CAMBRIDGE PRIMARY
Mathematics Name:
Skills Builder
4
Contents Numbers ..................................................... 4–11
2D and 3D shapes ................................... 49–53
Addition and subtraction (1) .................. 12–15
Area and perimeter ................................. 54–55
Multiplication and division (1) ................ 16–23
Special numbers ...................................... 56–58
Length, mass and capacity..................... 24–25
Fractions, decimals and division ............. 59–62
Time ........................................................... 26–27
Ratio and proportion ............................... 63–64
Organising, representing and interpreting data ...................................... 28–31
Using calendars and timetables ............. 65–67
Decimal numbers in context ................... 32–33 Number sequences ................................. 34–35 Addition and subtraction (2) .................. 36–39 Multiplication and division (2) ................ 40–43 Angles, position and direction................. 44–45 Symmetry .................................................. 46–48
Mary Wood
Graphs, tables and charts ....................... 68–69 Venn and Carroll diagrams ..................... 70–71 Fact files .................................................... 72–75 Photocopiable resources ......................... 76–82 Answers ..................................................... 83–88
University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 4843/24, 2nd Floor, Ansari Road, Daryaganj, Delhi – 110002, India 79 Anson Road, #06–04/06, Singapore 079906 Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: education.cambridge.org/9781316509166 © Cambridge University Press 2016 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2016 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 Printed in Spain by GraphyCems A catalogue record for this publication is available from the British Library isbn 978-1-316-50916-6 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
notice to teachers It is illegal to reproduce any part of this work in material form (including photocopying and electronic storage) except under the following circumstances: (i) where you are abiding by a licence granted to your school or institution by the Copyright Licensing Agency; (ii) where no such licence exists, or where you wish to exceed the terms of a license, and you have gained the written permission of Cambridge University Press; (iii) where you are allowed to reproduce without permission under the provisions of Chapter 3 of the Copyright, Designs and Patents Act 1988, which covers, for example, the reproduction of short passages within certain types of educational anthology and reproduction for the purposes of setting examination questions. notice to teachers in the uk The photocopy masters in this publication may be photocopied or distributed (electronically) free of charge for classroom use within the school or institution that purchased the publication. Worksheets and copies of them remain in the copyright of Cambridge University Press, and such copies may not be distributed or used in any way outside the purchasing institution.
This book is part of the Cambridge Primary Maths project. This is an innovative combination of curriculum and resources designed to support teachers and learners to succeed in primary mathematics through best-practice international maths teaching and a problem-solving approach. To get involved, visit www.cie.org.uk/cambridgeprimarymaths.
Introduction This Skills Builder activity book is part of a series of 12 write-in activity books for primary mathematics grades 1–6. It can be used as a standalone book, but the content also complements Cambridge Primary Maths. Learners progress at different rates, so this series provides a Skills Builder and a Challenge Activity Book for each Primary Mathematics Curriculum Framework Stage to support and broaden the depth of learning. The Skills Builder books consolidate the learning already covered in the classroom, but provide extra support by giving short reminders of key information, topic vocabulary and hints on how best to develop maths skills and knowledge. They have also been written to support learners whose first language is not English.
How to use the books The activities are for use by learners in school or at home, with adult support. Topics have been carefully chosen to focus on those common areas where learners might need extra support. The approach is linked directly to Cambridge Primary Maths, but teachers and parents can pick and choose which activities to cover, or go through the books in sequence. The varied set of activities grow in challenge through each unit, including: • closed questions with answers, so progress can be checked • questions with more than one possible answer
• Fact files are provided for two-dimensional shapes and handling data. When appropriate, diagrams are provided to aid understanding. Learners should be encouraged to use these pages to check meanings and spelling. • Hints prompt and assist in building understanding, and steer the learner in the right direction. • You will need gives learners, teachers and parents a list of resources for each activity. • Photocopiable resources are provided at the end of the book, for easy assembly in class or at home. • Links to the Cambridge International Examinations Primary Mathematics Curriculum Framework objectives and the corresponding Cambridge Primary Mathematics Teacher’s Resource are given in the footnote on every page. • Calculators should be used to help learners understand numbers and the number system, including place value and properties of numbers. However, the calculator is not promoted as a calculation tool before Stage 5. Note: When a ‘spinner’ is included, put a paperclip flat on the page so the end is over the centre of the spinner. Place the pencil point in the centre of the spinner, through the paperclip. Hold the pencil firmly and spin the paperclip to generate a result.
• activities requiring resources, for example, dice, spinners or digit cards • activities and games best done with someone else, for example, in class or at home, which give the opportunity to be fully involved in the child’s learning • activities to support different learning styles: working individually, in pairs, in groups.
1
2
5
3 4
How to approach the activities
Tracking progress
Space is provided for learners to write their answers in the book. Some activities might need further practice or writing, so students could be given a blank notebook at the start of the year to use alongside the book. Each activity follows a standard structure.
Answers to closed questions are given at the back of the book; these allow teachers, parents and learners to check their work.
• Remember gives an overview of key learning points. They introduce core concepts and, later, can be used as a revision guide. These sections should be read with an adult who can check that the learner understands the material before attempting the activities. • Vocabulary assists with difficult mathematical terms, particularly when English is not the learner’s first language. Learners should read through the key vocabulary. Where necessary, they should be encouraged to clarify their understanding by using a mathematical dictionary or by seeking adult help.
When completing each activity, teachers and parents are advised to encourage self-assessment by asking the students how straightforward they found the activity. When learners are reflecting on games, they should consider how challenging the mathematics was, not who won. Learners could use a 3/ ✗ or red/ green colouring system to record their self-assessment for each activity. These assessments provide teachers and parents with an understanding of how best to support individual learners’ next steps.
Reading, writing and partitioning numbers Vocabulary thousand,
Remember Whole numbers from 1000 to 9999 have four digits. The position of a digit in a number gives its value. Th 9 9
H 8
T 4
U 3
ten thousand, digit, partition, place value
Read as nine thousand, eight hundred and forty-three
0
0
0
8
0
0
combine
4
0
partition
9
8
4
3
3 9843 = 9000 + 800 + 40 + 3 The number that is one more than 9999 is 10 000 (ten thousand).
1
Missing numbers
Hint: These numbers are written
in expanded form, in thousands, hundreds, tens and units.
Write the missing numbers. +2
6742 = 6000 + 700 + 6359 =
+
5419 = 5000 +
4
+ +
+ +
3278 =
+
+
+
1234 =
+
+
+4
3507 =
+
+
+
Unit 1A: Number and problem solving CPM framework 4Nn1, 4Nn3; Teacher’s Resource 1.1
2
Think of a number
Marina is thinking of a four-digit number. She says: ‘It has a 2 in the hundreds place and in the units place.’ ‘It has a 5 in the thousands place and in the tens place.’ What is Marina’s number? Hint: It may help if you label
the columns Th 3
H
T
U.
Cross-number puzzle
Complete the cross-number puzzle. Then make a puzzle for someone else to try. 1
2
3
4
5
6
7
8
Across
Down
3
nine thousand, nine hundred
1
seven thousand and four
5
ten thousand
2
six thousand, one hundred and nine
6
six thousand, four hundred and thirty-nine
3
nine thousand and sixty-four
4
six thousand and fifty-eight
5
one thousand, nine hundred and nine
7
one thousand, three hundred and forty-eight
8
nine thousand, one hundred and nineteen
Unit 1A: Number and problem solving CPM framework 4Nn1, 4Nn3; Teacher’s Resource 1.1
5
4
Place values
What number is shown on the place-value chart? 1000
2000
3000
4000
5000
6000
7000
8000
9000
100
200
300
400
500
600
700
800
900
10
20
30
40
50
60
70
80
90
1
2
3
4
5
6
7
8
9
Write the number in figures. _________________________________________ Write the number in words. _________________________________________ Hint: Remember to use zero as a place-holder for the hundreds and units.
You could use arrow cards for 5000 and 50 and then combine them to make the number.
5
5
0
0
0
5
0
combine
5
0
5
0
Numbers all around us: an activity to keep coming back to
Write these numbers in words. Read each number to a friend. Find examples of numbers around you. You could start a scrapbook of examples. Sydney 2000 km Kumagaya 9362 km
Equator 5133 km Tokyo
9567 km
Find examples of numbers around you. You could start a scrapbook of examples. Hint: Practise saying big numbers correctly and not just saying the digits in
order. 5793 is five thousand, seven hundred and ninety-three, not ‘five, seven, nine, three’.
6
Unit 1A: Number and problem solving CPM framework 4Nn1, 4Nn3; Teacher’s Resource 1.1
Ordering, rounding and comparing four-digit numbers Remember When ordering numbers, compare each digit starting with the digit of greatest place value. For example, to order the numbers: 5005
550
a 10-sided dice or resource 1, page 76 for activity 3, 0–9 digit cards from resource 2, page 77 for activity 6
You will need:
5505
50: Th 5 5
largest
smallest
H 5 0 5
T 0 0 5 5
U 5 5 0 0
Vocabulary greater than >, less than <, round
When comparing numbers, < means ‘is less than’, for example, 5005 < 5505 > means ‘is greater than’, for example, 5505 > 5005 When rounding numbers to the nearest 10, look at the units digit, so 2364 rounds down to 2360 When rounding to the nearest 100 look at the tens digit, so 2364 rounds up to 2400
1
Ordering numbers
Hint: It will help if
Write these numbers in order, starting with the smallest. (a) 650 _____ (b) 898 _____
6005
6500
_____ 8009
_____
9008
_____
560
_____
989
_____
65 _____
you write the numbers in a column, lining up the units. 650 6005
8899
_____
_____
Unit 1A: Number and problem solving, 1.2 Ordering, comparing and rounding four-digit numbers; CPM framework 4Nn9, 4Nn10, 4Nn12, 4Pt8
7
2
Rounding numbers
Complete the dartboard. The numbers in the inner ring are rounded to the nearest 10 to give the numbers in the outer ring. Hint: There are
1270
4561 3782 2345
several options for the inner circle answers!
nearest 10
3700
9787 8080 6950
3
Smallest and largest
Roll the dice (or spin the 0â&#x20AC;&#x201C;9 spinner) four times and record the four digits. Make the smallest number and the largest number, then round these numbers to the nearest 10 and 100. The digits rolled are: smallest number
largest number
Rounded to the nearest 10 Rounded to the nearest 100 You could play against a partner. Take turns to roll the dice (or spin the spinner) four times. Record the digits in the table then independently find the answers. When you have both finished, compare your results. If necessary, agree on the correct answer. Hint: It might help to think of the target number on a
number line, for example, when rounding 2364 to the nearest 10, you can see that it lies between 2360 and 2370 but is closer to 2360.
8
Unit 1A: Number and problem solving, 1.2 Ordering, comparing and rounding four-digit numbers; CPM framework 4Nn9, 4Nn10, 4Nn12, 4Pt8
2364
2360
2370
4
Fill the boxes
Which whole numbers could go in the empty boxes? Write them on the lines below. 1234 <
< 1243
Hint: If you find it
difficult to remember what the signs mean, imagine a huge mouth opening towards the bigger meal.
__________________________________________ 5678 <
< 5674
__________________________________________ 5
Use the digits 3, 5, 8 and 9. Make as many different four-digit numbers between 3000 and 4000 as you can. Write your numbers in order, starting with the smallest. __________________________________________ Hint: Record your answers systematically.
This helps you check you have found all the numbers. 6
More or less – a game for two players
Shuffle the cards and place them face down. Players each choose one of the inequalities below. Player 1
<
Player 2
<
Take turns to choose a card and place it anywhere on your inequality. Players try to win by making their number line true and their partner’s line false. The winner scores 1 point. Play 5 times to find the overall winner. Unit 1A: Number and problem solving, 1.2 Ordering, comparing and rounding four-digit numbers; CPM framework 4Nn9, 4Nn10, 4Nn12, 4Pt8
9
Multiplying and dividing by 10 and 100 Remember When you multiply a number by 10, the digits move one place to the left.
You will need:
resource 1, page 76 for activity 3 and resource 3, page 78 for activity 4
When you multiply a number by 100, the digits move two places to the left. When you divide a number by 10, the digits move one place to the right. Division
Multiplication 79 × 10 = 790 H 7
T 7 9
U 9 0
79 × 100 = 7900 Th
H
7
9
T 7 0
U 9 0
790 ÷ 10 = 79 H 7
T 9 7
U 0 9
Multiplication and division are inverse operations. 6 6
1
× 10
60
÷ 10
60
Multiply and divide
Complete these calculations. 35 × 100 = 17 × 100 = × 10 = 3500
10
× 10 = 650 350 ÷ 10 = 900 ÷ 10 =
Unit 1A: Number and problem solving, 1.3 Multiplying and dividing by 10 and 100; CPM framework 4Nn7, 4Nc15, 4Nc25, 4Pt6
Hint: Use a
place-value grid to help you. Draw arrows to show the digits moving to the left and right.
2
Find at least 8 pairs of numbers where one number is ten times the other.
40
800
91
33
130
999
501
150
300
1
51
70
60
17
90
909
190
303
7
901
13
710
110
15
Complete the calculations.
707
11
404
4
400
14
13 and 130 has been done for you.
19
200
9
101
41
10
13
3
× 10 =
and
130
130
÷ 10 =
× 10 =
and
÷ 10 =
× 10 =
and
÷ 10 =
× 10 =
and
÷ 10 =
× 10 =
and
÷ 10 =
× 10 =
and
÷ 10 =
× 10 =
and
÷ 10 =
× 10 =
and
÷ 10 =
13
First past 1000 – a game for two players
Use the spinners from resource 1. Take turns to spin a number from 0–9 and an operation, for example, 6 and × 10. Work out the result. That is your score for the round. Each player keeps a running total of their scores. The first past 500 is the winner. 4
Multiply and divide by 10
Cut out the 12 pieces of the jigsaw from resource 3. Put the jigsaw together by matching each calculation to its answer. Unit 1A: Number and problem solving, 1.3 Multiplying and dividing by 10 and 100; CPM framework 4Nn7, 4Nc15, 4Nc25, 4Pt6
11
Mental strategies for addition and subtraction Remember When you add or subtract two numbers in your head, there are many different methods you can use. Addition
3 + 9 is 12 20 + 30 is 50 12 add 50 is 62
23 + 39
23 add 30 is 53 53 add 9 is 62
23 add 40 is 63 63 take away 1 is 62
The most efficient method will depend on the numbers involved. Subtraction 63 take away 30 is 33 33 take away 9 is 24
63 – 39
63 take away 40 is 23 Add 1 more is 24
You will need:
resource 1, page 76, for activity 3
Counting on from 39 to 59 is 20 then 4 more to 63. That’s 24 altogether
Vocabulary add, plus, total, increase, sum, subtract, take away, minus,
1
Cross pattern
decrease, difference
Use each of the numbers 1, 2, 3, 4 and 5 to complete the cross pattern. The total going across must be the same as the total going down. 2
Hint: Make a set of
cut out numbers so you can try them in different positions on the board. There is more than one answer.
Subtraction triples
Work mentally to complete these questions. 92 – 25 =
92 –
= 67
– 25 = 67
Explain to someone else how you worked out the answers.
12
Unit 1A: Number and problem solving, 2.1 Addition (1), 2.2 Subtraction (1); CPM framework 4Nc6, 4Nc9, 4Nc10, 4Pt1, 4Ps3
3
Add three – a game for two players
Take turns to spin the 0–9 spinner four times to give you four numbers. Add the four numbers together. If the answer matches a number on the board, write your name in that number’s hexagon. If the number is not there, or has already been taken, you miss that turn. The winner is the first player to have a block or line of four numbers. Explain to the other player how you work out each answer.
36
35 15
14
34 16
14 13
12
19
16
10
27 26
25 24
22 5
28
22
24
29
21
23
21 6
20
15
23
30
16
14
20 7
19
18
22
31
17
13
19 8
18
20
17
32
18
21
18 9
17
15
11
33
0 1
23 4
2 3
Hint: If two of your numbers total 10 add them first. For example, if you
have to add 3, 9, 5 and 7, add 3 + 7 first, then add on 9, then add on 5. Unit 1A: Number and problem solving, 2.1 Addition (1), 2.2 Subtraction (1); CPM framework 4Nc6, 4Nc9, 4Nc10, 4Pt1, 4Ps3
13
Addition and subtraction Remember Using an empty number line to add 86 + 38 = 124 Jumps along a number line
+ 30
86
+4
+ 30
116 120 124
+ 50
73 + 49 = 122 Compensation method
–1
73 Using an empty line to subtract 47 – 23 = 24 Jumps back along a number line 78 – 19 = 59 Jumps back along a number line with compensation
122 123 –3
– 20
20
27
47
– 20
+1
58
59
78
These methods can also be used with three-digit numbers.
1
Calculating on the number line
Complete these calculations. 37 + 24 =
You will need:
activity 3
resource 1, page 76 for
56 – 25 =
+ 20
+3
–5
+1
– 20
37
56
74 + 38 =
65 – 19 = + 40
– 20 –2
74
14
Unit 1A: Number and problem solving, 2.3 Partitioning to add and subtract; CPM framework 4Nc18, 4Nc19, 4Pt1, 4Ps3
+1
65
2
Number walls 60
The number in each brick is the sum of the numbers in the two bricks below it. Complete these number walls.
00 31
18 + 11 = 29
00 00 13
25 00
18
11
00 18
00
00 13
29
23
00 31
37
29
17
28
19
48 00 32
00
Hint: You will need to use addition and subtraction to complete the walls.
You can do the calculations mentally or draw a blank number line to help with the calculation. 3
Highest score â&#x20AC;&#x201C; a game for two players
Spin the 0â&#x20AC;&#x201C;9 spinner. Both players write the number in one of their boxes. Take turns to spin the spinner and write down the number until the four boxes are filled. Add the two two-digit numbers. The player with the highest total wins. The first player to win three rounds is the champion. +
= ________
+
= ________
+
= ________
Explain to the other player how you work out each answer. Hint: You can also play lowest score. This time you subtract the numbers. Unit 1A: Number and problem solving, 2.3 Partitioning to add and subtract; CPM framework 4Nc18, 4Nc19, 4Pt1, 4Ps3
15
Using multiplication facts Remember Multiples are like numbers in the times tables but they go on and on, for example:
You will need:
coloured pencils
Multiples of 2 are: 2, 4, 6, 8, 10 . . . . 52, 54, 56 . . . .
Vocabulary
Multiples of 5 are: 5, 10, 15, 20 . . . . 90, 95, 100, 105 . . . .
multiple
The order of multiplication is not important so 3 × 5 gives the same result as 5 × 3.
1
Hundred square
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
In a different colour, colour all the multiples of 5.
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
What do you notice about the numbers you have coloured twice?
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
Colour all the multiples of 2 on the hundred square.
Hint: Try to remember the 2× and 5× tables.
You you can use a number square to help you to: ● count forwards and backwards ● add and subtract tens and multiples of 10 ● colour in other table patterns
16
Unit 1A: Number and problem solving, 3.1 Learning and using multiplication facts; CPM framework 4Nn8, 4Nc4, 4Nc5, 4Nc13, 4Nc14, 4Ps4
2
Number machines
Complete each table for these number machines.
×3
IN
OUT
×6
IN
OUT
×9
IN
OUT
IN
3
OUT
IN
12
2
OUT
IN OUT
5
9 21
5 24
2
8 42
4 27
30
60
9 54
90
Hint: Remember that multiplication and division are inverse operations.
IN IN
×3
OUT
÷3
OUT
When you have completed the tables look back at your work and check that the multiples of 3 are also multiples of 6 and 9. 3
Number sequences
Complete these number sequences: 6, 12, 18,
, 30,
,
4, 8, 12,
, 20,
,
Unit 1A: Number and problem solving, 3.1 Learning and using multiplication facts; CPM framework 4Nn8, 4Nc4, 4Nc5, 4Nc13, 4Nc14, 4Ps4
17
4
Number maze
1
Follow the instructions to find your way out of the maze.
5
You will need to go from the centre to one of the outside hexagons in two steps.
2
16
The next hexagon you visit must be a multiple of 2.
6 13
17
10 START 14
25
Start in the centre.
11
9 4
The next hexagon you visit must be a multiple of 5.
18 20
3 15
7
Draw lines to show the different routes that you can take. Hint: Colour the multiples of 2 in one colour and the multiples of 5 in
a different colour before you plan the routes.
5
Multiplication grids
Complete these grids. ×
2
3
5
×
3
5
6
×
3
4
10
4
5
4
6
10
5
×
4 20
2 6
10 15
8
2
3 20
18
×
9 27
8 10
9
× 12 16
45
2
4
6
2
50 4 5
Hint: Practise your tables at home. Work on a different table each week.
18
Unit 1A: Number and problem solving, 3.1 Learning and using multiplication facts; CPM framework 4Nn8, 4Nc4, 4Nc5, 4Nc13, 4Nc14, 4Ps4
20