6 6 6 6 Homework Pack 6 Written by teachers for teachers to support the renewed Primary Framework, Collins New Primary Maths is a whole-school numeracy programme that builds and develops all the key skills needed to be successful in mathematics. Homework activities allow practice of the objectives covered in the daily lessons. Browse the complete Collins Education catalogue at www.collinseducation.com ISBN 978-0-00-722048-9 9 780007 220489 Homework Pack 6 Homework Pack 6 Peter Clarke Series Editor Peter Clarke Series Editor Linked to the daily lesson plans An average of one activity every two weeks Differentiated activities Target individual learning needs with activities structured at three levels Clear instructions Support children beyond the classroom with clear and stimulating activities HOMEWORK_PACK_6 27/7/07 15:54 Page 1
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Homework Pack 6Written by teachers for teachers to support the renewedPrimary Framework, Collins New Primary Mathsis a whole-school numeracy programme that buildsand develops all the key skills needed to be successful in mathematics. Homework activities allow practice of the objectives covered in the daily lessons.
Browse the complete CollinsEducation catalogue atwww.collinseducation.com
ISBN 978-0-00-722048-9
9 780007 220489
HomeworkPack 6HomeworkPack 6
Peter ClarkeSeries Editor
Peter ClarkeSeries Editor
Linked to the dailylesson plans An average of one activityevery two weeks
Differentiated activitiesTarget individual learningneeds with activitiesstructured at three levels
Clear instructionsSupport children beyondthe classroom with clearand stimulating activities
HOMEWORK_PACK_6 27/7/07 15:54 Page 1
Homework Pack 6
Series Editor: Peter Clarke
Authors: Jeanette Mumford, Sandra Roberts, Andrew Edmondson
7220489_CNPM_HCM_6_[01-06] 6/7/07 11:13 Page 1
Published by CollinsAn imprint of HarperCollinsPublishers 77 – 85 Fulham Palace RoadHammersmithLondon W6 8JB
The authors assert their moral rights to be identified as the authors of this work
Any educational institution that has purchased one copy of this publicationmay make unlimited duplicate copies for use exclusively within thatinstitution. Permission does not extend to reproduction, storage within aretrieval system, or transmittal in any form or by any means, electronic,mechanical, photocopying, recording or otherwise, of duplicate copies forloaning, renting or selling to any other institution without the permission ofthe Publisher.
British Library Cataloguing in Publication DataA Catalogue record for this publication is available from the British Library
Cover design by Laing&CarrollCover artwork by Jonatronix LtdInternal design by Steve Evans and Mark Walker DesignIllustrations by Steve Evans and Mark Walker Edited by Jean RusteanProofread by Ros Davies
Printed and bound by Martins
Browse the complete Collins catalogue atwww.collinseducation.com
William Collins’ dream of knowledge for all began with the publication of his first book in 1819.A self-educated mill worker, he not only enriched millions of lives, but also founded aflourishing publishing house. Today, staying true to this spirit, Collins books are packed withinspiration, innovation and practical expertise. They place you at the centre of a world ofpossibility and give you exactly what you need to explore it.
Collins. Freedom to teach.
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ContentsUnit A1HCM 1 Differences
Find the difference between a positive and a negative number
HCM 2 Making decimals Order decimals to two places
HCM 3 Revising multiplication and division Use known number facts for mental multiplication and division involving decimals
HCM 4 More brackets Use multiplication and division facts and brackets to solve number calculations
Unit B1HCM 5 Find the calculation
Use place value and multiplication and division facts to work out other facts involving decimals
HCM 6 Square numbersRecognise squares of numbers to 12 x 12
HCM 7 Puzzling triangular numbersDescribe and explain sequences, patterns and relationships
HCM 8 Counting patterns Recognise and extend number sequences
HCM 9 Constructing kitesUse mathematical vocabulary to describe the features of a 2-D shape
HCM 10 Investigating midpointsMake and draw shapes accurately; Describe and explain relationships
Unit C1HCM 11 All square measuring
Read and interpret scales accurately
HCM 12 DIY ranges and modesFind the mode and range
HCM 13 Documentary bar chartRepresent data in different ways and understand its meaning
HCM 14 Time for homework Find the mode and range; Represent data in different ways and understand its meaning
Unit D1HCM 15 Rocky Mountain motoring
Measure and calculate using imperial units (miles and kilometres)
HCM 16 Finding perimetersCalculate the perimeter of simple compound shapes that can be split into rectangles
HCM 17 Area workoutCalculate the area of a shape formed from rectangles
HCM 18 Making calculationsUse efficient written methods to add whole numbers and decimal numbers
3
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Unit E1HCM 19 Colouring fractions
Understand improper fractions and mixed numbers
HCM 20 Sharing pizzasRelate fractions to division
HCM 21 Percentages at homeUnderstand percentages as the number of parts in every 100
HCM 22 Decimal subtraction Use efficient written methods to subtract decimals
HCM 23 Multiplication methodsApproximate first. Use efficient written methods to multiply whole numbers
HCM 24 Design a snowman Solve a problem and check that the answer is correct
Unit A2HCM 25 Decimals decimals
Order decimal numbers with up to three places
HCM 26 Money problemsSolve multi-step problems
HCM 27 Multiplying mentallyMultiply mentally with whole numbers and decimals
HCM 28 Family holidayChoose and use appropriate strategies to solve problems
Unit B2HCM 29 Multiplication and division facts
Use table facts to work out related facts
HCM 30 Tests of divisibility (1)Know and apply simple tests of divisibility
HCM 31 Using square numbersKnow square numbers to 12 x 12
HCM 32 Prime numbers Recognise prime numbers less than 100
HCM 33 Co-ordinates of reflectionsRecognise where a shape will be after reflection
Write two numbers with a difference of 6 in each box.At least one of the numbers must be a negative number.
Write two numbers with a difference of 13 in each box.At least one of the numbers must be a negative number.
Look at the pairs of numbers you wrote with a difference of 13. On the back of thissheet, write a calculation for each of your differences, e.g. –3, 10 → –3 + 13 = 10.
• Find the difference between a positive and negative number
Decimals to two places In order Smallest Numbers in between
Largest
0 9 2 4 7
Use the digits on the cards to make decimal numbers to one decimal place.When you have made your numbers, put them in order starting with the smallest.
Use the digits on the cards to make numbers to two decimal places.When youhave made your numbers, put them in order, smallest to largest. In the thirdcolumn, write a number that comes between each of your numbers.
• Order decimals to two places
Making decimalsName _________________________Date ____________
1 Compare his range of times with Sara.2 Make a tally chart for the data.3 Draw a bar chart for the data.4 Who do you think did their homework quicker overall? Explain using the bar charts.
Sara and Bradley recorded their first five homework times for the Spring term.
Sara 32 28 51 16 24Bradley 29 17 34 20 48
Does this extra data affect any of your answers to the above questions? Do not drawnew bar charts.
Time (minutes) Tally Total10–1920–29
876543210
910 Sara’s homework times
Piec
es o
f hom
ewor
k
10–190–9 20–29 30–39 40–49 50–59
You need:
� squared paper
7220489_CNPM_HCM_6_[07-45] 6/7/07 11:16 Page 14
• Measure and calculate using imperial units (miles and kilometres)
In Canada, distances between destinations are given in both miles and kilometres.
1 Find these distances in kilometres.Distance by road from Banff. 5 miles ≈ 8 kilometres
2 Find these distances in miles.Distance by road from Golden. 8 kilometres ≈ 5 miles
You are staying at Lake Louise.Work out the distance, in miles and kilometres for this round trip. Use the back of thissheet for all your working.Lake Louise to Castle Mountain Junction Answer
to Radium Hot Springsto Goldenback to Lake Louise
Town miles × 8 ÷ 5 kilometres
Canmore 20 160 32 32
Calgary 85
Lake Louise 35
Radium Hot Springs 90
miles kilometres
Town kilometres ÷ 8 × 5 miles
Lake Louise 80
Radium Hot Springs 104
Castle Mountain 110
Banff 136
Y6 D1 L3HCM 15
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• Calculate the perimeter of simple compound shapes that can be split into rectangles
Finding perimeters
1 Find the perimeter of these shapes.
a P =
b P =
c P =
d P =
2 Write what you notice.
1 Work out the perimeter outlines of these shapes.
2 Record your results in a table.
3 Look for a pattern and complete the table.
1 Write a formula for the perimeter. P =
2 Use the formula to find the perimeter outline for these shapes:
Colour in the shapes. Describe each coloured fraction asan improper fraction and a mixed number.
Y6 E1 L2HCM 19
You need:
� colouringmaterials
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• Relate fractions to division
Sharing pizzas
1 How much pizza would each person get if:
a there were 8 friends?b there were 10 friends?c there were 6 friends?d there were 12 friends?
2 Now write all of your answers as a different but equivalent fraction.
Make up a story about friends eating pizzas together and fractions.There are 4 pizzas and 6 friends but everyone must end up eating a different amount of the pizzas.Write your story on the back of this sheet.
How much pizza would each person get if:a there were 6 friends?b there were 4 friends?c there were 5 friends?d there were 10 friends?
Use these digits to make 6 calculations to work out.Make the numbers to two decimal places.
Then complete each calculation. 7 4 3 1 2 8
9 7 6 4 3 01
1–
2–
3–
4–
5–
6–
1–
2–
3–
5–
6–
Example
–
3 1 4·72
48·31
Example
–
76· 1 39
40·7
Use these digits to make 6 calculations to work out.Make the numbers in each calculation with a differentnumber of decimal places.Then complete each calculation.
4–
Y6 E1 L10HCM 22
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• Approximate first. Use efficient written methods tomultiply whole numbers
Multiplication methods
For calculations c to h above, use the compact method to work out the answer.
Use the digit cards to make 10 decimal numbers to two places, then write thedecimal number that comes next.
Use the digit cards to make 10 decimal numbers to three places, then write thedecimal number that comes next.
Use the digit cards to make 10 decimal numbers to three places and with the same whole number.Write your numbers on the back of this sheet from largest to smallest.
What is the largest decimal number you have made?
What is the smallest decimal number you have made?
Sort the numbers into the correctboxes. Some numbers belong in morethan 1 box.
A number is divisible by:2 if it is an even number and it ends in 0, 2, 4, 6 or 83 if the sum of its digits is divisible by 34 if the tens and units digits divide exactly by 45 if it ends in 0 or 56 if it is even and it is also divisible by 38 if half of it is divisible by 4 or if its last three digits
are divisible by 89 if the sum of its digits are divisible by 9
10 if it ends in 0
176 368 496 1244
180 272 465 3000
1625
Divisible by 2 Divisible by 5
954 2100 3060 324
756 486 450 990
430
Divisible by 9 Divisible by 10
2634 1032 1422 4348
392 256 21641071
1830 720
Divisible by 3 Divisible by 4
4152 1336 1460 1072
600 780 3224 2368
2952
Divisible by 4 Divisible by 8
192 720 385 1584
3675 528 1056 4290
265 2688
Divisible by 5 Divisible by 8Divisible by 6
4692 468 1602 1152
324 37261161 392
5994 3273
2316
Divisible by 3 Divisible by 9Divisible by 6
Y6 B2 L5HCM 30
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• Know square numbers to 12 x 12
Using square numbers
Write the missing numbers in the grid.
Do not write in the shaded boxes.
1 Work out the missing numbers to complete the equations.Use the grid to help you.
a 2 + 2 = 40 b 2 + 2 = 90 c 2 + 2 = 113
d 2 + 2 = 29 e 2 + 2 = 106 f 2 + 2 = 73
2 Sanjay listed the squares of 1, 11 and 111.He noticed a pattern.
2 Write the initial letter on the number line to show the position of these mammals.E – elephant: 7 t G – giraffe: 2 t H – horse: 1.25 t KW – killer whale: 9 t
In Nonograms Supermarket all the stock lines are orderedin multiples of 9.
1 Use your calculator to complete lines 1 to 3 in each pattern.
2 Predict and enter the answers to the 4th and 5th lines.Then check with your calculator.
a 5 g × 9 = b (1 kg + 2 kg) × 9 =
5 g × 99 = (12 kg + 3 kg) × 9 =
5 g × 999 = (123 kg + 4 kg) × 9 =
= =
= =
a 9 t × 9 = 81 t b 12kg × 99 =
98 t × 9 = 23kg × 99 =
987 t × 9 = 34kg × 99 =
= =
= =
c 1 t ÷ 9 = 111.111kg d 9g × 9 =
2 t ÷ 9 = 99g × 99 =
3 t ÷ 9 = 999g × 999 =
= =
= =
You need:
� calculator
Example9 g × 6 = 54 g9 g × 66 = 594 g9 g × 666 = 5994 g9 g × 6666 = 59 994 g9 g × 66 666= 599 994 g
Y6 D2 L2HCM 39
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• Use co-ordinates and translate shapes on grids
Two-step translations
1 a Translate shape A 3 to the right, then 1 up to make shape B.
b List the co-ordinates of shape B.(4, 2) ( , ) ( , )
2 a Translate shape C 3 to the left, then 1 down to make shape D.b List the co-ordinates of shape D.
( , ) ( , ) ( , )
1 Translate the shape 1 unit to the right, then 3 units down.
2 Repeat the translation.
3 Using the same rule, (1r,3d) begin a translation ofthe same shape with its topleft vertex at (4, 10).Continue to fill the gridand highlight the pattern in colour.
You make a mystic rose by joining the points which are equally spaced around the circle.
The 6 point mystic rose has 15 lines altogether.Use a ruler to join each dot to every other dot forthis 16 point mystic rose.The 15 lines from point 1are already drawn. Begin at point 2 and completethe design.
Work out how many lines there are altogether in a 16 point mystic rose.
Use the digits to make 9 numbers with one or two decimal places.Thenorder the numbers, starting with the smallest.
Use the digits to make 14 numbers with one, two or three decimal places.Then orderthe numbers, starting with the smallest.
2 . 32 . 4 32 .
2 .
2 .
2 .
2 .
2 .
2 .
a 1, 3, 4 In order
smallest
largest
smallest
largest
smallest
largest
smallest
largest
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
0 .
a 3, 4, 5 In order
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
b 9, 8, 2 In order
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
6 .
b 5, 7, 2 In order
Y6 A3 L2HCM 49
7220489_CNPM_HCM_6_[46-72] 6/7/07 11:18 Page 49
Use these digits to make 6 calculations to work out.Make the numbers in each calculation to a differentnumber of decimal places.Then complete each calculation.
Use these digits to make 6 calculations to work out.You can use each digit more than once.Make the numbers to two decimal places.Then complete each calculation.
8 6 2
4 3 7
5 7 3
1 6 9
1+
2+
3+
4+
5+
6+
1+
2+
3+
4+
5+
6+
Example5 . 7 6 3
6 7 . 3 1 9+
Find the smallest and largest decimal with three places you can make using all thedigit cards in the section in each number.What is the total? What is the difference? Show your working out on the back of this sheet.
Example
+8 6 . 2 43 8 . 4 7
Y6 A3 L4HCM 50
7220489_CNPM_HCM_6_[46-72] 6/7/07 11:18 Page 50
• Approximate first. Use efficient written methods todivide whole numbers
The flagstones on the floor of anancient castle are marked with a spiralof numbers. Agent P must find the saferoute to the flagstone marked 1 torecover the microfilm.
The numbers show the days of holiday some people took last year.
1 Record the data in the tally and frequency columns on this table.Which do you think will be the most popular class?
2 a How many people took fewer than 20 days of holiday?b How many people took more than 29 days of holiday?c How many people took from 10 to 29 days of holiday?
1 Calculate the total frequency and write it in the table.
2 Convert the frequencies to percentages. Use your calculator.
3 Complete this percentage bar chart.
4 Was your prediction in Q1 correct?
On the back of this sheet calculate the mean, median, mode and range of the data in .
14 25 7 33 43 2111 6 14 18 38 2835 30 21 48 42
35 49 18 28 14 4235 26 28 21 40 287 30 42 42
35 36 28 14 18 3521 12 28 30 3819 28 42 49 9 42
Days Tally Frequency Percentage
0 –910 –1920 –2930 –3940 – 49
Total
Y6 C3 L9HCM 62
30
20
10
0
Perc
enta
ge (
%)
0 –9 10 –19Days of holiday
You need:
� ruler
7220489_CNPM_HCM_6_[46-72] 6/7/07 11:19 Page 62
• Know imperial units (gallons)• Know rough equivalents of litres and gallons
Litres and gallons
1 Complete the conversion scale for litres and gallons.
2 Find the tank capacity in litres, to the nearest litre, for each aquarium in the pet shop.
a 5·5 gallons b 3·3 gallons c 6·6 gallons
l l l
d 7·9 gallons e 8·6 gallons f 4·6 gallons
l l l
Pete, the pet shop owner, changes 25% of the water ineach tank once a week. Find how many litres of water hechanges for each tank in question 2, above.
You can work out the area of a shape made on a pinboard in 2 ways:
Find the area in square centimetres of these shapes.
area = cm2 area = cm2 area = cm2 area = cm2
area = cm2 area = cm2 area = cm2 area = cm2
area = cm2 area = cm2 area = cm2 area = cm2
Work out the area of the shapes in a and b below.Draw shapes with the areas given in c and d.
area = cm2 area = cm2 area = 2.5 cm2 area = 3.5 cm2
1 The sumof smallershapes
2 What youhave leftwhen you cutpieces off alarger shape
a b c d
Y6 D3 L4HCM 64
You need:
� ruler
7220489_CNPM_HCM_6_[46-72] 6/7/07 11:19 Page 64
• Find the surface area of a cuboid
Finding surface areas
A farmer fences off a rectangular field for his pigs and poultry. He leaves the restof the field for his sheep. Find the area of ground in square metres for:
a pigs Area = m2
b poultry Area = m2
c sheep Area = m2
A B C D
1 Work out the surface area of each cuboid. Record your answers in the table.
2 Find a pattern and use it to find the surface area of the next two cuboids, Eand F, in the sequence.
3 A cuboid in the sequence has a length of side of 10 centicubes.
Fill in the third number in each triangle.The three numbers go together to make an addition and subtraction fact. No number will be more than 20.
Write the two facts underneath.
Using the digits 1–9, make up 3 addition calculations and 3subtraction calculations. You can include decimal numbers.Each digit must be used in each calculation. Use the back ofthis sheet if you need more space.
What is the smallest answer you can get? What is the largest answer you can get?Show your working on the back of this sheet.
The ratio of the distance across a circle to the distancearound the edge of it is approximately 1 to 3.Find out if this statement is true by measuring 10 circularitems in your home.
You need:
� tape measure orstring / wool
� ruler
Object Distance Distance Ratioacross circle around circle
Y6 E3 L9HCM 70
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• Choose and use appropriate number operations tosolve word problems involving money
Do your working on the back of this sheet if you need more room.
a Buy 3 squash rackets and1 pair of ice skates.What is the total cost?
b Buy 2 snowboards. Howmuch change do youreceive from £200?
c The Rugby Club buy 12rugby balls. How much istheir bill?
d Top of the range snowskis cost 3 times morethan the pair shown here.How much do they cost?
c During the sale, there is a free footballfor every snowboard sold.The shop sells24 snowboards. How much money ismade altogether?
d The local sports club buys 7 rugbyballs, 12 footballs and 23 squashrackets. How much change is therefrom £1000?
a The ski-hire shop needs new equipment.The owner buys 8 snowboards, 9 pairsof skis and 15 pairs of ice skates.What is the total cost of the purchases?
b The sports store has 45 squashrackets to sell.The owner paidabout £1000 to the factory for therackets. How much profit will theymake if all rackets are sold?