42 19:37
Travett Centre 11:29 15:16 19:58
Somersby 12:24 16:03 20:35
Sophie leaves home at 1 pm.
She walks for 10 minutes to Dramford Lane station and catches the next train to Somersby.
When she arrives in Somersby she walks for 15 minutes to her grandmother’s house.
What time does she arrive at her grandmother’s house?
2 Lily has 8.4 kg of cat food.
Her cat eats 40 g of cat food each day.
How many weeks will the bag of food last? weeks
3 The table shows international athletics results.
a) Which country won the 100 m sprint?
b) Write Ethiopia’s time for the 1500 m hurdles in minutes and seconds.
c) What is the difference between the shortest and longest triple jump?
d) What is the difference between the two longest throws in the shot put?
4 One teaspoon holds 5 ml of milk. How many teaspoons of milk are there in 2 litres?
How am I doing?
Imperial and metric units
Challenge 1
1 Tick (✓ ) the longest length.
2 Tick (✓ ) the longest length.
3 1 kg is approximately 2.2 pounds.
Convert each of these weights into pounds.
a) 3 kg = pounds b) 40 0 kg = pounds
4 This table shows equivalent distances in miles and kilometres. Write in the missing values.
Challenge 2
1 There are 3 feet in 1 yard.
There are 12 inches in 1 foot. 1 inch = 2.5 cm
a) How many inches are there in 1 yard? inches
b) Which is longer – 1 metre or 1 yard?
c) What is the difference in length between 1 metre and 1 yard?
Give your answer in centimetres. cm
2 Write in the missing number.
1 k m = 5 8 miles
130 k m = miles
3 1 litre is approximately 7 4 pints.
Convert each of these amounts into pints.
a) 2 litres = pints
b) 5 litres = pints
4 Peter runs 15 km.
James runs 12 miles.
a) Who runs the furthest?
b) How many miles further did he run?
Challenge 3
1 Write in the missing number.
1 mile = 8 5 km
28 miles = km
2 1 litre = 1 3 4 pints
Convert 19 litres to pints.
3 The distance around the Earth, at the Equator, is approximately 40 0 00 k m.
How many miles is this? miles
4 In France, the speed limit in towns is 90 km per hour. What is this speed limit in miles per hour?
Give your answer to the nearest whole number. miles per hour
5 How many inches are there in 15 yards? inches
6 1 mile = 1760 yards
a) Convert 25 miles to yards. yards
b) Calculate an estimate for the number of miles equivalent to 10 00 0 yards.
How am I doing?
Perimeter and area
Challenge 1
1 Here is a rectangle.
Work out:
a) the perimeter of this rectangle. m
b) the area of this rectangle. m2
2 This shape is drawn on a centimetre squared grid.
Work out the area of this shape. cm2
3 The perimeter of a square is 36 m. What is the area of this square? m2
Challenge 2
1 Draw a rectangle with area 12 cm2 and the largest possible perimeter on this 1 cm grid.
All the side lengths should be whole numbers of centimetres.
2 Work out the perimeter and area of this shape.
= m
3 The area of a square is 121 cm2 . What is the perimeter of this square? cm
4 A rectangle is 5 cm long and 15 cm wide. Work out the area of this rectangle in square centimetres.
Challenge 3
1 Draw two different rectangles on the grid, that have the same area as this shape.
2 a) Write an equation for the area of this rectangle.
b) a and b are whole numbers. Write all the possible pairs of values of a and b.
How am I doing?
Area of triangles and parallelograms
Challenge 1
1 Use the formula to work out the area of the triangle below.
area of triangle = base × height 2
2 Use the formula to work out the area of the parallelogram below.
area of parallelogram = base × height
Challenge 2
1 Work out the area of each triangle.
2 Work out the area of each parallelogram.
3 The area of this parallelogram is 72 cm2 .
Work out the length of b, the base of the parallelogram.
Challenge 3
1 Work out the area of each shape.
2 The area of this triangle is 28 m2 .
Work out the height, h, of the triangle.
3 Work out the
How am I doing?
2-D shapes – triangles, polygons and circles
Challenge 1
1 Here is a triangle.
a) Tick (✓ ) the two correct statements.
All of its angles are equal.
It has two equal sides.
It has one line of symmetry.
b) Tick (✓ ) the name of this triangle.
equilateral right-angled isosceles
scalene
2 Three sides of a hexagon are drawn on a squared grid.
The dashed line is a line of symmetry.
Draw the other three sides of the hexagon.
Challenge 2
1 a) Make an accurate drawing of this triangle. Use a ruler and a protractor or angle measurer.
b) What type of triangle is it?
2 Here are some 2-D shapes.
A B C D
Write the letters of the shapes for each statement.
a) Shape(s) with at least two equal sides.
b) Shape(s) with a right angle.
c) Shape(s) with at least two parallel sides.
d) Shape(s) with at least one obtuse angle.
e) Shape(s) that are regular polygons.
3 Draw lines to match the labels to the diagrams.
Challenge 3
1 Work out the
2 Work out the
2-D shapes – quadrilaterals
Challenge 1
1 Fill in the description for each quadrilateral.
pair(s) of equal sides
pair(s) of parallel sides
pair(s) of equal sides
pair(s) of parallel sides c)
Name
pair(s) of equal sides
pair(s) of parallel sides
2 Here are two sides of a parallelogram.
Name
equal sides
pair(s) of parallel sides
Draw another two sides to complete the parallelogram.
Challenge 2
1 Here is a set of trapeziums.
Write the letters of the isosceles trapeziums.
2 Here are two sides of an isosceles trapezium.
Draw another two sides to complete the trapezium.
3 Complete the description of each quadrilateral. The first one is started for you.
Sides:
Vertices:
Lines of symmetry:
Name:
Challenge 3
Sides:
Vertices:
Lines of symmetry:
Name:
1 Write the name of the quadrilateral that has: 2 pairs of equal sides 2 pairs of parallel sides no right angles
2 Write the name of the quadrilateral that has: 2 pairs of equal sides no parallel sides 3 obtuse angles
3 These diagrams show the diagonals of some quadrilaterals. Write the name of each quadrilateral.
How am I doing?
3-D shapes and nets
Challenge 1
1 Complete the description for each 3-D shape. The first one has been started for you.
a) b)
Name:
Name: square faces square faces edges rectangular faces vertices edges vertices c) d)
Name:
Name: rectangular faces triangular faces edges rectangular faces vertices edges vertices
Challenge 2
1 Complete the description of a hexagonal prism. 2 faces
Some faces match to more than one 3-D shape.
2 a) Draw lines to match each 3-D shape to the shapes of its faces. One has been done for you.
b) Write the name of each 3-D shape.
3 Here is the net of a 3-D shape. Write the name of this 3-D shape.
Challenge 3
1 Here is part of a net of a tetrahedron.
Draw the rest of the net.
2 This cube has two shapes drawn on it.
Here is the net of the cube. Draw the missing pattern on the net.
3 Sketch the net of a square based pyramid.
Challenge 1
1 The volume of this cube is 1 cm3.
Work out the volume of each of these shapes made from 1 cm3 cubes.
2 Work out the volume of this cube.
Challenge 2
1 Work out the volume of this cube.
2 Work out the volume of this cuboid.
3 A cube has volume 8 cm3.
What is the length of one side of this cube? cm
4 Work out the volume of this cuboid shaped fish tank.
Challenge 3
1 Here is the net of a cuboid.
The net is folded up to make the cuboid.
Work out the volume of the cuboid. cm3
2 A steel beam is in the shape of a cuboid.
Work out the volume of steel in the beam.
Give your answer in m3.
3 The volume of this cuboid is 104 cm3.
Work out the height, h of the cuboid. h
How am I doing?
Progress test 3
1. Here is a function machine.
What is the input?
2. Here is a set of 3-D shapes.
a) Tick (✓ ) all of the shapes that are prisms.
b) Circle all of the shapes that are pyramids.
3. Work out the value of the letter in each equation.
a) x − 2 = 5 x = b) 4 × y = 12 y = c) t + 11 = 17 t =
d) r ÷ 6 = 8
4. An online shop uses this formula to work out the total price.
total price = price of item + £3.30 postage
Work out the total price for this microwave oven.
£79.99 £
5. On a separate piece of paper, make an accurate drawing of this trapezium. Use a ruler and a protractor.
6. x and y are positive whole numbers greater than 0 and less than 15.
x − y = 4
How many possible pairs of values are there for x and y?
7. Here is a net for a 3-D shape.
Write the name of the 3-D shape you can make with this net.
8. This shape is drawn on 1 cm squared paper.
Work out: the area of the shape. cm2 the perimeter of the shape. cm
9. Triangle B is an enlargement of triangle A by scale factor 8. Not drawn accurately
Work out the measurements of triangle A.
Label them on the diagram.
10. Here is a formula: y = 5x − 3
Work out the value of y when x = 8
11. The first term in a sequence is 80. The rule to get from one term to the next is subtract 14.
Write the first four terms in this sequence.
12. Work out:
3 8 + 1 4 + 5 16 =
13. Here is a sequence of patterns made from squares.
Pattern 1
Pattern 2
a) Complete the rule to get from one pattern to the next. Add squares
Pattern 3
b) How many squares will there be in pattern 5 in this sequence? squares
14. Label the parts of the circle using the words below.
15. Work out the area of this triangle.
16. Convert these measures.
17. Work out the volume of this cuboid.
18. This table shows equivalent distances in kilometres and miles. Write in the missing values.
19. There are 24 marbles in a bag. The table shows the number of each colour.
Work out the percentage of each colour.
Red
20. This triangle and parallelogram have the same area.
Work out the height of the triangle.
21. The formula for the volume of a cube with side length s is: V = s 3
Use the formula to work out the volume of this cube. 2
22. Sunita has 8 blue beads and 18 white beads. She puts some of the beads in patterns, in the ratio blue to white beads 2 : 3
a) How many complete patterns can she make?
b) How many beads does she have left over?
c) What colour are the leftover beads?
How am I doing?
Missing angles
Challenge 1
1 Work out the size of each angle labelled with a letter.
Challenge 2
1 Work
4 Work
1 This shape is 1 6 of a circle.
a) Work out the size of angle f.
b) Work out the diameter of the circle. cm
2 Work out the size of angle x. Not to scale
3 Here is an equilateral triangle.
Angle problems
Challenge 1
1 Work out the size of angle x.
2 Work out the size of angle y.
3 Here is an isosceles trapezium.
Work out the
Challenge 2
1 Here is an isosceles triangle.
Work out the
2 Here is a regular pentagon.
4 The shaded shape is an isosceles triangle.
The isosceles triangle is inside a rectangle. Work out the size of angle
Coordinates
Challenge 1
1 a) Plot these points on the coordinate grid.
(1, 1)
b) Join the points in order, with straight lines. What shape have you drawn?
Challenge 2
1 Write the coordinates of each point plotted on this coordinate grid.
Challenge 3
1 a) Plot these points on the coordinate grid. P (−5, 1) Q (−3, 5) R (3, 1) S (1, −3)
b) Join the points in order, with straight lines. What shape have you drawn?
2 a) Plot these points on the coordinate grid and join them with a straight line.
(3, 4) U (−3, −2)
b) Point V is the midpoint of the line TU. Label point V on the diagram.
c) Write the coordinates of point V. ( , )
Translations
Challenge 1
1 This rectangle is translated 3 squares up. Draw the rectangle in its new position.
2 This triangle is translated 4 squares right. Draw the triangle in its new position.
3 Describe the translation that takes shape A on to shape B.
Challenge 2
1 Shape C is translated 4 squares left and 2 squares down. Draw shape C in its new position.
2 Here are two shapes, D and E.
a) Describe the translation that maps shape D on to shape E.
b) Describe the translation that maps shape E on to shape D.
Challenge 3
1 Shape F is translated so that point A is mapped on to point B.
Draw the shape after the translation.
How am I doing?
Reflections
Challenge 1
1 Draw the reflection of each shape in the mirror line.
line
2 Draw the mirror line for each reflection.
Challenge 2
1 Draw the reflection of this shape in the x-axis.
Challenge 3
1 Here are four shapes on a coordinate grid.
a) Which shape is the reflection of shape C in the x-axis? Shape
b) Which shape is the reflection of shape C in the y- axis? Shape
2 a) Draw the reflection of this shape in the y-axis.
b) Describe the translation that takes the shape to its reflection.
Bar charts
Challenge 1
1 The bar chart shows the number of films people saw in one year. 16
Number of films watched in a year 0–10 11–20 21–30 31–40 Number of people 41–50 over 50
a) How many people saw fewer than 31 films?
b) How many people saw more than 20 films?
c) How many people are represented in the bar chart?
d) One person saw more than 50 films.
Draw a bar for this person on the bar chart.
Challenge 2
1 This bar chart shows the numbers of ice creams sold by two ice cream shops on different days. 100
of people Mon Tues Wed Thur Days
a) Which shop sold most ice creams on Tuesday?
Key
Nice Ices
Jolly Lollies
b) Which shop sold the fewest ice creams on Monday?
c) Which shop sold the most ice creams over the four days?
How many more did it sell?
d) Which day had the greatest difference between the numbers of ice creams sold by the two shops?
Challenge 3
1 The tally chart shows some people’s scores in a game.
a) Fill in the frequency column.
b) How many people’s scores are shown in the table?
c) This bar chart shows some of the information from the tally chart.
the bar chart.
Line graphs
Challenge 1
1 The line graph shows the temperature at different times during a day.
a) What time was the earliest temperature recorded?
b) How often was the temperature measured?
c) What was the maximum temperature recorded? °C
d) What time was the hottest temperature?
e) How many degrees colder was it at 10pm than at 5pm? °
f) For how long was the temperature greater than 14°C? hours
Challenge 2
1 The table shows the numbers of teddy bears a shop sells each month.
a) Complete the line graph on the next page to show the information in the table.
b) Between which two months did the sales decrease? and
c) Between which two months was the greatest increase in teddy bear sales? and
Challenge 3
1 This graph converts between pounds and kilograms.
a) Use the lines drawn on the graph to convert 10 pounds to kilograms.
b) Draw lines on the graph to convert 14
Pie charts
Challenge 1
1 60 children have music lessons.
The pie chart shows the instruments they play.Music lessons in Year 6
a) Which instrument is most popular?
b) Which instrument is least popular?
c) What fraction of the children play piano?
d) How many children play piano? children
e) Five children play recorder.
Estimate the number of children who play the trumpet. children
Challenge 2
1 The table shows the numbers of different fruits for a picnic.
Colour sections of the pie chart on the next page to represent this information.
Recorder
Trumpet Drums Piano
Challenge 3
1 The table shows children’s pets.
Colour sections of this pie chart to represent this information.
Colour the key to show what each section represents.
The mean
Challenge 1
1 Four children have these counters.
a) How many counters are there in total? counters
b) Lily collects up all the counters and then shares them out fairly between the 4 children.
How many counters does each child get? counters
2 Ryan has 12 sweets, Neil has 11 sweets and Meg has 7 sweets. Work out the mean number of sweets.
Challenge 2
1 Calculate the mean of these three numbers.
2 Badger Town Football Club played five matches. These are the numbers of goals they scored in each match:
Work out the mean number of goals.
Lily Ben Ravi Luca
3 Here are four parcels.
Work out the mean weight of these parcels. Mean = g
4 Here are the heights of six children, in centimetres.
Work out the mean height.
Challenge 3
1 The mean of four numbers is 14. Here are three of the numbers. 13 16 17
What is the 4th number?
2 a) Greg practices long jumps. Here are the lengths of his jumps.
=
Work out the mean length of his jumps.
= m b) Romy practices long jumps. Here are the lengths of her jumps.
Who has the longest mean jump length: Romy or Greg? Show working to explain.
How am I doing?
Progress test 4
1. Work out the value of x.
2. Work out the size of angle r.
3. This regular 12-sided shape has a number at each vertex.
Jules turns the pointer from 0, clockwise through 210° Which number is the pointer at now?
4. Here are Jen’s scores in five tests.
Work out Jen’s mean mark.
5. 32 children were asked: What is your favourite party food?
Each child chose one food.
The pie chart shows the results. burger hot dog nuggets veggie burger chips
a) What percentage of the children chose burger?
b) How many children chose hot dog?
c) What fraction of the children chose chips?
Write the coordinates of:
Point A ( , )
Point B ( , )
The midpoint of the line AB ( , )
7. Work out the radius of this circle.
8. Work out the size of angle
9. Triangle A is translated 4 squares right and 2 squares down.
Draw triangle A in its new position.
10. A gardener records the number of tomatoes on each tomato plant she grows. The bar chart shows the results.
a) How many tomato plants had 16–20 tomatoes?
b) How many tomato plants had more than 20 tomatoes?
11. Draw the reflection of triangle B in the y-axis.
12. The ratio of red to blue to yellow buttons is 4 : 3 : 1
There are 81 blue buttons. How many counters are there in total? counters
13. The line graph shows the minimum temperature each month in York.
a) What was the minimum temperature in York in February? °C
b) What was the minimum temperature in York in May? °C
c) What is the difference between the minimum temperatures in March and June? °C
d) The table shows the minimum temperatures in Poole in the same months.
Draw a line graph on the same axes to show the Poole temperatures.
14 . Here are the weights of four kittens.
Work out the mean weight of these kittens. Mean = kg
15. A theatre sells tickets at three different prices.
3 10 of the tickets are price A
1 4 of the tickets are price B
The rest of the tickets are price C
What fraction of the tickets are price C?
Answers
For questions worth 1 mark with several answer spaces, all answers should be correct to achieve the mark, unless otherwise indicated.
Pages 4–11 Starter test
1. £1.55
2. a) Terri b) 166 c) 36
3. 2. 44 2. 45 2.5 2.54 5.25 [2 marks if all correct, 1 mark if one incorrect]
4. one hundred and twenty-six thousand, three hundred and ninety-seven
5. a) 48 b) 2014
6. 8.10 am
7. 750 ml
8. 15 shelves
9. 29 8
10. 12 171
11. 6 sides
12. any 2 squares coloured
13. 150, 400
14. a) B and C ticked b) D A B C [2 marks if all correct, 1 mark if one incorrect]
15. 307 0 01
16. 32 cm3
17. 51 3
18. 72
19. £3450
20. 5
21. 15
22. 14 kg
23. a) 42 m2 b) 26 m
24 . 1, 2 , 4, 8, 16, 32 [2 marks if all correct, 1 mark if one incorrect or missing]
25. 1 3
26. 330 minutes
27. 40 0 ml
28 . 1 2 7 12 2 3 5 6 [2 marks if all correct, 1 mark if one incorrect]
29. a) 0.74 b) 0.1 c) 0.057
30. 652 g
31. any 12 squares coloured
32. a) 9 b) 121 c) 1000
33. 3 and 31 circled
34 . a) 3.3 b) 100 c) 33
35. 1 1 16
36. a) 360 b) 1.06 c) 3500 d) 145
37. a) Cardiff b) 5°C
38. a) 104° b) 35°
39. A (1, 4) B (4 , 2) C (0, 1) D (3, 0)
40. a) 30 b) 20 c) Thursday
41. Mirror line
42. a) 518 0 b) 5200 c) 5000
Pages 12–13
Challenge 1
1. a) seven hundred and ninety-four thousand, t hree hundred and two b) 2 000 000 c) 34 .06
2. 29 517 31 517 32 517
3. 0.002 0.03 0.07
0.14 0.6 [2 marks if all correct, 1 mark if one incorrect]
Challenge 2
1. a) nine million, nine hundred thousand and ninety-nine b) 8 452 0 00
2. a) 40 00 0 or 40 thousands or 4 ten thousands b) 60 or 6 tens
c) 9 t housandths
3.
Challenge 3
1. 3200 tens and 320 hundreds circled [2 marks if both correct, only 1 mark if ot her values circled]
2. 3 250 0 00, 4 500 0 00
3. a) 2.68
b) 2. 57 c) 2.669
4. a) 237 519
b) 2375.19
c) 2 4 00 0 00
d) 856 025
Pages 14–15
Challenge 1
1. −8°C −6°C −2°C 3°C 7°C [2 marks if all correct, 1 mark if one incorrect]
2. −9 °C
3. –1°C
Challenge 2
1. 15°
2. −8 °C
3. 16°
4. 9°C
5. 26°
6. −10°C
7. a) –1 b) 0 c) –5 d) 2 e) –3 f) 5
Challenge 3
1
2 A −25°C
3 51 metres
4 a) –5
d) – 6
Pages 16–17
Challenge 1
1.
4. Estimate 60. Jack is wrong because the total cost must be close to £60, but his cost is close to £600.
Challenge 3
1. a) 250 0 00 b) 324 999
2. a) 23 0 00, 20 0 00, 16 0 00, 21 0 00, 24 0 00, 15 0 00, 10 0 00 [2 marks if all correct, 1 mark if one incorrect] b) 129 0 00 c) 130 0 00
Pages 18–19
Challenge 1
1. a) 49 b) 1 c) 36
2. a) 27 b) 1 c) 9
3. 2 and 19 circled [2 marks if both correct, 1 mark if incorrect values included]
Challenge 2
1. a) > b) = c) > d) < e) > f) <
2. 36 , 49, 100 and 121 circled [2 marks if all correct, 1 mark if incorrect values included]
3. a) 8 b) 9 c) 3 d) 12 e) 10 f) 2
4. 1, 27, 64 and 125 circled [2 marks if all correct, 1 mark if incorrect values included]
5. 101
Challenge 3
1. 4 2. a) 29 b) 73 c) 90 0 d) 0 e) 14 f) 54 3. prime number square number square number 5 + 4 = 9
prime number square number square number 3 + 1 = 4
2. 5. 82 and 5.76 circled [2 marks if both correct, 1 mark if incorrect values included]
3. a) 526 .4 b) 526 c) 530
Challenge 2
1. 600, 300 60 0 × 300 = 180 000
2. 30, 12 30 × 12 = 360
3. a) 5 556 0 00 b)
prime number square number square number 7 + 9 = 16 4. square number square number square number 9 + 16 = 25 5. prime number multiples of 3 11 2 13 17 7 6 9 15 12 18 20 5 19 3 16 14 10
[4 marks: 1 mark for each section completely correct]
Pages 20–21
Challenge 1
1. a) 6 b) 10 c) 11 d) 5
2. a) 24 b) 6 c) 3 d) 4
Challenge 2
1. a) 32 b) 16 c) 11 d) 13
2. a) 14 b) 9 c) 10 d) 30
3. a) 21 b) 6 c) 29 d) 2
4. (4 + 5) × 7 – 2 = 61 [2 marks: 1 mark for a correct calculation with a lower answer]
5. a) 68 b) 28
Challenge 3
1. a) 13 b) 49 c) 19 d) 25
2. a) 8 b) 36 c) 0 d) 35
3. Jay 26 – 3 + 2 × (4 + 3) ✓
4. 2² + 4 × (5 + 7) ÷ 3
Pages 22–23
Challenge 1
1. a) 5350 b) 3650 c) 157 50 0 d) 1 0 04 8 00
2. a) £4 .69 b) £5.31
3. 1995
Challenge 2
1. a) 15 00 0 b) 4 000 000 c) 20 00 0 d) 20 e) 3600 f) 50
2. a) 22 .7 b) 34.9 c) 4 080 d) 171.4 e) 5000 f) 0.98
3. 48 00
4. 0.04
5.
3.5
Challenge 3
1. a) 2604 b) 740
2. a) 100 b) 10
3. a) 24 6 b) 40 c) 370 d) 275 e) 2 .7 f) 3. 36
4. a) 2000 b) 5000 c) 5 60 0 00 0 d) 2. 4 e) 4 .85 f) 0. 84
Pages 24–25
Challenge 1
1. a) 498 8 b) 20
Challenge 2
2. Yes, with working, e.g. 63 + 85 + 72 + 59 + 78 = 357 kg, or estimate: 60 + 90 + 70 + 60 + 80 = 360 kg
3. 1.034 and 0.966
4. a) 16. 25 b) 6. 315
Challenge 3
1. 2.4 m
2. £17.15
Pages 26–27
Challenge 1
1. 8, 16, 24, 32, 40
2. a) 1, 2 , 4, 7, 14, 28 b) 1, 2 , 4, 5, 8, 10, 20, 40 c) 1, 2 , 4
3. 102, 105 and 108 circled [2 marks if all correct, 1 mark if incorrect values included]
Challenge 2
1. 1, 2, 4, 8
2 a) 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
b) 4, 8 , 12, 16, 20, 24, 28, 32, 36, 40
c) 20, 40 (or any other multiple of 5 and of 4, e.g. 400)
3. a) 1, 2 b) 24 , 48, 72
4. 36 and 108 circled [2 marks if all correct, 1 mark if incorrect values included]
5. 13
Challenge 3
1. Any two common multiples of 2, 3 and 5, e.g. two of 30, 60, 90,…
2. 1, 2 , 4
3. 120
4. 28 (factors 1, 2, 4, 7, 14)
5. 24
Pages 28–29
Challenge 1
1. a) 336 b) 5658 c) 128 832
2. 4 5 × 2 3 1 3 5 9 0 0 1 0 3 5
3. 504 hours
Challenge 2
1. 7020 Indian rupees
2. 86 4 00
3. a) 32. 8 b) 29. 4
4. 4092
Challenge 3
1. 2025
2. 2197
3. 111 150 m2
4. <
Pages 30–31
Challenge 1
1. a) 53 b) 74 c) 327 d) 345
2. a) 2 b) 1
3. 37
Challenge 2
1. a)
2. a) 12 b) 18 c) 215
3. 22
4. a) 14 b) 24 cm
5. a) 65 1 2 b) 213 8 11
Challenge 3
1. £98.75
2. 0.625
3. a) 52 b) 223
4. 833
Pages 32–33
Challenge 1
1. a) 11 8 80 b) 1650
2. 3665 ml
3. 24
4. 2022
Challenge 2
1. 12
2. 595
3. a) 26 b) 50 g
4. 19
5. £131.50
Challenge 3
1. 9
2. 1344 kg
3. No, because 903 ÷ 14 = 64.5, which is not a whole number
4. 32
Progress test 1
Pages 34–37
1. 80, 280 2. 6 423 506 3. ×
4. 910
5. 0.003 0.02
0.3 [2 marks if all correct, 1 mark if one incorrect]
6. −4 00 200 800
7. a) 1 2 3 4 6 9 12 18 36 [2 marks if all correct, 1 mark if up to two factors missing or incorrect]
b) 1 2 3 4 6 12 [2 marks if all correct, 1 mark if any factors missing or incorrect]
8. 2299
9. a) 2 thousands or 2000 b) 2 tenths or 0.2 c) 2 hundred thousands or 200 00 0
10. 1426 875 1176 or 574 551 301 250
11. 37, 43, 67 and 97 circled [2 marks if all correct, 1 mark if one incorrect or missing]
12. a) 28 b) 4
13. Any three multiples of 6 and of 10, e.g. three of 30, 60, 90, 120, 150, 180, ….
14. 13°C
15. 16
16. 10 950
17. thirty-seven thousand, six hundred and nine
18. 9350
19. 109
20. 38 6
21. 16 , 81, 25 and 64 circled [2 marks if all correct, 1 mark if one incorrect or missing]
22. 13. 86
23. −9 °C
24 . 262 5
25. 6
26. a) 46 238 b) 46 24 0 c) 46 00 0 d) 50 000
27. 33
28 . Any calculation with correctly rounded numbers, e.g. 80 × 2 = 160 or 82 × 2 = 164
29. Answer between 13 and 15 m
30. £66.75
31. 27.3 cm
Pages 38–39
Challenge 1
1. a) Any two sections shaded. b) Any four sections shaded.
2.
3.
3. Any three fractions that simplify to 2 3 , e.g. 2 3, 4 6, 6 9, 24 36 , 36 54
4. a)
marks if all correct, 1 mark if one incorrect]
Challenge 3
1. 20 60 12 20 8 12 12 16 [2 marks if all correct, 1 mark if one incorrect]
2.
3. 5 8
Pages 40–41
Challenge 1
1. 1 3 of 120 = 40 1 4
Challenge 2 1. 30
Challenge 3
Pages 42–43
Challenge 1 1. a) 1 2 b) 3 8 c) 5 8 d)
Challenge 2
Challenge 3
23 40, 7 10
Pages 44–45
Challenge 1
3. a) 1 2 × 1 6 = 1 12 b) 1 4 × 1 8 = 1 32 c) 1 4 × 1 5 = 1 20 d) 3 4 × 1 9 = 1 12
Challenge 2 1. a) 4 35 b) 5 36 c) 15 88 d) 8 21 e) 21 160 f) 33 100 2. a) 1 6 b) 1 7 c) 1 4 d) 1 15
Challenge
Pages 50–51
Challenge 1
Pages
Challenge 2
b) English
Challenge 3
1. £54 0 00
2. Team B
Pages 52–53
Challenge 1
1. a) dogs 40 children, cats 100 children, rabbits 240 children, hamsters 20 children b) 60 children 2. a) 3 10 b) 53 100 c) 217 1000 d) 3 5 e) 21 50 f) 51 125 g) 2 25 h) 9 125 3. 0. 375 4. 0. 35
Challenge 2 1. 208 2. 60
3. a) 0.125 b) 0. 875 4. a) 8 4 b) 1 5
5. a) > b) < c) > d) >
Challenge 3
1. a) TVs R Us b) £36 .20
2. a) 0. 2 21% 0.23 1 4
[2 marks if all correct, 1 mark if one incorrect] b) 150% 9 5 1.9 1.95
[2 marks if all correct, 1 mark if one incorrect]
Pages 54–55
Challenge 1
1. a) 4 0 b) 14
2. Any 3 counters coloured black, the rest white
Challenge 2
1. The ratio of yellow to purple is 3 : 2 ✓ 2. a) 1 : 3 b) 4 : 1
: 1
: 5 2 : 3
4. 16 red, 12 yellow
Challenge 3
1. a) 3 : 6 b) 1 : 3 c) 10 : 2 d) 1 : 6 : 3
2. 9
Pages 56–57
Challenge 1
1. Square with sides 6 squares long. 2. 21 cm
3. 9
Challenge 2 1. 2 2.
Challenge 3
Pages 58–59
Challenge 1
1. a) 4 : 5 b) 5 9 c) 4 9
2. a) 3 4 b) 1 4 3. Ma x 8 grapes, Tilly 16 grapes
Challenge 2
1. a) 1 5 b) 6 red pens, 24 black pens 2. a) 3 7 b) 12 blue cars, 9 silver cars c) 3
3. a) 3 5 b) 12
Challenge 3 1. 36 red 24 blue 12 yellow 2. 4 green 2 blue 20 red 2 yellow 3. 30 0 ml mango juice
450 ml orange juice
750 ml sparkling water
Progress test 2
Pages 60–63 1. a) 1 5 b) 2 3 2. a) 0. 31 b) 0.7 c) 0. 54 3. 13 5 4. a) 3 10 b) 12 25 5. 10 6 cards 6. £4 .70 7. 4 : 1 1 : 3 1 : 4
: 1 8. 42 70 0 9. 3 10. 561 810 11. 12 18 15 18 8 18 (accept also equivalent fractions with denominator 36, 90 or other multiple of 18)
12. 120 kg
13. 20 04 14. a) £7 b) 18 kg
15. 12 5 = 2 2 5 16. a) 49 b) 8 c) 3 d) 9 17. 35 18. 1 24 19. 3 3 7
20. a) 2 5 b) 12 red balls, 8 blue balls c) 4
21. 20°C 22. 1 20
23. 32.43 33.34 33.4 33.43 34.04
[2 marks if all correct, 1 mark if one incorrect]
24. 0. 375
25. a) 27 blue marbles b) blue 15, green 25
26. 2
27. 30 cars
28 . a) 12 bananas b) 6 mangoes
29. 3 4 = 54 72 5 8 = 60 96 1 6 = 8 48 [2 marks if all correct, 1 mark if one incorrect]
Pages 64–65
Challenge 1
1. 8
2. × 3 or + 6
3. ÷ 3 or − 8
4. × 2
5. 12
Challenge 2
1. a) 9 b) 6 c) 11 d) 20
2. output 1, input 25
3. a) a = 1, b = 8 a = 2 , b = 7 a = 3, b = 6
a = 4, b = 5 a = 5, b = 4 a = 6 , b = 3
a = 7, b = 2 a = 8 , b = 1 [2 marks if all correct, 1 mark if at least six pairs correct] b) 8
Challenge 3
1. input 9, output 22
2. 6
3. a) 4 b) 10 c) 3.5 d) 42
Pages 66–67
Challenge 1
1. a) £6 £18 b) 4 hours
2. a) £102.94 b) £2 4.50
Challenge 2
1. 23
2. 1
3. a) £21.50 £4 8.50 b) 3 hats
4. n 3n
Pages 68–69
Challenge 1
1. 67, 75, 83
2. 90, 83, 69
3. a) b) 16 , 21 c) 26
Challenge 2
1. 580 and 700 circled
2. 1850, 1700, 1550, 1400
3. a) 4 counters b) 25 counters
Challenge 3
1. 104 and 124
2. 38
Pages 70–71
Challenge 1
1. a) 1 b) 5 c) 30 d) 2000 e) 3 f) 40 00 0
2. 1.65 litres or 1650 ml
3. 91 cm or 0.91 m
Challenge 2
1. 240 000 seconds 72 hours 4800 minutes 36 days 6 weeks [2 marks if all correct, 1 mark if one correct] 2. a) 0.75 b) 0.485 c) 1.67 d) 3600 e) 230 f) 10.09
3. 125 g or 0.125 kg
4. 1. 258 m or 125.8 cm or 1258 mm
Challenge 3
1. 16:18 or 4.18 pm
2. 30 weeks
3. a) Spain b) 6 minutes 12 seconds c) 1.63 m or 163 cm d) 0. 45 m or 45 cm
4. 40 0 teaspoons
Pages 72–73
Challenge 1
1. 1 inch ✓
2. 1 metre ✓
3. a) 6.6 pounds b) 88 0 pounds
4. miles km 5 8
Challenge 3
1. y = 2 b
2. 14 m2
Challenge 2
1. a) 36 inches b) 1 metre c) 10 cm
2. 81.25 miles
3. a) 3.5 or 3 1 2 pints b) 8.75 or 8 3 4 pints
4. a) James b) 2.625 miles
Challenge 3
1. 44.8 km
2. 33.25 or 331 4 pints
3. 25 000 miles
4. 56 miles per hour
5. 540 inches
6. a) 44 000 yards
b) Estimate 10 000 ÷ 2000 = 5 miles
Pages 74–75
Challenge 1
1. a) 24 m b) 32 m2
2. 7 cm2
3. 81 m2
Challenge 2
1. 1 cm by 12 cm rectangle drawn on the grid.
2. Perimeter = 104 m Area = 440 m2
3. 44 cm
4. 75 cm2
Challenge 3
1. 1 cm by 4 cm rectangle and a 2 cm by 2 cm rectangle (square) drawn on the grid.
2. a) a × b = 70
b) a = 1, b = 70 a = 2, b = 35 a = 5, b = 14
a = 7, b = 10 a = 10, b = 7 a = 14, b = 5
a = 35, b = 2 a = 70, b = 1
[2 marks if all correct, 1 mark if fewer than two incorrect or missing]
Pages 76–77
Challenge 1
1. 20 cm2
2. 54 cm2
Challenge 2
1. a) 21 cm2 b) 17.5 cm2
2. a) 66 cm2 b) 90 cm2
3. 6 cm
Challenge 3
1. a) 30 cm2 b) 20 cm2
2. 7 m
3. 22 cm2
Pages 78–79
Challenge 1
1. a) It has two equal sides. ✓ It has one line of symmetry. ✓
2.
b) isosceles ✓
Challenge 2
1. a) Accurate drawing of triangle 5 cm 30 o 70 o b) scalene
2. a) A, C, D b) B c) C d) A, C, D e) A, C
3. circumference diameter radius
Challenge 3
1. 8 cm
2. 5.5 cm
3. 25.9 cm
Pages 80–81
Challenge 1
1. a) (isosceles) trapezium, 1 pair of equal sides, 1 pair of parallel sides
b) parallelogram, 2 pairs of equal sides, 2 pairs of parallel sides
c) kite, 2 pairs of equal sides, 0 pairs of parallel sides
d) rhombus, 4 equal sides, 2 pairs of parallel sides
2.
Challenge 2
1. A, C
2.
3. a) Vertices: 4 right angles, Lines of symmetry: 4, Name: square
b) Sides: 4, 1 pair of parallel sides, Vertices: 4, 2 right angles, Lines of symmetry: 0, Name: trapezium
Challenge 3
1. parallelogram
2. kite
3. a) parallelogram b) square c) rhombus
Pages 82–83
Challenge 1
1. a) Name: cube, 6 square faces
b) Name: cuboid, 2 square faces, 4 rectangular faces, 12 edges, 8 vertices
c) Name: cuboid, 6 rectangular faces, 12 edges, 8 vertices
d) Name: triangular prism, 2 triangular faces, 3 rectangular faces, 9 edges, 6 vertices
Challenge 2
1. 2 hexagon(al) faces, 6 rectangular faces, 18 edges, 12 vertices
2. a) Rectangle matches to Pentagon matches to Circle matches to Square matches to Triangle matches to
[2 marks if all correct, 1 mark if one or two errors]
b) cylinder, cone, cuboid, square-based pyramid, pentagonal prism, triangular prism.
3. pentagon(al) prism
Challenge 3
1. Drawing of 4 equilateral triangles joined along their edges, e.g.
Pages 84–85
Challenge 1
1. a) 12 cm3 b) 9 cm3
2. 64 cm3
Challenge 2
1. 125 cm3
2. 56 m3
3. 2 cm 4. 3000 cm3
Challenge 3 1. 45 cm3
2. 0.18 m3 3. 4 cm
Progress test 3
Pages 86–89 1. 63 2. a) ✓ ✓ b)
3. a) 7 b) 3 c) 6 d) 48 4. £83.29
5. Accurate drawing of trapezium [1 mark for each correct angle, 1 mark for each side of correct length (3 labelled sides only)]
6. 10
7. triangular prism 8. a) 8 cm2 b) 16 cm
9. A 22 cm 12 cm 16 cm
10. 37
12. 15 16
13. a) 3 b) 16 squares
14. radius diameter circumference
15. 12 cm2
16. a) 1. 2 km b) 0. 55 kg c) 2. 45 m d) 80 00 ml
17. 40 cm3
18. km miles 8 5 32 20 40 25
19. Blue 25% Red 50% White 12.5% Green 12.5%
20. 8 cm
21. 8 cm3
22. a) 4 b) 6 c) white
Pages 90–91
Challenge 1
1. a) 25° b) 45° c) 29° d) 263°
Challenge 2
1. 125°
2. 55°
3. 56°
4. 120°
Challenge 3
1. a) 60° b) 24 cm
2. 25°
3. a = 60°, b = 60°, c = 60°
Pages 92–93
Challenge 1
1. 75°
2. 45°
3. a = 115° b = 65°
Challenge 2
1. d = 70° e = 4 0°
2. u = 108° w = 108°
3. 135°
4. 96°
Challenge 3
1. 48°
Pages 94–95
Challenge 1 1.
[1 mark for each point correct] b) square
Challenge 2
1. A (2, 3)
Challenge 3 1. a)
[1 mark for each point correct] b) parallelogram
2. a) and b)
[1 mark for each point correct, 1 mark for V label] c) V (0, 1)
Pages 96–97
Challenge 1
1.
3. 2 squares left and 3 squares down
Challenge 2
2. a) 4 right, 5 down b) 4 left, 5 up
Challenge 3 1.
Challenge 3 1. a) A b) D
Challenge 2
1. a) Nice Ices b) Nice Ices c) Jolly Lollies, 10 d) Thursday
Challenge 3
1. a)
[1 mark for each bar, 1 mark for correct labels]
Pages 102–103
Challenge 1
1. a) 10 am b) every hour c) 24°C
d) 2 pm e) 12° f) 8 hours
Challenge 2
a)
[1 mark for each point, 1 mark for correct labels]
b) August and September
c) July and August
Challenge 3
1. a) 4.5 kg
b) 6. 5 kg (accept answers between 6.2 kg and 6.5 kg)
Pages 104–105
Challenge 1
1. a) piano b) recorder c) half 1 2
d) 30 children
e) 10 children (accept answers between 8 and 12)
Challenge 2
1. Pie chart coloured with 3 sections for Apple, 2 sections for Orange, 1 section for Banana, plus key completed to show the colour of sections for each fruit.
Challenge 3
1. Pie chart coloured with 4 sections for Cat, 3 sections for Dog, 2 sections for Rabbit, 1 section for Hamster, plus key completed to show the colour of sections for each pet.
Pages 106–107
Challenge 1
1. a) 20 b) 5
2. 30 ÷ 3 = 10
Challenge 2 1. 6
2. 4 goals
3. 150 g 4. 135 cm
Challenge 3 1. 10
2. a) 1. 8 m b) Romy, Reason Romy’s mean = 1.9 m OR Romy’s jumps total 9.5 m, which is greater than Greg’s total (9 m) [1 mark if all correct, 0 marks if no working or reason given]
Progress test 4
Pages 108–111 1. 125° 2. 58 ° 3. 7 4. 13 5. a) 50% b) 8 c) 1 16
6. Point A (1, −4) Point B (7, −2) The midpoint of the line AB (4, −3) 7. 9 cm
105°
10. a) 6 b) 36
12. 216 counters
[7 marks: 1 mark for each point correctly plotted, 1 mark for joining with straight lines]
14. 2. 4 kg
15. 9 20
Progress test charts
Use these charts to record your results in the four Progress tests. Colour in the questions that you got right to help you identify any areas that you might need to study and practise again. (These areas are indicated in the ‘See page…’ row in the charts.)
Progress test 1:
See page… 12-1312-13 22-2324-25 12-13 14-15 26-2722-23 12-13 24-25 18-19 32-33 26-27 14-1520-21 22-23
Progress test 2: Q16 Q17 Q18 Q19 Q20 Q21 Q22Q23Q24Q25Q26 Q27 Q28Q29 TOTAL /51
See page… 12-1312-13 22-2324-25 12-13 14-15 26-2722-23 12-13 24-25 18-19 32-33 26-27 14-1520-21
See page… 18-19 24-25 44-45 48-49 52-53 14-15 42-43 12-13 52-53 58-59 52-5352-53 54-55 38-39
Progress test 3:
Progress test 4:
page… 90-9190-91
What am I doing well in?
What do I need to improve?