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Including
CD-ROM for
whiteboard use
or printing
MASTERING THE MATHEMATICS CURRICULUM
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YEAR 6
Written by Laura Sumner
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MASTERING THE MATHEMATICS CURRICULUM
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YEAR 6
Written by Laura Sumner
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Acknowledgements:
Author: Laura Sumner
Cover and Page Design: Jerry Fowler
Illustration: Kathryn Webster
The right of Laura Sumner to be identified as the author of this
publication has been asserted by her in accordance with the
Copyright, Designs and Patents Act 1998.
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HeadStart Primary Ltd
Elker Lane
Clitheroe
BB7 9HZ
T. 01200 423405
E. [email protected]
www.headstartprimary.com
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 the publisher.
Published by HeadStart Primary Ltd 2016 © HeadStart Primary Ltd 2016
A record for this book is available from the British Library
ISBN: 978-1-908767-56-1
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MASTERING THE MATHEMATICS CURRICULUM
Teachers’ Notes – Year 6
RATIONALE
Background
This book has been written taking into account the principles outlined in the current
Mathematics curriculum. It focuses on a mastery approach to teaching mathematics,
as outlined by NCETM’s director, Charlie Stripp, in the short paper entitled ‘Mastery
approaches to mathematics and the new national curriculum’. In addition, account is
taken of the Oxford University Press series ‘Teaching for Mastery.’
Achieving mastery
Emphasis is placed on the importance of children fully mastering mathematical concepts
and principles so that, as well as being able to complete mathematical tasks, they are able
to gain a deep understanding about why mathematical procedures work. Underlying this,
is an expectation that all children can accomplish high standards. Consequently, teachers
need to be able to focus their time on planning highly effective strategies to teach and
model mathematical concepts for children.
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Charlie Stripp highlights the value of well-planned and focused lessons, where teachers
explore and enhance children’s understanding through highly effective and precise
questioning. Additionally, he points to the importance of effective practice and
consolidation of key concepts.
Therefore, the over-riding aim of this book is to provide examples for children to practise
the concepts they are being taught, thereby allowing teachers more time to focus on
achieving high quality teaching. Consequently, for each objective within the mathematics
curriculum, as outlined in the ‘Statutory requirements’ and the ‘Notes and guidance’, there
is at least one page of pertinent questions which children can complete during a lesson or
for homework. For objectives such as ‘performing mental calculations’, a number of pages
are available for children to practise a range of appropriate strategies. Focused discussion,
with teachers and other adults, about the concepts highlighted will enhance children’s
depth of understanding and mastery of the curriculum.
© Copyright HeadStart Primary Ltd
YEAR 6
MASTERING THE MATHEMATICS CURRICULUM
Teachers’ Notes – Year 6
Embedding mastery
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Opportunities for children to practise and demonstrate their mastery of mathematical
concepts run through all the pages within the book. So that children can gain an
in-depth understanding of each concept, the book is designed to provide examples
precisely matched to each specific objective. Having this deep understanding will enable
children to apply their knowledge and skills to different contexts, sometimes requiring an
understanding of a range of objectives and concepts. Therefore, the book also includes
further pages to provide an opportunity for children to practise and demonstrate this
level of mastery. So, for each domain within the curriculum, there are specific pages
linked to each objective, as well as further mastery pages which draw together the
concepts within the whole domain.
DIFFERENTIATION
The ‘Teaching for Mastery’ Oxford University Press series recommends that the class
should work “together on the same topic, whilst at the same time addressing the need
for all pupils to master the curriculum and for some to gain greater depth of proficiency
and understanding”. The NCETM paper ‘Mastery approaches to teaching mathematics
and the new national curriculum’ suggests that “differentiation occurs in the support and
intervention provided to different pupils”.
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The book is designed to meet these recommendations. Some groups of children may
benefit from additional adult support and intervention to complete the examples, and
develop their proficiency and understanding. In general, the examples are arranged so
that they become progressively more difficult within each question or on each page.
The ‘Teaching for Mastery’ series suggests that there should not be a need for additional
‘catch-up programmes’. However, some groups may require targeted intervention to
reinforce their understanding of their own year group’s concepts through carrying out
work at a level appropriate to their current ability. Therefore, some children could work on
relevant pages from the HeadStart books for other year groups, whilst still working on the
same topic as the rest of the class.
ASSESSING CHILDREN’S PROGRESS
This book is not designed to be used as a summative tool. Nevertheless, as the book
is based on the Year 6 expectations within the mathematics curriculum, it can support
teachers in making formative assessments about children’s progress towards those
expectations. Furthermore, the book can provide diagnostic information about aspects
of the curriculum for which individual children, or groups of children, may need further
support or enhancement.
© Copyright HeadStart Primary Ltd
YEAR 6
MASTERING THE MATHEMATICS CURRICULUM
Teachers’ Notes – Year 6
USING THE BOOK
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The book is designed so that children are able to write answers on the photocopied or
printed sheets, which may be particularly useful if given as homework. However, for
most pages, pupils can easily transcribe the work into their exercise books. If the children
complete work on photocopied or printed sheets and substantial ‘working out’ is to be
completed, this may need to be carried out separately or in exercise books.
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In addition to photocopying or printing the pages for the children’s use, the enclosed CD
can be used to project pages onto an interactive whiteboard, thereby enabling them to
be used for modelling and clarification purposes.
© Copyright HeadStart Primary Ltd
YEAR 6
CONTENTS
Number – number and place value
Objectives
Pages 1–2
Read and write numbers up to 10,000,000
Page 3
Compare and order numbers up to 10,000,000
Page 4
Determine the value of each digit in numbers up to 10,000,000
Page 5
Round whole numbers to the nearest 1000
Page 6
Round whole numbers to the nearest 10,000
Page 7
Round whole numbers to the nearest 100,000
Page 8
Round whole numbers to the nearest 1,000,000
Page 9
Round whole numbers to a required degree of accuracy
Page 10
Calculate the difference between numbers across zero
Page 11
Use negative numbers in context
Pages 12–14
Solve problems involving number and place value
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Page
Number – addition, subtraction, multiplication and division
Objectives
Pages 15–16
Multiply multi-digit numbers up to 4 digits by a two-digit whole number using
the formal written method of long multiplication
Pages 17–18
Divide numbers up to 4 digits by a two-digit whole number using the formal
method of long division
Pages 19–20
Divide numbers up to 4 digits by a two-digit whole number, using long division,
and interpret remainders as whole numbers, fractions or decimal fractions
Page 21
Divide numbers up to 4 digits by a two-digit whole number, using long division,
and interpret remainders as whole numbers, fractions or decimal fractions, as
appropriate for the context
Page 22
Divide numbers up to 4 digits by a two-digit whole number, using long division,
and round its remainder up or down, as appropriate for the context
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Page
Pages 23–24
Divide numbers up to 4 digits by a two-digit whole number using the formal
written method of short division
Pages 25–26
Divide numbers up to 4 digits by a two-digit whole number, using short division,
and interpret remainders as whole numbers, fractions or decimal fractions
Page 27
Divide numbers up to 4 digits by a two-digit whole number, using short division,
and interpret remainders as whole numbers, fractions or decimal fractions, as
appropriate for the context
Page 28
Divide numbers up to 4 digits by a two-digit whole number, using short division,
and round the remainder up or down, as appropriate for the context
Pages 29–37
Perform mental calculations, including with mixed operations and large numbers
Page 38
Identify common factors
Page 39
Identify common multiples
© Copyright HeadStart Primary Ltd
YEAR 6
CONTENTS
Identify prime numbers
Page 41
Use knowledge of the correct order of operations to carry out calculations
involving the four operations
Pages 42–43
Solve addition and subtraction multi-step problems in context
Page 44
Solve multi-step problems, using all four operations
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Page 40
Fractions (including decimals and percentages)
Objectives
Page 45
Use common factors to simplify fractions
Page 46
Use common multiples to create equivalent fractions
Page 47
Use a common multiple to express fractions in the same denomination
Page 48
Compare and order fractions
Pages 49–50
Add and subtract fractions with different denominators and mixed numbers,
using the concept of equivalent fractions
Page 51
Multiply simple pairs of proper fractions, writing the answer in its simplest form
Page 52
Divide proper fractions by whole numbers
Page 53
Associate a fraction with division and calculate decimal fraction equivalents
Page 54
Understand the relationship between fractions and division to find whole
quantities
Pages 55–56
Identify the value of each digit to three decimal places and multiply and divide
numbers by 10, 100 and 1000 giving answers up to 3 decimal places
Page 57
Multiply one-digit numbers with up to two decimal places by whole numbers
Page 58
Multiply one-digit numbers with up to two decimal places by whole numbers
in context
Page 59
Use written division methods in cases where the answer has up to two decimal
places, including rounding to a specified degree of accuracy
Page 60
Solve division problems in context, rounding answers as appropriate
Page 61
Recall and use equivalence between fractions, decimals and percentages
Page 62
Recall and use equivalence between fractions, decimals and percentages in
different contexts
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Page
Ratio and proportion
Page
Objectives
Pages 63–65
Solve problems involving the relative size of quantities using multiplication
and division
Page 66
Solve problems involving the calculation of percentages
Page 67
Solve problems involving the use of percentages for comparison
© Copyright HeadStart Primary Ltd
YEAR 6
CONTENTS
Pages 68–69
Solve problems involving similar shapes where the scale factor is known or can
be found
Pages 70–71
Solve problems involving unequal sharing and grouping using knowledge of
fractions and multiples
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Algebra
Page
Objectives
Pages 72–73
Use simple formulae for area and volume
Pages 74–75
Use simple formula to find missing angles
Page 76
Find missing co-ordinates
Pages 77–78
Find one unknown number where it is represented by symbols or letters
Pages 79–80
Generate and describe linear number sequences
Page 81
Use formula to generate a number sequence
Page 82
Express missing numbers algebraically
Pages 83–84
Use algebraic formula to solve missing number problems
Pages 85–86
Solve equivalent equations, where a symbol or letter represents one unknown
number
Pages 87–88
Find pairs of numbers that satisfy and equation with two unknowns
Pages 89–90
Enumerate the possibilities of two variables
Page 91
Solve equations using the correct order of operations
Pages 92–93
Solve equations with an unknown number on both sides
Measurement
Objectives
Page 94
Use, read, write and convert between standard units of measure from a smaller to
a larger unit and vice versa, using decimal notation of up to three decimal places
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Page
Page 95
Solve problems involving the calculation and conversion of units of length, using
decimal notation up to three decimal places
Page 96
Solve problems involving the calculation and conversion of units of mass, using
decimal notation up to three decimal places
Page 97
Solve problems involving the calculation and conversion of units of capacity,
using decimal notation up to three decimal places
Page 98
Solve problems involving the calculation and conversion of units of volume, using
decimal notation up to three decimal places
Page 99
Solve problems involving the calculation and conversion between analogue and
digital time
Pages 100–101 Solve problems involving the calculation of time in timetables and calendars
Page 102
Solve problems involving the calculation and conversion of units of time
© Copyright HeadStart Primary Ltd
YEAR 6
CONTENTS
Convert between miles and kilometres
Page 104
Convert between metric and imperial units
Page 105
Recognise that shapes with the same area can have different perimeters and
vice versa
Page 106
Recognise when it is possible to use formulae for area and volume
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Page 103
Page 107
Calculate the area of parallelograms
Page 108
Calculate the area of triangles
Page 109
Calculate and compare the volume of cubes and cuboids using standard units
Page 110
Use compound units such as miles per hour
Geometry – properties of shapes
Page
Objectives
Page 111
Draw 2-D shapes using given dimensions and angles
Page 112
Recognise and describe 3-D shapes
Page 113
Recognise and describe nets of 3-D shapes
Page 114
Compare and classify geometric shapes based on their properties and sizes
Page 115
Find unknown angles in triangles, quadrilaterals and regular polygons
Page 116
Illustrate, name and use facts about parts of a circle
Page 117
Recognise angles where they meet at a point, are on a straight line or are
vertically opposite, and find missing angles
Geometry – position and direction
Objectives
Page 118
Describe positions on the full co-ordinate grid
Page 119
Draw and translate shapes on the co-ordinate plane
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Page
Page 120
Draw and reflect shapes in the axes of a co-ordinate plane
Statistics
Page
Objectives
Page 121
Interpret and construct pie charts and use them to solve problems
Page 122
Interpret and construct line graphs and use them to solve problems
Page 123
Connect mile/kilometre conversion to its graphical representation
Page 124
Know when it is appropriate to find the mean of a set of data
Page 125
Calculate and interpret the mean as an average
© Copyright HeadStart Primary Ltd
YEAR 6
CONTENTS
FURTHER MASTERY PAGES FOR EACH DOMAIN
Page
Domain
Pages 126–127 Further mastery – number and place value
Pages 128–129 Further mastery – addition and subtraction
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Pages 130–131 Further mastery – multiplication and division
Pages 132–133 Further mastery – fractions and decimals
Pages 134–135 Further mastery – ratio and proportion
Pages 136–137 Further mastery – algebra
Pages 138–139 Further mastery – measurement
Pages 140–141 Further mastery – geometry
Pages 142–143 Further mastery – statistics
ANSWERS
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Pages 144–154
© Copyright HeadStart Primary Ltd
YEAR 6
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Number
Number and place value
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Read and write numbers up to 10,000,000
1
Write the following numbers in digits.
a Eight thousand, four hundred
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and sixty-two
b Sixty two thousand, eight
hundred and forty
c Seventy three thousand, four
hundred and twenty-one
d Five hundred and sixty-seven
thousand, nine hundred and forty-two
BIG BANK
e Two hundred and eight thousand,
five hundred and three
2
a
A lottery gave out winnings. Complete the cheques below by writing the amounts
in digits.
Date
BIG BANK
Pay
BIG BANK
The Smit h Family
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Nine million, seven hundred and eighty seven
thousand, seven hundred and ninety
"123456"
b
891011
pounds
LUCKY LOTTERY
Mr Silver
121314
Date
BIG BANK
Pay
20/12/2014
20/12/2014
The Friends Syndicate
Two million, one hundred and one thousand
and ninety-nine
"123456"
891011
pounds
LUCKY LOTTERY
Mr Silver
121314
Continued overleaf
© Copyright HeadStart Primary Ltd
1
Number – number and place value
YEAR 6
Name
Class
Date
Round whole numbers to the nearest 1000
1
Round the following numbers to the nearest 1000.
e 56,427
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a 1472
b 8326
f
c 4576
g 476,499
d 17,876
h 1,872,384
2
Circle the numbers which round to 8000.
8642
3
8473
7398
8416
7982
Complete the table below.
NUMBER
6472
8846
362
NEAREST
1000
3738
9000
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4
327,897
827
7000
For each of the numbers below, write the range of whole numbers which would round to
it, as the nearest 1000. An example is shown.
3000
2500
to
a 6000
to
b 2000
to
c 9000
to
© Copyright HeadStart Primary Ltd
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3499
Number – number and place value
YEAR 6
Name
Class
Date
Round whole numbers to a required degree of accuracy
1
Complete the table below.
NEAREST
1000
NEAREST
10,000
NEAREST
100,000
NEAREST
1,000,000
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NUMBER
6827
7000
86,472
1,000,000
772,664
3,472,830
2,946,241
2
a
Solve these problems, which involve rounding.
2,386,424 people watch a TV programme.
To the nearest 100,000, how many
people watched the programme?
A sweet factory makes 14,726 sweets.
The wrapper factory makes wrappers
in batches of 100. How many batches
should the sweet factory order to make
sure each sweet has a wrapper?
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b
2,950,000
c
A football club estimates that over a
season there will be 426,440 spectators.
Tickets with the club’s logo can be
ordered in bundles of 10,000.
How many bundles should the football
club order?
© Copyright HeadStart Primary Ltd
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Number – number and place value
YEAR 6
Name
Class
Date
Julie had a target time of 30 seconds to swim 25 m. She recorded each of her attempts
above and below her target as follows.
15
a
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+4 seconds –3 seconds 0 seconds +2 seconds –1 seconds –2 seconds
What was the difference between her fastest and slowest time?
b
How many seconds was her third fastest swim?
c
seconds
In her next race, her time was 25 seconds. What would she have
recorded her time as?
16
a
SA
If the starting temperature was 10°C, how long would it take for the
temperature to drop to –25°C?
17
seconds
Aisha was writing a horror story. The villain, Professor Freezem, tried to put victims
in a room which lowered the temperature at a rate of 7°C per second.
If the starting temperature of the room was 18°C, what would be the
temperature after 5 seconds.
b
seconds
o
C
seconds
The number function machine takes in numbers and then gives out numbers which
are 6000 less. Complete the functions below.
IN
OUT
9462
16,872
4138
182,156
–232
2349
© Copyright HeadStart Primary Ltd
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Number – number and place value
YEAR 6
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Number
Addition, subtraction,
multiplication and division
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Multiply multi-digit numbers up to 4 digits by a two-digit whole
number using the formal written method of long multiplication
1
Solve the following.
c 92 × 13 =
b 43 × 22 =
d 83 × 61 =
2
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a 41 × 12 =
Have a go at multiplying these 3-digit numbers.
a 212 × 14 =
c 321 × 47 =
b 102 × 23 =
d 842 × 84 =
3
Now try these 4-digit numbers.
a 3432 × 12 =
d 7824 × 73 =
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b 3021 × 33 =
c 3927 × 23 =
4
e 8423 × 84 =
Now try these. You will need to use your knowledge of inverse operations
to find the missing numbers.
a
÷ 54 = 121
c
÷ 31 = 4639
b
÷ 742 = 24
d
÷ 8391 = 53
Continued overleaf
© Copyright HeadStart Primary Ltd
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Number – addition, subtraction,
multiplication and division
YEAR 6
Name
3
Class
Date
Solve the following, writing the remainder as a fraction.
a 387 ÷ 18 =
f
b 630 ÷ 27 =
g 4634 ÷ 21 =
c 968 ÷ 32 =
h 3804 ÷ 27 =
d 675 ÷ 54 =
i
5483 ÷ 79 =
e 724 ÷ 36 =
j
8407 ÷ 85 =
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4
889 ÷ 28 =
For these, write the remainder as a fraction in its lowest terms.
f
b 741 ÷ 26 =
g 3690 ÷ 36 =
c 891 ÷ 36 =
h 2526 ÷ 24 =
d 960 ÷ 42 =
i
8950 ÷ 35 =
e 902 ÷ 33 =
j
8745 ÷ 88 =
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a 888 ÷ 18 =
© Copyright HeadStart Primary Ltd
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770 ÷ 56 =
Number – addition, subtraction,
multiplication and division
YEAR 6
Name
Class
Date
Divide numbers up to 4 digits by a two-digit whole number, using
long division, and round its remainder up or down, as appropriate for
the context
2
3
4
710 eggs were put into egg boxes holding 12 eggs.
How many boxes were filled?
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1
A coach can carry 34 passengers. How many coaches will be needed
to carry 798 passengers?
Rashid had collected 1642 football stickers. He put them onto sheets
with 24 stickers on each sheet. How many sheets had stickers on?
A group of archaeology students found 2647 old coins.
Forty six coins could be packed in a box.
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How many boxes were needed?
5
5427 people go to the stadium. There are 52 seats in each row.
How many rows were full of people?
6
The chocolate factory makes 8426 chocolates. Twenty-seven chocolates
fit in each bag. How many full bags of chocolates can be made?
© Copyright HeadStart Primary Ltd
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Number – addition, subtraction,
multiplication and division
YEAR 6
Name
Class
Date
Perform mental calculations, including with mixed operations
and large numbers
For these questions, counting up from the smaller to the larger number may help.
EXAMPLE
6000 – 1785.
Start with 1785. Add 5 (1790). Add 10 (1800). Add 200 (2000).
Add 4000 (6000). Add together the jumps counted up in. Answer = 4215.
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1
a 8000 – 6785 =
b 9000 – 6675 =
c 7000 – 2465 =
d 8000 – 2343 =
e 7020 – 3467 =
f
8125 – 2376 =
g 18,045 – 12,884 =
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h 24,152 – 19,341 =
i
17,200 – 4765 =
j
120,100 – 29,385 =
k 160,110 – 8764 =
l
267,212 – 6771 =
Continued overleaf
© Copyright HeadStart Primary Ltd
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Number – addition, subtraction,
multiplication and division
YEAR 6
Name
Class
Date
Identify common factors
1
Write the common factors for each of the following sets of numbers. (Don’t include 1)
a 18, 27
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c 12, 72
d 48, 144
b 12, 36
2
Add the greatest common factor to the smallest common factor. ( Don’t use 1 )
+
48, 64, 80
3
=
Write two numbers in each section of the sorting diagram. An example is shown.
Factor of 24
Not a factor of 24
Factor of 30
10
Not a factor of 30
Complete the sentences below. (Don’t include 1)
SA
4
a
Every number with a factor of 6 must also have factors of
b
Every number with a factor of 20 must also have factors of
5
Find the prime factors of these numbers.
and
a 20 =
×
×
c 52 =
×
×
b 30 =
×
×
d 99 =
×
×
© Copyright HeadStart Primary Ltd
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Number – addition, subtraction,
multiplication and division
YEAR 6
Name
Class
Date
Identify prime numbers
1
Circle the prime numbers below.
2
3
4
On the line below, write all the prime numbers greater than 50, but less than 100.
Add together the prime numbers between 140 and 170. Show your calculation.
Is 351 a prime number? Yes / No. Explain your answer.
Look at the numbers below and investigate them
to help you complete the sentence. The numbers
which are prime numbers are circled.
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5
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29273 17335 412 45
If the sum of a number’s digits is a multiple of ,
that number is not a prime number because
36
414
37
5419
5421
73
1023
© Copyright HeadStart Primary Ltd
40
52,176
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Number – addition, subtraction,
multiplication and division
YEAR 6
Name
Class
Date
Use knowledge of the correct order of operations to carry out
calculations involving the four operations
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B O D M A S
brackets
order
2 (3 + 4)
(or other things
means the same e.g. – squares)
as 2 × (3 + 4)
1
division
multiplication
addition
Use BODMAS to complete the following.
a 76 _ 3 × 6 =
f (6 + 27 × 2) ÷ 10 =
b (4 + 7) 9 =
g 14 × 36 –
c 18 ÷ 3 – 2 =
h
d 3 × 9 + 14 =
i (53 + 116 – 81) ÷ 11 =
e 16 + 12 – 17 =
j (272 – 64 × 3) ÷ 8 + 1 =
= 475
× 63 ÷ 9 = 182
Give the correct answer and explain the error made.
EXAMPLE
SA
2
subtraction
48 + 12 ÷ 2 =
54
30
The addition, rather than division, was calculated first.
a 70 + 60 × 2 = 260
b (31 + 163 – 72)6 +2 =
© Copyright HeadStart Primary Ltd
976
41
Number – addition, subtraction,
multiplication and division
YEAR 6
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Number
Fractions
(including decimals and percentages)
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Add and subtract fractions with different denominators and
mixed numbers, using the concept of equivalent fractions
a
For each of the following, add the fractions by finding the lowest common denominator.
1
3
b
3
4
c
1
4
d
2
2
+
+
+
3
10
6
1
8
1
3
+ 3
=
6
=
+
1
2
1
2
+
=
+
=
=
+
=
3
_
1
3
4
b
6
_
2
2
3
7
c
6
+
+
=
=
Now try subtracting these fractions.
=
SA
a
5
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1
3
4
=
_ 1 5 =
8
_
=
_
=
_
=
Continued overleaf
© Copyright HeadStart Primary Ltd
49
Number – fractions (including
decimals and percentages)
YEAR 6
Name
Class
Date
Multiply simple pairs of proper fractions, writing the answer
in its simplest form
a
Multiply the fractions below.
1
3
b
1
5
2
a
×
2
1
×
4
=
c
1
4
=
d
5
2
4
7
2
×
9
=
=
3
×
×
2
6
1
8
=
=
=
=
c
5
6
×
4
9
=
=
Multiply each pair of fractions and put the answer on the ladder, starting with the smallest.
3
3
5
×
6
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9
3
1
Multiply the following and write the answer in its simplest form.
4
b
1
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1
×
×
1
8
1
4
×
4
5
7
10
1
3
10
10
© Copyright HeadStart Primary Ltd
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Number – fractions (including
decimals and percentages)
1
×
2
×
5
4
YEAR 6
Name
Class
Date
Understand the relationship between fractions and division to find
whole quantities
Solve the following problems.
2
A ribbon measures 15 cm.
How long is 1 of the ribbon?
5
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1
15 cm
cm
There are 35 people on a bus. One fifth of them are children.
How many children are on the bus?
3
m
2
It rained for 5 of Tom’s holiday.
He was on holiday for 25 days.
SA
4
1
The perimeter of a garden is 392 m. 7 of it is a wall.
What is the length of the wall?
a
For how many days did it rain?
b
If Tom’s holiday had been 2 days longer and it had rained on both days,
what fraction of Tom’s holiday would have been rainy?
Put your answer in its simplest form.
© Copyright HeadStart Primary Ltd
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Number – fractions (including
decimals and percentages)
YEAR 6
Name
4
Class
Date
Now use division to complete this table.
4·05
14·1
16·3
2356
7527
M
PL
E
Number in
Divided by
10
100
1000
1000
10
Number out
5
Complete the calculations in the function machine.
Number in
Function
Number out
× 100
36·3
476
÷ 1000
0·67
× 10
SA
37·2
372
0·23
× 1000
3
÷ 100
0·764
7·64
© Copyright HeadStart Primary Ltd
56
Number – fractions (including
decimals and percentages)
YEAR 6
Name
Class
Date
Recall and use equivalence between fractions, decimals and percentages
1
Complete the table below to identify equivalent fractions, decimals and percentages.
1
4
1
2
M
PL
E
Fraction
0.75
Decimal
0.4
20%
Percentages
2
Draw lines between any values which are equivalent.
60%
70%
1
8
12·5%
3
5
3
0.125
7
10
0.6
0·7
0·125
Put the values in the correct position on the number line. For some, you will need
to estimate the position. For each value, write the equivalent fraction, decimal and
percentage. An example is shown.
9
10
SA
0·25
0·5
0
0·125
1
20
1·45
120%
1.5
0·5
50%
1
2
© Copyright HeadStart Primary Ltd
61
Number – fractions (including
decimals and percentages)
YEAR 6
M
PL
E
SA
Ratio and proportion
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Solve problems involving the calculation of percentages
2
3
In Mr Seedat’s class, 40% of the 30 children were girls. How many girls were there?
M
PL
E
1
The class made badges for a business enterprise. The takings were
£120 and 60% was profit. How much profit was there?
£
Nick is writing an essay. He writes 20 pages. He draws a bar chart to show the
number of words on each page he writes.
6
Number
of pages
4
2
0
<1 1–200
201–210 211–220 221–230 231–240
>241
Number of words on a page
What percentage of the pages have 231–240 words?
%
b
What percentage have 230 words or fewer?
%
c
Which of the ranges shown above represents 15% of the pages?
SA
a
4
There were 60 pupils in Year 6. 20% liked swimming best. 15 liked football.
15% liked athletics and the rest did not know.
a
How many children liked athletics best?
b
What percentage liked football best?
c
How many children knew which sport they liked best?
© Copyright HeadStart Primary Ltd
66
%
Ratio and proportion
YEAR 6
M
PL
E
SA
Algebra
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Use simple formulae for area and volume
The formula to find the area of a rectangle is A (Area) = l (length) × w (width).
Use this to find the missing values in the table below.
l
w
Rectangle A
4 cm
5 cm
cm2
Rectangle B
8 cm
9 cm
cm2
Rectangle C
3m
mm
Rectangle E
36 m2
m
Rectangle D
2
A
M
PL
E
1
9 mm
2·5 m
117 mm2
m
45 m2
Use the formula V (Volume) = l × w × h (height) to find the volume of the cuboids.
Not to scale
a
b
V=
3 cm
5 cm
a
m3
2m
3·5 m
Use the formulae above to identify two possible sets of missing values
(each side is a whole number).
Area = 16 cm2
16 cm2 =
b
V=
5m
12 cm
SA
3
cm3
cm
×
cm
or 16 cm2 =
cm
×
cm
Volume = 24 cm3
24 m3 =
or 24 cm3 =
cm
×
cm
×
cm
×
cm
cm
×
cm
Continued overleaf
© Copyright HeadStart Primary Ltd
72
Algebra
YEAR 6
Name
Class
Date
Use simple formula to find missing angles
The sum of the interior angles in a triangle = 180°
The sum of the angles on a straight line = 180°
M
PL
E
The sum of the angles at a point = 360°
The sum of the interior angles in a quadrilateral = 360°
The sum of the interior angles in a pentagon = 540°
1
Use the formulae above to find the missing angles.
a
Angle a =
b
a
91°
°
74°
91°
75°
d
a
106°
98°
81°
42°
c
°
Angle c =
70°
SA
Angle a =
°
e
c
e
118°
12°
125°
83°
84°
120°
Angle e =
°
Angle c =
c
23°
°
Continued overleaf
© Copyright HeadStart Primary Ltd
74
Algebra
YEAR 6
Name
3
Class
Date
Complete the table by putting numbers in all the empty boxes. Examples are shown.
6n–8
3n+7
8n÷2
M
PL
E
n = 12
n=
10
n=
n=
4
14·5
n + 5 is greater than 30. n – 5 is less than 30. If n represents a whole number, find
all the numbers that n could be.
Find the missing numbers below, so that 4x + 6y = 68. An example is shown.
SA
5
44
If
x = 2, y = 10
a If x = 8, y =
c If x = 5, y =
b If y = 4, x =
d If y = 8·5, x =
© Copyright HeadStart Primary Ltd
78
Algebra
YEAR 6
Name
Class
Date
Express missing number problems algebraically
1
For each problem below, circle the equation which could be used to solve it.
Shabnam had some red and blue buttons. She had 81 buttons altogether and
15 were red. How many were blue ( b )?
M
PL
E
a
b = 81 + 15
b
15 = 81 + b
There were 128 girls in 8 classes. What was the average number of girls per
class ( g )?
128 + 8 = g 2
b = 81 _ 15 128 _ 8 = g 128 ÷ 8 = g
Write down a suitable equation to solve this problem. Then solve it.
Marc spent £18.72 and Freddie spent £31.96.
How much more did Freddie spend than Marc ( s )?
s=
This is an equation to solve a problem: p = 64 + 73 + 29 ( p stands for people )
What could the problem have been?
SA
3
© Copyright HeadStart Primary Ltd
82
Algebra
YEAR 6
Name
Class
Date
Find pairs of numbers that satisfy an equation with two unknowns
1
Find the missing values. Write your answer in the box.
d y = 49 + 26
= 23 + 56
= + 43
M
PL
E
a
y = 3a
=
b
a=
e 56 ÷ b = 28
= 14 × 2
= +
b + 481 = x
x=
=
c
2
x=9×9
f 13y = 200 – 57
x = 47 + y
y=
2y = 47 – x
x=
Find the missing values in each of the following.
a + 17 = 46
a=
4a = 79 + b
b=
SA
a
b
c
× 17 = 272
=
+
=
+
= 384 ÷
x + x + 24 = 92
102
x =y+y+y
x=
y=
Continued overleaf
© Copyright HeadStart Primary Ltd
87
Algebra
YEAR 6
Name
Class
Date
Solve equations using the correct order of operations
To make sure we carry out calculations in the correct order, we use BODMAS.
M
PL
E
B O D M A S
brackets
order
2 (3 + 4)
(or other things
means the same e.g. – squares)
as 2 × (3 + 4)
1
division
multiplication
addition
subtraction
Use BODMAS to find the missing values.
a
e
= ( 10 + 11 ) ÷ 7
a =
=
b
f
= 36 ÷ ( 3 × 3 )
SA
g
x = 4 + 7 × 13
y = 23( 43 – 34 )
h
9x = 16 + 3( 68 ÷ 17 ) – 1
x =
y=
© Copyright HeadStart Primary Ltd
3b = ( 36 ÷ 4 )12 – 15
b =
x=
d
6y = 255 – 13 × 9
y =
=
c
a = ( 38 ÷ 2 – 4 ) + 5
91
Algebra
YEAR 6
M
PL
E
SA
Measurement
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Use, read, write and convert between standard units of measure from
a smaller to a larger unit and vice versa, using decimal notation of up
to three decimal places
2
Convert between the standard units of capacity.
M
PL
E
1
a
4600 ml =
b
6·8 l =
l
ml
c
3741 ml =
d
4·326 l =
ml
Complete the table below, which shows the conversion between grams and kilograms.
grams
550
kilograms
3
l
1·4
30
2·6
Complete the table below to show the conversion of units of length.
mm
2,000,000
cm
500,000
600
1200
SA
m
km
4
2
3·2
Now convert between these standard units of time.
a 84 days =
b 420 seconds =
© Copyright HeadStart Primary Ltd
c 6·5 hours =
weeks
minutes
94
d 10·25 years =
Measurement
minutes
months
YEAR 6
Name
Class
Date
Solve problems involving the calculation and conversion between
analogue and digital time
Draw lines to match up to the times shown. One is done for you.
M
PL
E
1
8:00
2
15:40
04:30
18:20
07:15
Sophie’s watch showed a time of quarter past 7. Her alarm went off 25 minutes later.
What time did her alarm go off? Give your answer as a digital time.
:
3
The watch shows the time in the morning when Nafisa set off to her cousin’s house.
The digital 24-hour clock shows the time she arrived. How long did it take her?
14 : 08
SA
hours
4
5
minutes
Jessica, James and Amy set off on a school trip at 18:10. They arrived at their
destination at quarter past eight the next morning. For how many hours
and minutes were they travelling?
hours
minutes
One of the clocks is 5 minutes fast. One is 3 minutes slow. What is the correct time?
:
11 : 23
© Copyright HeadStart Primary Ltd
99
Measurement
YEAR 6
Name
Class
Date
Calculate the area of parallelograms
1
M
PL
E
Look at the parallelograms on the centimetre grid. Calculate their areas.
A
B
D
C
A=
2
cm2
B=
C=
cm2
D=
cm2
cm2
A parallelogram had an area of 20 cm2. Its base measured 4 cm.
What was the perpendicular height?
cm2
3
Complete the table below.
Perpendicular
Height (cm)
Parallelogram
A
3·2
4·6
Parallelogram
B
12
SA
length (cm)
Parallelogram
C
© Copyright HeadStart Primary Ltd
Area (cm2)
42
17
107
714
Measurement
YEAR 6
Name
Class
Date
Use compound units such as miles per hour
2
Naseeba travelled to work at a rate of 30 miles per hour.
She travelled for 30 minutes at a constant speed.
How many miles did she travel?
miles
M
PL
E
1
The graph below shows the speed Mr and Mrs Haworth travelled on their journey
to their holiday destination.
Average speeds
(miles per hour)
70
60
50
40
30
20
10
Hour 1 Hour 2 Hour 3 Hour 4
a
What was the average speed travelled for the second hour?
b
The third hour was from 12 midday until 1 pm. The family stopped
for lunch from 12:00 until 12:30. How many miles did they travel
between 12:30 and 1 pm?
What was the average speed travelled over all 4 hours?
SA
c
d
3
miles per hour
miles
miles per hour
During their holiday, the family went on a trip.
They travelled 50 miles at a rate of 40 miles per hour.
How long did the journey take?
hours
Aaron wanted to eat a healthy diet of no more than 150 grams of carbohydrates per day.
a
How many days should he take to eat 450 grams?
b
What would be the maximum
carbohydrates he should eat in 7 days?
© Copyright HeadStart Primary Ltd
110
days
grams
Measurement
YEAR 6
M
PL
E
SA
Geometry
Properties of shapes
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Draw 2D shapes using given dimensions and angles
Use paper or your exercise book to answer the following questions.
2
Draw the following rectangles as accurately as you can.
M
PL
E
1
a
Length 5 cm, width 3 cm
c
Length 4·4 cm, width 3 cm
b
Length 6 cm, width 6 cm
d
Length 3 1 cm, width 6 1 cm
2
2
Draw the following triangles.
a
An equilateral triangle with sides measuring 4 cm.
b
An isosceles triangle with a base of 4·5 cm and an interior angle of 50º at either side
of its base.
c
5·5 cm
d
Not actual size
8 cm
6 cm
4 cm
Not actual size
Julia made a scarecrow using 2D shapes. Use the information below to draw Julia’s
scarecrow as accurately as you can. You will need to use your knowledge of the
properties of shape.
SA
3
4·5 cm
Not actual size
© Copyright HeadStart Primary Ltd
Part of
scarecrow
top of hat
brim of hat
head
body
arms
fingers
legs
feet
buttons
knee patches
eyes
nose
mouth
111
Shape
Dimensions
rectangle
rectangle
circle
rectangle
rectangles
0·5 cm × 2 cm
0·4 cm × 3 cm
diameter 3 cm
4 cm × 6 cm
3·5 cm × 1·2 cm
base 0·4 cm
right angle triangles
height 1 cm
2 cm × 4c m
parallelograms
60° × 2 120° × 2
rectangles
3 cm × 1 cm
equilateral triangles
sides 1cm
squares
1 cm2
diameter 0·2 cm (approx)
circles
sides approx 0·2 cm
triangle
to fit
arc of a circle
Geometry – properties of shapes
YEAR 6
Name
Class
Date
Find unknown angles in triangles, quadrilaterals and regular polygons
1
Without using a protractor, work out the size of Angle A in each of the shapes below.
5 cm
d
°
75°
°
M
PL
E
a
5 cm
5 cm
40°
A
A
90°
b
e
°
A
2 cm
A
60°
4 cm
70°
4 cm
110°
c
f
°
A
4 cm
4 cm
6 cm
6 cm
not actual sizes
°
2 cm
4 cm
4 cm
°
4 cm
A
4 cm
75°
2
Calculate the value of the missing angles.
50°
SA
b
a
3
c
40°
a=
°
b=
°
c=
°
The shaded shape shows an isosceles triangle drawn inside a regular pentagon.
A
What is the size of Angle A?
°
Explain how you worked out your answer.
© Copyright HeadStart Primary Ltd
115
Geometry – properties of shapes
YEAR 6
M
PL
E
SA
Geometry
Position and direction
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Draw and translate shapes on the co-ordinate plane
1
3
Sketch the new position of the shape after it has
been translated 2 units up and 3 units to the left.
2
M
PL
E
1
–3
–2
–1 0
1
2
3
1
2
3
–1
–2
–3
2
3
Sketch the position of the shape after a rotation
of 180°.
2
1
–3
–2
–1 0
–1
–2
–3
9
8
7
6
5
4
3
2
1
SA
3
C
B
A
0
1 2 3 4 5 6 7 8 9 10 11 12
Above is a sequence of rectangles. Write the co-ordinates for each vertex
of the next rectangle.
(
,
)
(
,
© Copyright HeadStart Primary Ltd
)
(
,
)
119
(
,
)
Geometry – position and direction
YEAR 6
M
PL
E
SA
Statistics
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Interpret and construct pie charts and use them to solve problems
1
There are 32 children in the class.
a
How many children liked Science best.
M
PL
E
Maths
P.E.
English 45°
45° 135°
90°
45°
Art
Science
2
b
How many children liked Art best?
c
What percentage of the class did not
choose Maths or English?
d
What fraction of the class chose P.E?
%
72 people were asked about their favourite sport. Their answers are shown in the
table. Use this information to complete the pie chart.
rugby
swimming
netball
football
tennis
9
9
18
27
9
netball
3
Gabriel and Isaac collected autumn leaves. They each made a pie chart of their collection.
Isaac – 60 leaves
SA
Gabriel – 72 leaves
oak
ash
90° 90°
135° 45°
beech
c
Who collected the most
ash leaves?
b
How many beech leaves were
collected altogether?
oak
ash
elm
a
120°
90°
60° 90°
beech
elm
Gabriel said, “Our pie charts show that we have collected
the same number of oak leaves.” Explain why he is wrong.
© Copyright HeadStart Primary Ltd
121
Statistics
YEAR 6
Name
Class
Date
Calculate and interpret the mean as an average
1
Tom drew the graph below to show the distance he jumped over 5 standing jumps.
1·2
What was the average
distance Tom jumped?
M
PL
E
a
1
distance 0.8
(metres)
0.6
m
0.4
0.2
0
b
2
3
2
3
jumps
4
5
Tom only jumped 0·6 m for his 6th jump. To the nearest centimetre,
what was his new average?
Anya is saving for some trainers which cost £28.95.
On average, how much would she need to save each
week for 5 weeks?
cm
£
Linzi collects £8.16 for charity. Robert collects £7.54 and Joseph
collects £9.20. What is the average amount collected?
£
Dale was investigating how long he could stand on one foot. His results are shown in
the table below.
SA
4
1
attempt
1
2
3
4
5
time in
seconds
18
17
13
19
18
a
What was his average time?
b
Dale wanted to increase his average to 18 seconds.
For how many seconds would he have to stand on one foot
in his sixth attempt to achieve this?
© Copyright HeadStart Primary Ltd
seconds
125
seconds
Statistics
YEAR 6
M
PL
E
SA
Further mastery
© Copyright HeadStart Primary Ltd
YEAR 6
Name
Class
Date
Further mastery – addition and subtraction
b
2
Jez had to complete the calculation 1426 + 340 + 260.
He decided to use the associative rule to complete the calculation,
in his head. Explain what Jez did.
M
PL
E
1 a
Now look at the calculation 184 + 1653 + 816 + 7. Explain how
you would complete the calculation, giving your reasons and
then find the answer.
For each of the following, decide whether you would carry out the calculation mentally
or using a written calculation. Explain your reasons, then solve the calculation.
a 148·3 + 120·4 =
mental / written because
mental / written because
b 2356·4 + 1783·32 =
SA
c 12,426 + 2574 =
3
mental / written because
Write the correct digits on the lines to make the calculations correct.
a 12,745 + 1
7 = 14,562
b 127·39 _ 3
·47 = 88·
2
Continued overleaf
© Copyright HeadStart Primary Ltd
128
Further mastery – addition
and subtraction
YEAR 6
Name
Class
Date
Further mastery – fractions and decimals
1
For each of the following, write > , < or = to make the number sentence correct.
b
2
5
8
c 0·65
3
5
1
8
0·125
d 1
3
12
1
2
5
Put a whole number less than 20, in each box, to make the number sentence correct.
There may be more than one possible answer.
a
b
4
=
6
1
<
3
c
÷4= 2·
d
8
÷
= 1·25
This time, put a whole number less than 10 in each box.
SA
3
2
3
M
PL
E
a
a
1
2
×
3
b
×
c
1
÷ 3=1_
2
=
=
d
6
1
÷=
3
6
21
Continued overleaf
© Copyright HeadStart Primary Ltd
132
Further mastery – fractions
and decimals
YEAR 6
Name
Class
Date
Further mastery – ratio and proportion
1
2
M
PL
E
Cost of 4 jars of coffee = £7.80
a
How much would 3 jars of coffee cost?
b
2
A small jar of coffee costs 3 as much as one of the jars shown above.
How much does a small jar of coffee cost?
£
£
A pizza needs four times as much cheese as a cheese and onion pie. Chef Charlotte
makes 5 pizzas and uses 240 g of cheese. How much cheese would she need to make
a cheese and onion pie?
g
Sofia has 75 red and blue building bricks in a box. The ratio of red to blue is 3 : 2.
How many fewer blue bricks than red bricks are there?
SA
3
4
Samir and Lennox collect football cards. They have 155 altogether. Lennox has 37 more
football cards than Samir.
a
How many cards does Samir have?
b
Lennox’s friend said, “For every 3 cards you’ve got, I’ll give you 50p”.
How much money would Lennox get if he decided to sell all his cards to his friend?
£
Continued overleaf
© Copyright HeadStart Primary Ltd
134
Further mastery – ratios
and proportion
YEAR 6
Name
3
Class
Date
Use your knowledge about area of rectangles to explain how you can find the area
of this triangle. Then explain your working.
Not actual size
3 cm
Area =
4
M
PL
E
5 cm
cm2
The diameter of a sphere is 2 cm. Which of the following boxes could hold 10 spheres?
(each with a diameter of 2 cm).
a
2 cm
2 cm
10 cm
4 cm
2 cm
10 cm
Box 1
b
How many spheres would fit in the other box?
Explain your answer.
weighs 1 1 times as much as a cube.
2
weighs 0·4 kg. A cuboid
A cube
SA
5
Box 2
How much does a cylinder weigh?
Give your answer in kilograms and grams.
0
kg
1
5
kg
4
2
3
© Copyright HeadStart Primary Ltd
g
139
Further mastery – measurement
YEAR 6
Name
Class
Date
Further mastery – statistics
1
walk
5%
The pie chart shows the results of a survey
of 500 people’s mode of travel to work.
Some percentages are shown. Four times
as many people travel to work by bus than
walk and twice as many people cycle to
work than walk to work.
M
PL
E
cycle
bus
car
train 25%
a
What percentage of the 500 people travel to work by car?
b
How many people cycle to work?
c
How many more people travelled to work by car than walked?
d
If the survey had included another 200 people and the proportions
of mode of travel to work remained the same, how many people
would have used each mode of public transport?
walk
bus
train
car
SA
cycle
%
2
A shoe company wanted to know which shoe size they should make the most of.
The manager thought that finding the mean average shoe size for 5000 people
would generate the data needed.
Do you think that was a sensible idea?
Explain your answer.
Continued overleaf
© Copyright HeadStart Primary Ltd
142
Further mastery – statistics
YEAR 6
M
PL
E
SA
Answers
© Copyright HeadStart Primary Ltd
YEAR 6
ANSWERS
Page 25
1 a) 56 r7 b) 89 r3 c) 21 r14 d) 39 r18 e) 22 r2
f ) 21 r3 g) 102 r4 h) 123 r3 i) 98 r11 j) 261 r16
Page 32
5 a) 90 b) 209 c) 309 d) 368 e) 368 f ) 456 g) 24·8
h) 45·9
2
6
a) 63·5 b) 79·25 c) 49·25 d) 11·5 e) 13·25
f ) 110·5 g) 135·75 h) 132·75 i) 106·25 j) 148·75
4
M
PL
E
Page 26
1
6
5
6
b) 4212
or 4212 c) 3025
or 15 d) 3018
or 3013
3 a) 1311
7
3
5
3
4
e) 4413
f ) 5815
or 5815 g) 11112
h) 10117
i) 10821
j) 10629
75
a) 5612 b) 8213 c) 6213 d) 3415 e) 2323 3
g) 10211
h) 10223 i) 4216 j) 58638 Page 33
7 a) 168 b) 126 c) 114 d) 207 e) 136 f ) 154
f ) 1119
8
Page 27
126·4
3
12·5 or 1212
4
each pupil got 55 tickets and the teacher got 50
10 a) 27, 125, 216, 343
b) 512 because 8 × 8 × 8 = 512
Page 35
11 a) 0·65 b) 0·16 c) 2·19 d) 0·04 e) 10·77
f ) 0·164 g) 0·119 h) 5·55
5£3
Page 28
1104
12 a) 36·2 b) 1748 c) 0·36 d) 300 e) 173 f ) 0·36
g) 3·742 h) 0·64
269
3102
13 a) 0·08 b) 3·6 c) 4·2 d) 1·35 e) 0·125 f ) 0·9 g) 5
h) 1·6
4208
5173
697
SA
Page 29
1 a)1215 b) 2325 c) 4535 d) 5657 e) 3553 f ) 5749
g) 5161 h) 4811 i) 12,435 j) 90,715 k) 151,346
l) 260,441
Page 30
2 a) 81 b) 139 c) 601 d) 795 e) 602 f ) 999
g) 1218 h) 2397 i) 4997 j) 28,004 k) 46,030
l) 280,030
a) 441, 536 b) 5560, 2830 c) 1254, 622
d) 9862, 8972 e) 786, 3144
Page 31
4 a) 60 b) 90 c) 130 d) 170 e) 1300 f ) 2400
g)13,000 h) 20,000 i) 80,000 j) 114,000
k) 36,470 l) 80,320
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a) 94 b) 77 c) 202 d) 290 e) 511 f ) 1860
g) 6953 h) 6450
Page 34
9 a) 36 b) 64 c) 10 d) 7 e) 130 f ) 93
2307·4 l
3
row 1: 8, 40, 50, 600
row 2: 7, 42, 56, 280, 350, 2800, 4200
row 3: 9, 72,108, 360, 3600, 5400
row 4: 66, 88, 132, 550, 4400, 6600
row 5: 78, 156, 520, 650, 5200
row 6: 15, 120, 180, 600, 750, 6000, 9000
Page 36
14 a) 119 b) 3520 c) 97 d) 93 e) 152 f ) 81 g) 8
h) 253, 22·3 i) 0·09 j) 130 k) 343 l) 1·64
m) 3640 n) 144 o) 57,240
Page 37
15 a) 131,660 b) 15,374 c) 71,370 d) 799 e) 144, 11, 9000 f ) 529 g) 217 h) 161 i) 2930
j) 64, 216, 343 k) 370 l) 2·6 m) 48,007
n) 100,715 o) 658, 1706
Page 38
1 a) 3, 9 b) 2, 3, 4, 6, 12 c) 2, 3, 4, 6, 12
d) 2, 3, 4, 6, 8, 12, 24, 48
2
8 + 2 = 10
3
row 1: 2 from: 2, 3, 6/1 from 5, 15
row 2: 2 from: 4, 8, 12/any appropriate numbers
4
a) 3 & 2 b) 2, 4, 5, 10
5
a) 2 × 2 × 5 b) 2 × 3 × 5 c) 2 × 2 × 13 d) 3 × 3 × 11
146
YEAR 6
M
PL
E
MASTERING THE MATHEMATICS CURRICULUM
YEAR 6
covers all National Curriculum objectives
focuses on the mastery approach
supports lesson planning and saves teacher time
SA
provides evidence for formative progress judgements
T. 01200 423405
E. [email protected]
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