problem solving, reasoning & investigating · page 124 solve problems with linear number...

Primary

6Year

Includes CD-ROM for

whiteboard use or printing

MATHEMATICS CURRICULUM

Problem Solving, Reasoning & Investigating

Year 6

Maths Problem Solving,Reasoning & Investigating

Lizzie MarslandSusannah Palmer

Acknowledgements:Author: Lizzie Marsland, Susannah PalmerSeries Editor: Peter SumnerCover and Page Design: Kathryn Webster, Jo Sullivan

The right of Lizzie Marsland and Susannah Palmer to be identified as the authors of this publication has been asserted by them in accordance with the Copyright, Designs and Patents Act 1998.

T. 01200 423405E. [email protected]

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 2018 © HeadStart Primary Ltd 2018

A record for this book is available from the British Library - ISBN: 978-1-908767-62-2

HeadStart Primary LtdElker LaneClitheroeBB7 9HZ

© Copyright HeadStart Primary Ltd

INTRODUCTION

Year 6: NUMBER - Number and place value

Page ObjectivesPage 1 Read and write numbers to at least 10,000,000Page 2 Read and write numbers to at least 10,000,000Page 3 Order and compare numbers to at least 10,000,000 Order and compare numbers to at least 10,000,000Page 5 Determine the value of each digit in numbers up to 10,000,000 Page 6 Determine the value of each digit in numbers up to 10,000,000 Page 7 Round any whole number to a required degree of accuracyPage 8 Round any whole number to a required degree of accuracyPage 9 Use negative numbers in context and calculate intervals across zeroPage 10 Use negative numbers in context and calculate intervals across zero Page 11 Solve problems involving number and place valuePage 12 Solve problems involving number and place valuePage 13 Solve problems involving number and place value

Pages 14 - 21 MASTERING - Number and place value

Year 6: NUMBER - Addition, subtraction, multiplication and division

Page 22 Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplicationPage 23 Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplicationPage 24 Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long divisionPage 25 Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long divisionPage 26 Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division and interpret the remainder as a whole numberPage 27 Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division and interpret the remainder as a fractionPage 28 Divide numbers up to 4 digits by a two-digit whole number using the formal

written method of long division, rounding the remainder as appropriate for the context

CONTENTS Year 6


CONTENTS Year 6

Page 29 Interpret remainders appropriately for the context Page 30 Divide numbers up to 4 digits by a two-digit whole number using the formal written method of short division, interpreting remainders according to the contextPage 31 Perform mental calculations, including with mixed operations and large numbers Page 32 Identify common factors, common multiples and prime numbersPage 33 Identify common factors, common multiples and prime numbersPage 34 Use knowledge of the order of operations to carry out calculations involving the four operationsPage 35 Solve addition and subtraction multi-step problems in contextPage 36 Solve problems involving addition, subtraction, multiplication and divisionPage 37 Solve problems involving addition, subtraction, multiplication and divisionPage 38 Solve problems involving addition, subtraction, multiplication and division

Pages 39 - 52 MASTERING - Addition, subtraction, multiplication and division

Year 6: NUMBER - Fractions (including decimals and percentages)

3 Use common factors to simplify fractionsPage 54 Use common multiples to express fractions in the same denominationPage 55 Compare and order fractions, including fractions greater than 1Page 56 Compare and order fractions, including fractions greater than 1Page 57 Add fractions with different denominators, using the concept of equivalent fractionsPage 58 Subtract fractions with different denominators, using the concept of equivalent fractions Page 59 Add or subtract fractions with different denominators, using the concept of equivalent fractionsPage 60 Add or subtract mixed numbers, using the concept of equivalent fractions Page 61 Multiply simple pairs of proper fractions, writing the answer in its simplest formPage 62 Divide proper fractions by whole numbersPage 63 Associate a fraction with division and calculate decimal fraction equivalentsPage 64 Identify the value of each digit in numbers to three decimal placesPage 65 Identify the value of each digit in numbers to three decimal placesPage 66 Divide numbers by 10 giving answers up to 3 decimal placesPage 67 Divide numbers by 100 giving answers up to 3 decimal placesPage 68 Divide numbers by 1000 giving answers up to 3 decimal placesPage 69 Multiply one-digit numbers with up to two decimal places by whole numbers


CONTENTS Year 6

Page 70 Multiply one-digit numbers with up to two decimal places by whole numbersPage 71 Use written divison methods in cases where the answer has up to two decimal placesPage 72 Solve problems which require answers to be rounded to specified degrees of accuracyPage 73 Recall and use equivalences between simple fractions, decimals and percentages, including in different contextsPage 74 Solve problems involving percentagesPage 75 Solve problems involving percentagesPage 76 Solve problems involving fractionsPage 77 Solve problems involving fractionsPage 78 Solve problems involving fractions, decimals and percentagesPage 79 Solve problems involving fractions, decimals and percentages

Pages 80 - 98 MASTERING - Fractions, decimals and percentages

Year 6: RATIO AND PROPORTION

Page 99 Solve problems involving the relative size of quantities using division and multiplicationPage 100 Solve problems involving the relative size of quantities using division and multiplicationPage 101 Solve problems involving the calculation of percentagesPage 102 Solve problems involving the comparison of percentagesPage 103 Solve problems linking percentages, angles and pie chartsPage 104 Solve problems involving scaling by multiplicationPage 105 Solve problems involving scaling by divisionPage 106 Solve problems involving scaling by multiplication and divisionPage 107 Solve problems involving scaling of shapesPage 108 Solve problems involving unequal groupings using knowledge of fractions and multiplesPage 109 Solve problems involving unequal quantitiesPage 110 Solve problems involving unequal quantities

Pages 111 - 122 MASTERING - Ratio and proportion

Year 6: ALGEBRA

Page 123 Solve problems involving finding missing numbers using simple formulaePage 124 Solve problems with linear number sequencesPage 125 Express missing number problems algebraicallyPage 126 Express missing number problems algebraicallyPage 127 Solve problems involving equations with two unknown numbersPage 128 Enumerate possibilites of combinations of two variables

Pages 129 - 142 MASTERING - Algebra


CONTENTS Year 6

Year 6: MEASUREMENT

Page 143 Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal placesPage 144 Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal placesPage 145 Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal placesPage 146 Solve problems involving converting measurements of lengthPage 147 Solve problems involving converting measurements of massPage 148 Solve problems involving converting measurements of volume Page 149 Solve problems involving converting measurements of time Page 150 Solve problems converting between miles and kilometresPage 151 Solve problems involving perimeter and areaPage 152 Solve problems recognising that shapes with the same areas can have different perimeters and vice versaPage 153 Solve problems using formulae for areaPage 154 Solve problems using formulae for volumePage 155 Solve problems by calculating the area of parallelogramsPage 156 Solve problems by calculating the area of triangles Page 157 Solve problems by calculating the area of compound and mixed shapesPage 158 Solve problems by calculating and comparing the volume of cubes and cuboids using cubic centimetresPage 159 Solve problems by calculating and comparing the volume of cubes and cuboids using cubic metresPage 160 Solve problems by calculating and comparing the volume of cubes and cuboids extending to other units (mm3 and km3)

Pages 161 - 172 MASTERING - Measurement

Year 6: GEOMETRY - Properties of shapes / Position and direction

Page 173 Solve problems involving 2D shapes using dimensions and anglesPage 174 Solve problems involving 2D shapes using dimensions and anglesPage 175 Solve problems involving the properties of 3D shapesPage 176 Solve problems involving nets of 3D shapes Page 177 Solve problems involving the properties of 2D and 3D shapesPage 178 Solve problems involving angles in triangles


CONTENTS Year 6

Page 179 Solve problems involving angles in quadrilaterals Page 180 Solve problems involving angles in regular polygonsPage 181 Solve problems involving the parts of a circlePage 182 Solve problems involving anglesPage 183 Solve problems involving position and directionPage 184 Solve problems involving position and direction

Pages 185 - 191 MASTERING - Geometry

Year 6: STATISTICS

Page 192 Interpret pie charts and use these to solve problemsPage 193 Interpret pie charts and use these to solve problemsPage 194 Interpret pie charts and use these to solve problems Page 195 Interpret line graphs and use these to solve problems Page 196 Interpret line graphs and use these to solve problems Page 197 Interpret line graphs and use these to solve problems Page 198 Calculate and interpret the mean as an averagePage 199 Calculate and interpret the mean as an averagePage 200 Calculate and interpret the mean as an average

Pages 201 - 209 MASTERING - Statistics

Pages 210 - 222 INVESTIGATION - Cake Sale

Pages 223 - 234 ANSWERS


INTRODUCTIONThese problems have been written in line with the objectives from the Mathematics Curriculum. Questions have been written to match all appropriate objectives from each content domain of the curriculum.

Solving problems and mathematical reasoning in context are difficult skills for children to master; a real-life, written problem is an abstract concept and children need opportunities to practise and consolidate their problem solving techniques.

As each content domain is taught, the skills learnt can be applied to the relevant problems. This means that a particular objective can be reinforced and problem solving and reasoning skills further developed. The first section of each content domain is intended to provide opportunities for children to practise and consolidate their problem solving skills. Each page has an identified objective from the National Curriculum; the difficulty level of the questions increases towards the bottom of each page, thus providing built-in differentiation.

Mastering a skill involves obtaining a greater level of understanding of the skill, the ability to transfer and apply knowledge in different contexts and explaining understanding to others.

The MASTERING and INVESTIGATION sections provide extra challenges as children’s problem solving skills and confidence increase. The problems in the MASTERING sections encompass several objectives from the relevant curriculum domain. The INVESTIGATION covers objectives from across the whole curriculum.

At HeadStart, we realise that children may need more space to record their answers,

working out or explanations. It is recommended, therefore, that teachers use their

discretion as to where children complete their work.

Since a structured approach to problem solving supports learning, developing a

whole-school approach is highly recommended.


Throughout this book,6 children are solving problems.

Their names are:

Bisma

William

Asha

Max

Sufyan

Scarlett


Number and place value

NUMBER

These are all about

number and place value!

It may be appropriate for children to use exercise books or paper to record their answers, working out or explanations.

© Copyright HeadStart Primary Ltd 1 Name .............................................

The bingo caller shouts out the number 89.How would he write this in words on the bingo board?

Asha writes the number five hundred and twenty two in numerals.What does Asha write?

A television costs one thousand, two hundred and ninety nine pounds.How would you write this in numerals?

William types the number 10,756 into his calculator. How would he write this number in words in his maths book?

Scarlett writes the number fifty three thousand, six hundred and eleven in numerals. What does she write?

Bisma’s mum has twenty eight thousand, six hundred and sixty five pounds in her bank account.How much money does she have in numerals?

Asha works out that the answer to a maths calculation is two million, four hundred and fifteen thousand, three hundred and sixty one. She writes down the number 2,450,361. Is she correct? Explain your answer.

Mr Taylor wins £9,423,603 on the lottery. Write this figure in words.

NUMBER - Number and place value Year 6

Read and write numbers to at least 10,000,000

1

2

3

5

4

6

7

8


Number and place value

MASTERING

You’ll need your brain on full power to solve these!


© Copyright HeadStart Primary Ltd Name .............................................14

On Monday, Mrs Malik has £35 in her bank account.On Tuesday, she spends £17 on lunch, £6 on a book and £46 on clothes.

What is the balance of Mrs Malik bank account now?

Mrs Malik gets paid £550 on Friday. The bank will charge her £2.50 for each of the 2 days she is overdrawn. What will her bank balance be after she has been paid and the bank

charges have been paid?

William multiplied three different numbers together and got 1000.He said, “All of my numbers were larger than 10.”

Explain why this cannot be true.

Sufyan started counting down in 10s from 1000.Max started counting up in 100s from 100.They stop when Sufyan says a smaller number than Max.

What numbers are the boys saying when this happens for the first time?

Year 6MASTERING - Number and place value

1

2

3

a

b

Sufyan Max

£

£

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

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


Year 6MASTERING - Number and place value

2

−1 3 −2

−4

−2 5

-2 -4

-1

2 0

4

5

6

a

a

b

b °C

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

In a magic square, every row, column and diagonal adds up to the same number. Solve this magic square using positive and negative numbers.

At 4pm, the temperature in Birmingham was 4°C.At 3am, the temperature had dropped by 12°C.

At 4pm, the temperature in Moscow was −3°C.At 3am, it was 3°C colder.

Where was it colder at 3 am?

How many degrees colder?

Complete these addition number walls by putting the sum of two adjacent boxes in the box directly above them. One is done for you.

50°

40°

30°

20°

10°

0°

-10°

-20°


Addition, subtraction,multiplication and division

NUMBER

These are all about

addition, subtraction, multiplication and division



NUMBER - Addition, subtraction, multiplication and division Year 6

One section of a library had 23 shelves. There were 24 books on each shelf. How many books were on the shelves altogether?

There are 30 children in Year 6. Each child is given 27 house points. How many house points were given in total?

Carrots come in packs of 15. The chef buys 18 packs for his restaurant. How many carrots has he bought?

Max is making cupcakes. He bakes 125 trays of cakes. There are 24 cakes on each tray. How many cakes has he baked altogether?

Bisma's sister earns £185 each month from working in the café at the weekends. She saved this money for 38 months. How much money did she save in total?

Miss Khan is saving up for a new car. She saves £1125 a month. She saves up for 17 months. How much money has she saved in total?

A library has 1245 shelves with 45 books on each shelf. How many books are there altogether?

Multiply 6742 by 49 using a formal written method of multiplication.

Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

1

2

3

5

4

6

7

8


Addition, subtraction,multiplication and division

MASTERING

These are tough but

don’t let them beat you!


Max wanted to buy a computer game costing £74.95. He saved his pocket money for 12 weeks and had a total of £69.60.

How much more money did Max need to save in order to have enough money to buy the computer game?

Estimate how much Max saved each week to the nearest £1.

If Max saved the same weekly amount, calculate exactly how much he saved each week.

Asha needs to put a border of paper around a display board which measures 550 cm by 340 cm.

What length of paper does Asha need?

Asha has a roll of paper which is 20 m long. How much paper will be left over?

Mr Siddique bought a sofa for £950. He paid a 10% deposit and 5 monthly instalments of £150.

How much does Mr Siddique have left to pay?

Year 6MASTERING - Addition, subtraction, multiplication and division

1

2

3

a

a

b

b

c

£

£

£

£

cm

cm


Birmingham Bullring car park has 1015 spaces.

Edgbaston Street car park has 165 fewer spaces.

The total number of spaces in Birmingham Bullring car park, Edgbaston Street car park and Moor Street car park is 3060.

How many spaces in total are there in Edgbaston Street car park and Moor Street car park?

What is the difference between the capacity of the largest and smallest car park?

13 square tiles have a total area of 637 cm2. Calculate the length of one side of each tile.

Asha had 91 gymnastic stickers.William had 105 football stickers.

They arranged their stickers into their albums. They both put the same number of stickers on each page.

They both had only full pages when they had finished.They used all their stickers.

How many stickers did they put on each page?

Year 6MASTERING - Addition, subtraction, multiplication and division

4

5

6

a

b

cm


Fractions (including decimals and percentages)

NUMBER

These are all about

fractions, including decimals and percentages!



Year 6

Asha’s teacher asked her to simplify the fraction 68 . What common factor

could she use to do that?

Simplify 69 . What common factor did you use?

Write 1416 in its simplest form.

Mr Naveed writes down the fraction 1014 on the whiteboard. He asks his

class to write the fraction in its simplest form. What should their answer be?

Bisma’s and Max’s favourite dessert is apple pie. Bisma eats 46 of a pie and Max eats 1

3 . Who has eaten more? Explain how you worked out the answer.

Scarlett collects buttons. She has 36 altogether and 6 are blue. What fraction of Scarlett’s buttons are blue? Give your answer in its simplest form.

Bisma ran 13 of the track and Asha ran 16

24 of the track. Work out who ran further by simplifying one of the fractions. Explain your answer.

49 out of 84 packets of crisps in a box are plain. What fraction of the box are plain? Give your answer in its simplest form.

264 people out of 512 adults were women. What fraction of the total were men? Give your answer in its simplest form.

Use common factors to simplify fractions

NUMBER - Fractions (including decimals and percentages)

1

2

3

5

4

6

7

9

8


Fractions, decimalsand percentages

MASTERING

You’ll need all your

skills to solve these!



Max, William and Sufyan take a spelling test each week.Here are their results from two weeks.

Who has improved the most?

What percentage has his score increased by?

Max has £50.He buys a computer game, which is twice the price of the book he buys in the next shop.He spends half of what he has left on a CD leaving him with £10.

How much did each item cost?

Year 6MASTERING - Fractions, decimals and percentages

1

2

410

810

510

910

310

910

Max William Sufyan

Week 1

Week 2

%

computer game book

CD

a

b

£

£

£


In each number sentence, write different whole numbers less than 20 in the boxes so the number sentence is true.

Miss Morgan wants to buy a new car.It will use 15 less petrol than the one she has now.Miss Morgan's current car uses 17 less petrol than Mr Smith's car.Mr Smith's car costs £700 per year for petrol.What would the new car cost Miss Morgan for petrol per year?

Max and Asha were playing tennis.Asha drank 31

2 bottles of water.In total they drank 67

8 bottles of water.How many bottles did Max drink?

Year 6

1

32

7

4

48

35

=

=

=

=

MASTERING - Fractions, decimals and percentages

3

4

5

a

c

b

d

£


RATIO AND PROPORTION

These are all about ratio and proportion!



Year 6

Mrs Noble is cooking a meal. Chicken has to be cooked for 50 minutes for every 1 kg. How long does it take her to cook a 3 kg chicken?

To make three cakes, Max needs twelve eggs. How many eggs would Max need to make seven cakes?

To make two mosaic tiles, Scarlett needed 60 small blocks. How many blocks would she need to make ten mosaic tiles?

Bisma uses 3 oranges to make half a litre of tropical juice. How many litres can she make from 21 oranges?

Turkey must be cooked for 46 minutes for every 1 kg. For how long would a 31

2 kg turkey need to be cooked?

To make four pizzas, William needed 160 grams of tomatoes and 200 grams of cheese. How many grams of tomatoes and cheese would he need to make seven pizzas?

To make 3 jugs of juice, Mrs Hardy mixed 1.5 litres of water with 0.75 litres of fruit concentrate. How many litres of water and fruit concentrate, together would Mrs Hardy need to make 5 jugs of juice?

To make 2 pies, Asha needed 6 cooking apples, 90 g of sugar and 100 g of flour. How much of each ingredient would she need to make 10 pies?

Solve problems involving the relative size of quantities using division and multiplication

RATIO AND PROPORTION

1

2

3

5

4

6

7

8


Ratio and proportion

MASTERING

Use everything you have learnt to

solve these!



A recipe for a chocolate cake uses 260 g flour, 180 g sugar, 220 g butter,4 eggs, and 24 g cocoa powder.The recipe makes enough for 8 people.How much of each ingredient is needed to bake a cake for:

Mr Smith buys a pencil for every child in his class.There are 24 children in the class and the total cost of all the pencils is £30. Two more children join the class, so he buys two more pencils.How much did the two extra pencils cost?

Mrs Higgins wants to organise a trip to the adventure playground for the 24 children in her nursery class.While at the nursery, the ratio of adults to children is 1 : 6.When on a trip, the ratio must be 1 : 4.

How many additional adults must Mrs Higgins ask to come on the trip for the ratio to be correct?

Year 6MASTERING - Ratio and proportion

£

1

2

3

a

b

c

flour sugar butter eggs cocoapowder

4 people

6 people

10 people


Max has 32 Manchester United football stickers, 8 Everton football stickers and 12 Chelsea football stickers.He arranges them on a page as shown in the table.Complete the table to show three ways he could have arranged his stickers so they are in the same proportions.

The width : height ratio of my digital television screen in my lounge is16 : 9. I want to buy a new TV measuring 96 cm by 54 cm.Is this in the ratio of 16 : 9?

I am making peanut butter and jam sandwiches.The ratio of the peanut butter to the jam is 3 : 2.I use 6 teaspoons of jam.How many teaspoonfuls of peanut butter do I need?

The caretaker is making 2 shelves.The shelves are different lengths in the ratio 7 : 4.His piece of wood is 1.43 m long.The shorter shelf is 50 cm long.

Does he have enough wood for the longer shelf?

How much wood does he have left after making the shelf?

Year 6MASTERING - Ratio and proportion

Number of pages

Manchester United Everton Chelsea

1 32 8 12

4

3

Yes / No

Yes / No

cm

4

5

6

7

a

a

b

b


ALGEBRA

These are all about algebra!



Year 6ALGEBRA

The Year 6 teacher was asking some missing number questions. He said, “A number plus twenty seven equals eighty three. What is the missing number?” What should the answer have been? Show your working.

Next, the teacher wrote: n ÷ 3 = 9. He asked the class to find the value of n. What should their answer have been?

Mr Pile was fitting carpets in two different rooms, each with an area of 16 m2. The hallway’s length was 8 m. The study’s width was 4 m. Use the formula for area (length × width) to find the width of the hallway and the length of the study.

The coordinates of one end of a straight line (A) are (4, 3).Scarlett is told that the coordinates for the other end of the line are: x-axis = A + 3, y-axis = A + 0. What are the coordinates for the other end of the straight line?

Bisma was using this formula to find the missing angles in a triangle: A + B + C = 180°. She knew angle A was 50° and angle C was 85°. Use the formula to find angle B.

Next, Bisma was finding angles in a quadrilateral. She knew that the sum of all four angles was 360°. Write a formula to find the angles of a quadrilateral. Use the formula to find out the missing angle in a quadrilateral where one angle is 95°, one is 110° and one is 70°.

Solve problems involving finding missing numbers using simple formulae

1

2

3

5

4

6


Algebra

MASTERING

Put your powers of

reasoning to the test with

these!


Name .............................................© Copyright HeadStart Primary Ltd 129

Sufyan measured the perimeter of the playground. He forgot the measurements of the length and the width, but he knew the perimeter was 60 m. When he looked at the plan he had drawn, he saw that he had labelled the width as x and the length as 2x.

Complete the equation below to find the perimeter (P).

Now find the actual dimensions of the playground.

Max went ten-pin bowling. On his first go he knocked down x pins. On his second go he knocked down y pins. Max knocked down all ten pins with his two goes. Write an equation to show how many pins Max knocked down.

Substitute numbers to show how Max might have knocked down the pins. How many solutions can you find?

Year 6MASTERING - Algebra

P = 2 ( + )

length m width m

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

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

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

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

2x

x

1

2

a

a

b

b


William has £5. He spends xp in one shop and yp in another shop. Each time he uses only one silver coin. He has £z left. Write an equation to show how much money William has left.

How much money might William have left?

Asha has three identical bags each with x apples in.She takes an apple out of the first bag.She now has (x – 1) apples in bag 1.Max takes two apples out of bag 2.

Write an expression to show how many apples there are left in bag 2.

Bisma gives Asha 4 apples which she puts into bag 3. Write an expression to show how many apples there are in bag 3.

Asha knows that she had 12 apples altogether to start with. How many apples does she have in each bag now?

Year 6MASTERING - Algebra

bag 1 = bag 2 = bag 3 =

£

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

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

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

3

4

a

a

b

b

c

x x x


MEASUREMENT

These are all about

measurement!



Year 6MEASUREMENT

Max travelled 36.45 km by car, 1000 m on foot and 7.8 km by bus. How far did he travel in kilometres?

Sufyan cut 35 cm from 6.5 m of rope. How many centimetres of rope were left?

Asha had 4 pieces of ribbon, each measuring 64 cm. How many metres of ribbon did she have altogether?

William had a 1 litre bottle of squash. He drank 0.625 litres. How much squash was left? Give your answer in millilitres.

564 ml of water was in the fish tank. Another 2978 ml were added. How much water was in the fish tank now? Give your answer in litres.

A bowl of soup in Hawthorne Café contains 255 ml. How many litres of soup will be needed for 9 bowls of soup?

Some children made 5500 g of biscuits for the school fair. They divided them up into bags with 0.5 kg in each bag. How many bags of biscuits were there altogether?

Four children tried to share 1.636 kg of sugar to make some cakes. How many grams did they get each?

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

1

2

3

5

4

6

7

8


Measurement

MASTERING

Some of these are

hard! Ask for help if you need it.


161© Copyright HeadStart Primary Ltd Name .............................................161

A hedgehog is walking across a road which is 6.48 m wide. The hedgehog still has 125 cm left to walk to get to the other side of

the road. How far has the hedgehog walked already?

The hedgehog takes 6 minutes to walk 1 metre. How long will it take the hedgehog to walk 125 cm?

Calculate the area of the shaded section of this diagram.

Remember: the area of a rectangle = length × width

the area of a triangle = length × width

Year 6MASTERING - Measurement

not to scale

18 cm

5 cm

4 cm

2

1 a

b

2

minutes

m

cm2

171© Copyright HeadStart Primary Ltd Name .............................................

Year 6 go to Walton Towers for a trip.

To go on the rides, you must be over 1.4 m tall.Max knows that he is 5 feet tall.

1 foot is approximately equal to 30 cm. Is Max tall enough to go on the rides?

Explain your answer.

Year 6MASTERING - Measurement

23

Yes / No

171

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

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

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

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


GEOMETRYProperties of shapes / Position and direction

These are all about geometry!



GEOMETRY - Properties of shapes / Position and direction Year 6

Asha's lawn was oblong-shaped. The length was 5.4 metres and the width was 2.7 metres. What was the distance all the way around?

Bisma lived next door to Asha. Her garden was shaped like a regular pentagon. Each side measured 4.2 metres. What was the distance all the way round?

Scarlett's lawn was rhombus-shaped. One side measured 5.4 metres. What was the distance all the way round?

What is the size of Angle A in an equilateral triangle?

One side of a regular trapezium measures 14 cm. The opposite parallel side measures 22 cm. A third side measures 6.5 cm. What is the length of the fourth side?

Max was making a regular heptagon with string. Each side measured 2 cm. How much string would he need?

What is the total number of degrees in the interior angles of a square, an oblong and a triangle?

Asha's teacher asked her to explain the similarity and difference between a regular and an irregular octagon. What should she have said? Explain your answer using side and angle properties.

Solve problems involving 2D shapes using dimensions and angles

1

2

3

5

4

6

7

8


Geometry

MASTERING

Turn your brain power up to full to help you with

these!



Max builds a cuboid with a volume of 36 cm3.None of the edges is less than 2 cm.What could the dimensions of the cuboid be?

William draws an isosceles triangle with one angle of 26°. What are the sizes of the other two angles?

Is there a different solution?

Asha draws a square. She draws the diagonals and realises that they cross at right angles. She says, "The diagonals of all quadrilaterals are always perpendicular."

Is Asha correct?

Explain your answer. You can draw one or more quadrilaterals to help you. (Use your book or some paper.)

Asha also notices that the diagonals bisect each other.

Use your diagrams from to decide which other quadrilaterals have diagonals that bisect each other.

Year 6

a

MASTERING - Geometry

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

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

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

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

1

a

b

2

3

cmlength =

Angle A =

Angle A =

cmwidth =

cmheight =

26°

26°

Yes / No

Angle B =°

Angle B =°

Angle C =°

Angle C =°


Look at this diagram of two equilateral triangles and two right-angled triangles drawn inside an equilateral triangle.Label all the angles that you can see.

Here are two vertices of an isosceles triangle drawn on a coordinate grid.Where could the other vertex be?

Year 6

xaxis

y axis

MASTERING - Geometry

8

7

6

5

4

3

2

1

0

-1

-2

-3

-4

-5

-6

-7

-8

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

× ×

E

FDG H

IJ KBA

LC

A °

B °

C °

G °

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I °

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F °

J 90°

K °

L °

4

1

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2

2

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STATISTICS

These are all about statistics!



STATISTICS Year 6

Interpret pie charts and use these to solve problems

Look at the favourite subjects of the pupils in Asha's class and answer the questions below.

What percentage of the class like PE lessons best?

What fraction is this?

What fraction of the class like English best?

What percentage of the class like English best?

What percentage of the class did not choose Maths as their favourite subject?

What fraction is this?

If there were 32 children in the class, how many children liked PE best?

If there were 29 children in Asha's class, could this chart represent the class? Explain your answer.

a

a

a

b

b

b

1

2

3

4

5

English

Maths135o

45o

180oPE


Statistics

MASTERING

Don’t give up on these. They are

hard but you can do it!


Name .............................................

This pie chart shows the flavours of crisps chosen by children in Year 6.

Which flavour of crisps was most popular? How do you know?

What fraction of the children chose:

There are 64 children in Year 6. Work out the number of children who chose each flavour of crisps.

Year 6MASTERING - Statistics

© Copyright HeadStart Primary Ltd 201

i)

ii)

iii)

iv)

i)

ii)

iii)

iv)

salt andvinegar

cheeseand

onion

prawn

plain

salt and vinegar

prawn

cheese and onion

plain

salt and vinegar

prawn

cheese and onion

plain

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

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

1

a

b

c

Name .............................................

This pie chart shows the flavours of crisps chosen by children in Year 5.

Bisma says, "The same number of children chose salt and vinegar crisps in Year 5 and Year 6." Explain why Bisma may not be correct.

What size of angle is at the sector that shows prawn crisps? How do you know?

12 children chose plain crisps. Work out the number of children who chose each flavour of crisps.

Year 6MASTERING - Statistics

© Copyright HeadStart Primary Ltd 202

i)

ii)

iii)

iv)

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

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

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

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

60°

salt and vinegar

prawn

cheese and onion

plain 12

salt andvinegar

cheeseand

onion

praw

n

plain

2

a

b

c


Cake Sale

INVESTIGATION

Use everything you have learnt in Year 6 to solve these.Good luck!


210© Copyright HeadStart Primary Ltd Name .............................................

1

2

3

Year 6 are holding a cake sale for their parents to raise money for the Year 6 adventure holiday. First, they ask their friends what cakes they would like to have at the sale so they know which cakes to make. Here are the results:

Complete the table by filling in the frequency column.

Year 6 draw a pie chart to show the results.

Complete the table above by calculating the number of degrees for each sector on the pie chart.

Use a protractor to construct a pie chart to show this information.

Year 6INVESTIGATION - Cake Sale

Type of cake Tally Frequency Degrees

chocolate

Victoria sponge

carrot

coffee

lemon drizzle

Total

A pie chart to show the cakes for the Year 6 Cake Sale


11

12

13

14

This travel graph shows the girls’ journey to and from the supermarket.

How far is the journey to the supermarket?

How long does it take the girls to travel to the supermarket?

At what speed do the girls cycle to the supermarket?

At 3 pm, Asha's mum collects the girls and takes them to another shop to buy new cake tins. The journey takes 15 minutes and the shop is 5 km from Asha's house. They spend 15 minutes in the shop and then drive straight home, arriving at a quarter to 4.

Complete the travel graph to show this information.

Year 6INVESTIGATION - Cake Sale

6 km

5 km

4 km

3 km

2 km

1 km

013:45 14:00 14:15 14:30 14:45 15:00 15:15 15:30 15:45

time

dist

ance

from

Ash

a's

hous

e

y

x

km

minutes

km per hour


Max's mum buys a whole cake. She cuts the cake up like this:

Complete the labels, choosing words from the box.

Fill in the sizes of the missing angles.

Year 6

b

a

INVESTIGATION - Cake Sale

A = B =° °

circumference

radius

diameter

12

3

115°

BA

39

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Primary

Primary

covers all National Curriculum objectives

incorporates built-in differentiation

includes ‘Mastering’ sections to provide additional challenge

features a multi-objective, extended investigation

HSP-113-KW

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eadStart Prim

ary

Problem Solving, Reasoning & Investigating

6Year

MATHEMATICS CURRICULUM

problem solving, reasoning & investigating · page 124 solve problems with linear number...

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