CAMBRIDGE PRIMARY
Mathematics Games Book
Emma Low
6
CD-ROM Terms and conditions of use University Printing House, Cambridge cb2 8bs, United Kingdom 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: www.cambridge.org/9781107667815 © Cambridge University Press 2014 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 2014 Printed in Poland by Opolgraf A catalogue record for this publication is available from the British Library isbn 978-1-107-66781-5 Paperback Cover artwork: Bill Bolton 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 in the uk It is illegal to reproduce any part of his 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 licence, 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 for the purposes of setting examination questions. notice to teachers 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.
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Contents Number
The rectangle area and perimeter game
67
Place value challenge
1
The four in a row scale game
69
More or less
1
Time zones game
71
Factors in a row
5
The compound area game
75
Domino multiplication
5
Gallon man game
78
Sequence trail
8
Time intervals game
78
Nine Men’s Morris
28
Geometry
Decimal in-between
28
Irregular area game
87
Order five
31
Collecting quadrilaterals game
90
Mathematical bingo
31
Don’t make a cube game
90
Division line
36
Angles of a triangle
95
Place the numbers in the square
36
Co-ordinates
97
Place your numbers now
41
The dodecahedron and octahedron game
97
Sum to one snap
41
Co-ordinates games (2)
103
Find the total
44
The drawing angles game
103
Finding fractions of numbers
44
Handling Data
Equivalent fractions dominoes
48
The pie chart game
106
Percentages of numbers
48
The mean game
106
The smoothie ratio
52
The equally likely game
110
Measure The ordering lengths game
59
The length competition game
59
Earlier or later times
64
Matching times
64
Introduction This Games Book consolidates and reinforces mathematical learning for Stage 6 learners (usually 10–11 years). It can be used as an independent resource for anyone wanting to encourage mathematical learning in children, or as a supplementary part of the Cambridge Primary Mathematics series.
Cambridge Primary Maths brings together the world-class Cambridge Primary mathematics curriculum from Cambridge International Examinations, high-quality publishing from Cambridge University Press and expertise in engaging online enrichment materials for the mathematics curriculum from NRICH.
If used as part of the series alongside the Teacher’s Resource 6 (9781107694361), then you will often be going directly to a specific game and page number according to the reference in the ‘More activities’ section in the Teacher’s Resource and will therefore already be familiar with the learning outcome of the game. If you are using the book as an independent resource, you can use the Objective map on the CD-ROM to help you determine what game you might want to play according to what learning outcome you are after, or you can simply read the ‘Maths focus’ at the start of each game to decide if it’s appropriate.
Teachers have access to an online tool that maps resources and links to materials offered through the primary mathematics curriculum, NRICH and Cambridge Primary mathematics textbooks and e-books. These resources include engaging online activities, best-practice guidance and examples of Cambridge Primary Maths in action.
The games are grouped by strand, i.e. ‘Number’, ‘Geometry’, ‘Measure’ and ‘Handling data’ so that an independent user can easily navigate the pool of games. For those of you using this book alongside the Teacher’s Resource 6, you will find that the games within a strand are ordered according to the order in which they are referenced in the Teacher’s Resource 6 (if you grouped all chapters of a given strand together). Please note that the Games Book on its own does not cover all of the Cambridge Primary mathematics curriculum framework for Stage 6. All games boards, game cards and record sheets provided within the printed book are also available on the CD-ROM for quick printing if preferred. Some games boards and resources will also be provided as Word documents so that you can adapt them as required. The CD-ROM also provides child-friendly instructions for each game, which can be displayed at the front of the class or sent home with the games for independent play. Nets for making dice, spinners and other useful mathematical resources are also provided as printable PDFs on the CD-ROM. This publication is part of the Cambridge Primary Maths project. Cambridge Primary Maths 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.
The Cambridge curriculum is dedicated to helping schools develop learners who are confident, responsible, reflective, innovative and engaged. It is designed to give learners the skills to problem solve effectively, apply mathematical knowledge and develop a holistic understanding of the subject. The Cambridge Primary Maths textbooks provide best-in-class support for this problem-solving approach, based on pedagogical practice found in successful schools across the world. The engaging NRICH online resources help develop mathematical thinking and problem-solving skills. To get involved visit www.cie. org.uk/cambridgeprimarymaths The benefits of being part of Cambridge Primary Maths are: • the opportunity to explore a maths curriculum founded on the values of the University of Cambridge and best practice in schools • access to an innovative package of online and print resources that can help bring the Cambridge Primary mathematics curriculum to life in the classroom. This series is arranged to ensure that the curriculum is covered whilst allowing teachers to use a flexible approach. The Scheme of Work for Stage 5 has been followed, though not in the same order and there will be some deviations. The components are: • Teacher’s Resource 6 ISBN: 9781107694361 (printed book and CD-ROM). • Learner’s Book 6 ISBN: 9781107618596 (printed book) • Games Book 6 ISBN: 9781107667815 (printed book and CD-ROM). For associated NRICH activities, please visit the Cambridge Primary Maths project at www.cie.org.uk/cambridgeprimarymaths
Place value challenge
More or less
Maths focus: writing and reading large numbers (six-digit numbers with two decimal places).
Maths focus: practising using the symbols ! and " correctly.
A game for two players You will need: • Game board (page 2). • 0–9 spinner (CD-ROM).
A game for two players You will need: • Game board (page 3). • Two sets of Game cards (page 4). How to play
How to play 1. Players take turns to spin the spinner and write the number shown in to a box on their row on the game board.
1. Players have one row on the grid each. Shuffle the game cards and place them face down in a pile.
2. Players then read out their numbers.
2. Players take turns to take a card and place it anywhere on the grid.
3. The winner is the player with the highest number when all the boxes have been filled.
3. Players try to win by making their number sentence true and their opponent’s number sentence false.
Players can just fill the boxes in from right to left, or they can choose a box for each number. Some will realise that they need to try to save the boxes on the left for the biggest numbers.
4. At the end of the round any player with a correct number sentence is awarded a point.
Challenge
5. At the end of an agreed number of rounds, the winner is the player with the most points.
For a more challenging game, include a second spinner that has the following numbers on it: 10, 100, 1000, 10000, and 100000; or the words: ten, hundred, thousand, etc. The players spin both spinners and have to multiply them together to get a third number, this number is then written in the appropriate place on the game board. If the player spins a 100 for example but they already have a digit written in the hundreds place on their grid, then they miss a turn.
Cambridge Primary Mathematics Games Book 6: Number
1
HTh TTh
Th
H
T
U
t
h
Player 1:
Player 2:
Original material Š Cambridge University Press 2014
Place value challenge – Game board
Player 1
! Player 2
" More or less – Game board
Original material Š Cambridge University Press 2014
More or less – Game cards
0 1 2 3 4 5 6 7 8 9 Original material Š Cambridge University Press 2014
Factors in a row
Domino multiplication
Maths focus: finding factors of two-digit numbers.
Maths focus: multiplying pairs of multiples of 10 and 100.
A game for two players
A game for two or four players
You will need: • Game board (page 6). • Counters (or alternative); different colour per player. • Two 1–6 dice or spinners (CD-ROM).
You will need: Multiplication dominoes (page 7). How to play 1. Suffle the dominoes and place them face down on the table.
How to play 1. Players take turns to roll both dice and use the numbers to make a two-digit number. 2. They find all the factors of the number and cover one copy of each factor on the game board with a counter. If all copies of a number are already covered, the player cannot place their counter. Example:
2. Each player chooses their dominoes (seven each if there are four players and fourteen each if there are two players). 3. The player with the domino showing 81 000 (the highest number) lays it down to start the game. 4. Players then take turns to match one end of a domino from their ‘hand’ to one of the two ‘ends’ in the growing line of dominoes on the table. Dominoes are matched so that the multiplication calculation on one domino is matched with the correct product on another domino. Example:
5600 4 on one dice and 2 on another dice can be used to make 24 or 42. If the player chooses to make 42: 2, 3, 6 and 7 are all factors of 42, so the player can cover these numbers (four squares) with counters.
30 # 40
1200
50 # 30
1500
600 # 20
5. If a player is unable to place a domino, they miss that turn. 6. Play continues until one player has laid all their dominoes. That player is the winner.
3. The first player to have five counters in a row is the winner.
Cambridge Primary Mathematics Games Book 6: Number
5
7 6 5 4
6 5 4 3
Factors in a row – Game board
8
7
3
4
5
6
5
6
7
8
3
4
5
6
7
6
7
8
3
4
5
6
7
8
7
8
3
4
5
6
7
8
9 11 2
Original material Š Cambridge University Press 2014
8
3
4
5
6
7
8
9
9 11
9 11 2
9 11 2
9 11 2
9 11 2
9 11 2
3
9 11 2 8
4
3
11 2
5
4
3
2
Domino multiplication – Multiplication dominoes
5600
30 # 40
1200
50 # 30
1500
600 # 20
12 000
50 # 70
3500
80 # 90
7200
900 # 90
81 000
100 # 20
2000
400 # 70
28 000
300 # 70
21 000
300 # 30
9000
500 # 50
25 000
400 # 60
24 000
50 # 90
45 000
50 # 50
2500
700 # 50
35 000
50 # 80
4000
600 # 70
42 000
90 # 70
6300
40 # 60
2400
60 # 60
3600
500 # 40
20 000
100 # 10
1000
70 # 30
2100
60 # 80
4800
600 # 90
54 000
800 # 70
56 000
900 # 50
45 000
70 # 80
Original material Š Cambridge University Press 2014
Sequence trail
Example trail card
-60
Maths focus: practising with sequences. A game for individuals (or pairs) You will need: • A set of trail cards (9–26). • Recording sheet for each player (page 27).
Sara makes a sequence of numbers starting with 100. She subtracts 45 each time.
How to play 1. Place the trail cards in a prominent position around the room (numbers in order).
100
55
10
2. Each player (or pair of players) is given a recording sheet. 3. Players can start at any card. They record the number at the top of their chosen first trail card anywhere on their recording sheet. Players then answer the question on the trail card and record the answer on their recording sheet, in the circle that is to the right of their starting number. All other numbers must be filled in on the next circle to the right of their previous answer. They make their way to the trail card with that number at the top, and continue until the loop is complete. 4. If doing this as as class activity, the winner is the first player (or pair) who completes their loop correctly. An alternative to a classroom trail is to reduce the cards in size and give a set to a pair of players to place in a loop. Answers (start anywhere in the loop): $60 → $35 → 6 → 65 → 1210 → 1025 → 1046 → 8 → 22 → 17 → 120 → 12 → 15 → -2 → 7 → 162 → 3 → 1027 →
8
Cambridge Primary Mathematics Games Book 6: Number
What is the next number in the sequence?
Please note that it is important to make it clear to the players that the answer sheet does not generate a sequence, it represents a loop generated between the game cards. The practise with sequences comes only from the questions on the game cards themselves and the purpose of the game is not to generate a sequence on the answer sheet. The answer sheet is merely a way to record which game cards they have been to, and which one they need to go to next.
55
10
Original material Š Cambridge University Press 2014
What is the next number in the sequence?
100
She subtracts 45 each time.
Sara makes a sequence of numbers starting with 100.
-60
-35 18
Pablo makes a sequence of 5 numbers. The first number is 2 and the last number is 18. His rule is to add the same amount each time.
2 What is the next number after 2?
Original material Š Cambridge University Press 2014
25
What is the missing number?
13
The rule for this sequence is: double and subtract 1
-2
Original material Š Cambridge University Press 2014
49
9
35
3 67
131
...
A sequence of numbers starts at 11 and follows the rule double the last number and then subtract 3
11 What is the smallest number, greater than 1000, in the sequence?
Original material Š Cambridge University Press 2014
-25
Original material Š Cambridge University Press 2014
What is the first number in her sequence?
45
Miriam makes a sequence of numbers. She chooses a starting number and then subtracts equal amounts each time. The third number in her sequence is 45. The tenth number in her sequence is -25.
6