Maths on the Go
Also available Maths on the Go
1
Book
i t ivi
r o f es
a
ct
mat Rob Vingerhoets
ISBN 0732978807 ISBN 9780732978808
About the author Rob Vingerhoets is an experienced primary maths teacher and author. He is a popular and engaging presenter of maths ideas for busy teachers and understands the demands of a full curriculum. His books show how it is possible to squeeze more maths into less time!
Book
5 to 45 minute
More ideas from the best-selling author of Maths on the Go Book 1 !
22 Book
Book 2
The activities in Maths on the Go Book 2: • are easy to organise and implement • require minimum equipment, or none at all • are easily adapted across a range of year and age levels • cover the important content strands: Mental Computation, Measurement, Space, Number, and Chance and Data • can be readily used as part of any maths program • are perfect for revision or extension.
y r l a e v m i els r p la l
hs
Make the most of every minute of the teaching day . . . • 30 minutes before morning recess • 20 minutes between library and lunch • 5 minutes at the end of the day.
Space Number Measurement
Chance and Data Mental Computation
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5 Book 2
5 to 45 minute activities for all primary levels • Mental Computation • Measurement • Space • Number • Chance and Data
Rob Vingerhoets
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Acknowledgements To Mick Ymer, a great friend and a terrific maths person, for the ideas behind ‘Date Maths’ and ‘Closest to 1’ and other ideas he gladly allowed me to use for this book — something I really appreciate, as they were just too good not to appear in someone’s book somewhere. To those teachers in Australia and New York who personally requested — or whose classes inspired — the sort of activities found here, and who were only too happy to allow me to trial new activities with their students; in particular, Adrian Dilger and Lorraine Kennedy for ‘We’re Going on a Shape Hunt’, ‘Thinking Linking 1’, ‘Thinking Linking 2’ and ‘Two Coins on a Ruler’. As always, to my wonderful wife Marg, for her support and advice; and for not running away and leaving me to write another book on my own!
This edition published in 2021 by
Matilda Education Australia, an imprint of Meanwhile Education Pty Ltd Melbourne, Australia T: 1300 277 235 E: customersupport@matildaed.com.au www.matildaeducation.com.au First edition published in 2006 by Macmillan Science and Education Australia Pty Ltd Copyright © Rob Vingerhoets/Macmillan Education Australia 2006 Maths on the Go Book 2 ISBN 978 1 4202 0931 0 ISBN 1 4202 0931 0 Publisher: Sharon Dalgleish Cover design and illustration: Cliff Watt Text design: Domenic Lauricella Editors: Tricia Dearborn, Laura Davies Printed in Australia by Courtney Brands 1 2 3 4 5 6 7 25 24 23 Copying of this work by educational institutions or teachers The purchasing educational institution and its staff, or the purchasing individual teacher, may only reproduce pages within this book in accordance with the Australian Copyright Act 1968 (the Act) and provided the educational institution (or body that administers it) has given a remuneration notice to the Copyright Agency Limited (CAL) under the Act. For details of the CAL licence for educational institutions, contact: Copyright Agency Limited Level 15, 233 Castlereagh Street Sydney NSW 2000 Telephone (02) 9394 7600 Facsimile (02) 9394 7601 Email info@copyright.com.au Reproduction and communication for other purposes Except as permitted under the Act (for example, any fair dealing for the purposes of study, research, criticism or review), no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher.
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Contents Introduction 5 Activity Focus Level
Duration (minutes)
Equipment/ Worksheet
Page
Mental Computation 1 Mind-Reader
Number, space, logic, recall
Years 0–6
10–15
✗
7
2 How Much in
Number, logic
Years 2–6
10–15
✓
9
3 Heads or Hips?
Number
Years 2–6
5–15
✗
12
4 What is the Question?
Number, working backwards
Years 2–6
5–10
✗
14
5 The Number Formerly
Number
Years 2–6
all day
✗
15
6 Date Maths
Number
Years 3–6
10–15
✗
16
7 And the Biggest
Number, operations
Years 3–6
15–25
✗
18
8 In the Ballpark
Number, division and multiplication
Years 4–6
20–30
✓
21
9 If You’ve Got It —
Applying common units of measurement
Years 1–2
25–30
✓
24
10 Steppin’ Out
Applying standard units of measurement
Years 3–5
25–30
✓
26
11 Like a Pendulum
Making predictions, identifying trends and patterns, hypothesising
Years 0–6
10–20
✓
29
12 Triangular Areas
Working out area of right-angled and equilateral triangles
Years 5–6
25–35
✓
32
Shape recognition, attributes
Years 0–6
10–15
✗
34
Years 0–6
10–25
✓
36
Years 0–6
20–25
✗
38
Years 4–6
20–30
✓
42
My Pocket?
Known As . . .
Answer Is . . .
Measurement Measure with it
Swings
Space 13 Tell Me Ten Things About . . .
14 Left, Right, Compass and Clock
15 We’re Going on a Shape Hunt
16 The Big Space Quiz
of shapes, spatial terminology Spatial and directional terminology Recognition of 2D and 3D shapes 2D and 3D shapes, angles, directions, spacial terminology
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Activity Focus Level
Duration (minutes)
Equipment/ Worksheet
Page
Years 0–6
10–20
✓
44
Number 17 The Human Number Line
Place value, odd and even numbers, cardinal and ordinal numbers
18 The Magic 8
Number
Years 0–2
20–30
✓
47
19 Pattern Block
Addition, shape, fractions,
Years 1–2
20–35
✓
49
Numbers
logic
20 Pick It Out
Place value, operations
Years 0–6
30–45
✓
52
21 Connect the Numbers
Operations
Years 2–6
25–35
✗
56
22 Grab a Zero
Operations, properties of
Years 3–6
20–30
✓
61
Years 4–6
30–45
✗
63
Years 5–6
20–30
✓
65
Years 0–2
10–15
✗
67
Years 0–2
10–15
✗
69
Years 0–3
10–15
✓
71
operations, multiplying by tens
23 Match-Up to 1
Adding and/or subtracting simple fractions, decimals and percentages
24 Closest to 1
Comparing and ordering fractions
Chance and Data 25 Thinking Linking 1
Sorting/classifying people by attributes
26 Thinking Linking 2
Sorting/classifying people by attributes, collecting simple data
27 The Human Birthday Graph
Sorting/classifying people by attributes, collecting/ interpreting simple data
28 Four Corners
Probability
Years 1–6
10–15
✓
74
29 Two Coins on a Ruler
Probability, data interpretation
Years 2–6
15–20
✓
77
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Introduction More than a little bit of water has passed under the mathematical bridge since Maths on the Go was published back in 2001, and I have to say that this time it’s been a bit of a dual continental effort. Good thing I’m ‘bi-hemispherical’, as Dame Edna would put it. Maths On The Go Book 2 is based on the premise that students need to be engaged in mathematics, and on my firm belief that maths doesn’t have to hurt. The book was largely written in New York City, and is a combination of ideas and activities I had used in Australia, those I had seen first hand (Mick Ymer) and those I steadily put together over time while working in various grades. The New York activities (from Brooklyn and Queens elementary schools in the Big Apple) included ones I thought of on the spot, others I worked on in my head over time, some I witnessed or read about and then modified, and many others that arose in response to teacher requests for me to model lessons on a range of topics. What all the activities in this book have in common is that all of them have been tried and tested on kids in living, breathing classrooms — and, luckily, they all worked well! Some needed some improving, but the audiences I tried them on were only too willing to give me (brutally) honest critiques on my new activities. None of the activities are hypothetical or theoretical — they are all soundly practical and mathematical. What the activities also have in common is a steadfast commitment to engage students in their mathematics. It simply isn’t sufficient to merely teach your students mathematics, working them through a set of rules to get through a mound of content: students must be able to relate to maths. They must be able to use it to make sense of their everyday lives. We, as teachers, must set up the mathematical experiences so that students discover the maths. The vast majority of primary school students already believe that you, the teacher, are wise beyond belief: you don’t need to convince them you’re clever. Let them do the discovering — don’t take this opportunity away by providing them with the answers and/or the methods.
Maths On The Go Book 2 As for the original Maths on the Go, this edition also contains activities that cover the strands of Measurement, Space, Number, and Chance and Data. There is also a specific section in this book on Mental Computation. It has been placed before the other sections as I believe that having well-honed mental computation skills (and this doesn’t just mean automatic response) is absolutely critical to students’ success in their mathematical and everyday lives. And the best part is that it can be plain, good fun.
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The activities span the range of Years 0 to 6, and the duration of the activities varies from 5 to 45 minutes. Most of the activities require a minimum of equipment, if any. Some include a worksheet; others don’t. The majority of the activities presented here can be used repeatedly throughout the year. They are not one-offs, but activities students will improve in and benefit from each time you use them — and the great thing is that you will find students in your class asking for them regularly. For each activity there is an indication of the main focus, the age level/s the activity is suitable for, the duration of the activity, a list of required equipment (if any), objectives, organisation (whole class, small groups, etc.), guidelines for implementing the activity, and variations that allow for enrichment or taking it back a step or two.
Hints on Using Maths on the Go Book 2 • For many of the activities, it is actually not essential that the whole class participate or that every individual get a turn. In fact, to keep activities dynamic and involved it is often better to have half the class or seven or eight students participate in a given activity: ‘Steppin’ out’, ‘Closest to 1’ and ‘Thinking Linking’ are good examples in this book. • It’s a good idea to have available many copies of the list of students in your class. When only a limited number of students will be involved in an activity, you can allay students’ fears of never getting a turn by writing the name of the activity at the top of the class list and ticking off the names of those involved today. Tell students you will choose different people next time you do this activity. • Many of the activities presented here can and should form part of your regular classroom routines. For example, you could decide that every Tuesday and Thursday morning during Term 2, between this time and that time, the class is going to play ‘Mind-Reader’. This would be apart from and in addition to the daily maths lesson. • Other activities detailed in the book can be part of your day-today lesson format. Many of them are ideal for warm-up activities, particularly the mental computation activities. Simply rotate them on a regular basis so that they remain fresh and challenging. • Finally, many of the activities presented here represent ‘full-on’ maths lessons and can be readily incorporated into your regular maths program. Read through them, make a judgement about where they might fit into your program/planning and then give them a go!
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Maths on the Go Book 2 MENTAL COMPUTATION
Activity 1
FOCUS AGE LEVEL DURATION EQUIPMENT
Mind-Reader Number, space, logic, recall Years 0 to 6 (5- to 12-year-olds) 10 to 15 minutes None
Objective To develop in students the capacity to think logically and draw conclusions from information presented to them.
Organisation This activity can be conducted in table groups; or do it with the whole class and have individuals raise their hand when they think they know the answer.
Introduction When played in groups, ‘Mind-Reader’ is a good cooperative group activity as students must discuss probable or likely solutions and reach a consensus. It’s good for mixed ability groups, as students enjoy the fact that all groups receive similar type clues.
Procedure Have students sit in their table groups, or in groups of four or five. Tell students you are going to give each group some clues to a number. After all the clues have been provided, the group needs to discuss possible answers, or the definitive answer, and reach a consensus. When 30 seconds to a minute have elapsed (depending on the age and abilities of the class/ group), ask a group member to nominate the number they believe matches all the clues. Go over the clues in terms of the number suggested by the group. If all clues match, the group receives the coveted ‘It’s a match!’ accolade. (Frequently more than one number can meet all the criteria/clues.) This activity can also be done with the whole class, with individuals raising their hands when they think they have the right answer, or being selected to give a response. I prefer the group approach as it promotes sharing of knowledge, communication, listening skills, reaching consensus and teamwork. ‘Mind-Reader’ is a very good once- or twice-a-week activity. You need only give one ‘Mind-Reader’ per group — although students will ask for more. It can be used as a warm-up session, as an activity any time during the day, or as a regular routine.
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Maths on the Go Book 2 MENTAL COMPUTATION
A sample game Remind students to wait until you have given them all five clues. Tell them if someone in the group is sure they know the answer, that person should share their answer with the rest of the group and say why they think it is right, so everyone in the group understands. Give them their clues. Clue 1: It’s a two-digit number. Clue 2: It’s an odd number. Clue 3: The tens digit is even. Clue 4: One of the digits is twice as big as the other one. Clue 5: The sum of the two digits is 9. Repeat the clues. (With younger classes, it is likely you will need to repeat the clues at least three times.) The group now gets into a huddle so as to reach consensus on the number. If students are not unanimous, it should be a case of majority rules. Call for a spokesperson or choose one of the group randomly to say the number and justify the choice by juxtaposing the number with the clues. For example, a spokesperson for Group 1 suggests the number is 63. Is 63 a two-digit number? Yes. Is it an odd number? Three is an odd number, so yes. Is the numeral in the tens place even? Six is an even number, so yes. Is 6 twice as big as 3? Yes. When I add 6 and 3, do I get 9? Yes. It’s a match! You will find that the remaining tables will all have attempted Group 1’s ‘Mind-Reader’. I encourage this by informing the whole class that if Group 1 misses, I’ll go to Group 2 for their answer, and so on. Here are some ‘Mind-Readers’ to get you started. Make up your own, and have your students create some to give to other groups. Clue 1: I am a number between 1 and 10. Clue 2: I am supposed to be a lucky number. Clue 3: I am bigger than 5 and less than 9 Clue 4: I only have straight lines in my number. Clue 5: I am the number of days in one week.
Clue 1: I am a two-digit number. Clue 2: I am an odd number. Clue 3: Both my digits are odd. Clue 4: One of my digits is 3 times the other one. Clue 5: When you add my two digits together you get 12.
Clue 1: I am a threedigit number. Clue 2: I am an odd number. Clue 3: My first and last digits (ones and hundreds) are the same Clue 4: The digit in the middle is even. Clue 5: When you add my three digits it totals 8.
Clue 1: I am a threedigit number. Clue 2: I am an even number. Clue 3: All of my three digits are even. Clue 4: The digit in the tens is twice the digit in the hundreds. The digit in the ones is twice the digit in the tens. Clue 5: The sum of my digits is 14.
I don’t want to spoil ‘the fun’ and challenge of you yourself working these out but, if necessary, here are the answers —7, 39, 323, 248
Variations ‘Mind-Reader’ also works well for geometrical challenges. For example, for a trapezium: Clue 1: I am a four-sided shape. Clue 2: My top and bottom sides are parallel. Clue 3: The top side is smaller in length than the bottom side. Clue 4: The left- and right-hand sides are the same length but smaller than the top and bottom sides. They are not parallel. Clue 5: There are no right angles.
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Maths on the Go Book 2 MENTAL COMPUTATION
Activity 2
FOCUS AGE LEVEL DURATION EQUIPMENT
How Much in My Pocket? Number, logic Years 2 to 6 (7- to 12-year-olds) 10 to 15 minutes Dollars totalling various amounts (real notes/coins if you can)
Objective To develop in students the ability to think logically and apply these logical thoughts in formulating effective questions.
Organisation A whole-class activity.
Introduction ‘How Much In My Pocket’ is one of those activities that you could and should play on a regular basis, for example once every two weeks. It also makes a very effective warm-up or mini-lesson.
Procedure Take some notes and $1 and/or $2 coins, total them up, and place them in your pocket. I normally double-check the amount and commit it to memory before entering the classroom The total doesn’t really matter, but it’s good to vary the amount so students don’t always know you have between $5 and $10, or $10 and $20. Inform the class that they have eight questions they can ask to try to narrow down the range of amounts it could be. (Eight questions works well for Years 4 and 5; seven works well for Year 6; and nine or ten is good for Years 2 and 3.) After that, they must guess a specific amount. Quickly put the following on the board:
HOW MUCH IN MY POCKET? 1. 5.
2. 6.
3. 7.
4. 8.
I now put the challenge into context by stretching my arms out to the sides and telling students that my outstretched arms represent the range of specific amounts I could have in my pocket. I could have $1 (wiggle left hand); I could be doing the grocery shopping after school and have $200 (wiggle right hand); or it could be any amount in between. Students have to find out, and they can only ask eight questions before they have to guess the amount.
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Maths on the Go Book 2 MENTAL COMPUTATION
Particularly with Years 2 to 4 students, now is the time to emphasise that students should not be guessing specific amounts until all the questions have been used up. Make it clear that there is a big difference between asking a question that can give a lot of information and rule out many numbers in one go and making a guess that eliminates only one number. I illustrate this by using my outstretched arms and saying that questions that get rid of many numbers in one go — for example, ‘Is it less than $50?’ — have this effect (I bring in my arms about a quarter of the distance). Asking me a specific amount like ‘Is it $10?’, on the other hand, has this effect (I move my arms in a minuscule amount). If students ask me if it is a specific amount eight times, they have little chance of working out the amount and it will forever remain a mystery! Each student gets one question only, and each question must be one that you can answer with ‘Yes’ or ‘No’. Students should turn around and discuss with someone else the question they are thinking of asking, to check that it is a good question that can get rid of many numbers in one go. Tell students also that you will write up on the board next to the ‘Yes’ or ‘No’ response exactly what they find out from their question. This is very important, no matter what Year level, as students are likely to drop out of the activity if they cannot recall the clues or vital information they have gained from initial questions. It also enables you to review what they have learned after every three or four questions.
A sample game Question 1: Do you have more than $50? Answer 1. No. (It is < $50.) Illustrate how effective this question was by stretching your arms out and bringing them in by a substantial amount. Reassure students that getting a ‘No’ answer doesn’t mean it’s a bad question. Record what students have learned (It is < $50) on the board. Use the ‘less than’ (<) and ‘more than’ (>) symbols; simply put them into words as you use them. Question 2: Do you have less than $20? Answer 2. No. (It is > $20 but < $50.) Illustrate how effective this question was by again bringing in outstretched arms by a significant amount. Question 3: Is it $25? Answer 3. No. (It is not $25.) Prepare yourself for the single, specific amount question, even after all the initial explanation and illustration. Illustrate how ineffective this question was by bringing in your arms a centimetre or two. You won’t need to say much! Question 4: Is it more than $30? Answer 4. Yes. (It is > $30.) Bring in the arms even more. Now is a good time to go over what students have found out through their questions so far. We know it’s less than $50 and more than $30. There are actually two bits of information we don’t need that might distract us. Which bits of information are they? Students should tell you that we no longer need the information acquired from questions 2 and 3. Remove them from the board. Getting rid of superfluous information is a good word problem strategy, so encourage this.
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Maths on the Go Book 2 MENTAL COMPUTATION Question 5: Is it an odd number? Answer 5. Yes. (It is odd.) Bring in your arms by half the remaining distance as this is exactly what this question achieved — halving the possible numbers. Question 6: Is it between $40 and $50? Answer 6. No. (It is not between $40 and $50.) Show with arms, and review what is known: odd and less than $40 but greater than $30. Question 7: Is it between $30 and $37? Answer 7. Yes. (It is between $30 and $37.) Your hands should now be nearly touching. Ask students what numbers are left that it could be. Since it is between $30 and $37 and odd, it could be $31, $33 or $35. Question 8. Is it $35? Answer 8. No. (Not $35.) Move your hands even closer together. All allowed questions have now been asked, and students must now guess the amount. I sometimes choose a student here, or better still put it to a class vote. As it turns out, 15 have voted for $33 and 11 think it is $31. So it’s $33 by a margin of 4 votes. I bring out the money and count it, out loud: ‘I have a $20 note and a $5 note (= $25: students will do the adding up) and another $5 note (= $30) and a $1 coin (= $31) and a $2 coin (= $33). Well done!’
Variations Not all examples will play out as well as the one above. In the first one or two challenges you conduct with students (particularly in Years 4 and below), you will invariably get some inappropriate, illogical and one-number-specific questions. Persevere. Students will learn from the experiences, and they will get better. It generally only takes one child to ask one good question to generate good questions from others. Limiting it to one question per student stops students from leaving the questions up to just a few. If students are struggling after four or five questions, allow them to have a discussion with a person alongside them. As they get better, allow them one fewer question, or try some decimals, for example in Years 5/6 set the amount at $27.60.
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Maths on the Go Book 2 MENTAL COMPUTATION
Activity 3
FOCUS AGE LEVEL DURATION EQUIPMENT
Heads or Hips? Number Years 2 to 6 (7- to 12-year-olds) 5 to 15 minutes None
Objective To have students perform addition/subtraction/multiplication operations mentally in order to determine whether their answer is under or over a given number.
Organisation A whole-class activity.
Introduction This simple, enjoyable activity makes a very good warm-up or regular mental computation activity (say, once every two to three weeks).
Procedure Start with all students standing. Think of a number. Twenty works well for Year 2 students, 50 is a good number for Years 3 and 4, and 100 for Years 5 and 6 students. Tell students you are going to tell them a number. For this example, say you have Year 3 so the number is 50. You are then going to give them a problem that they need to work out in their heads. If they believe the answer to the problem is over 50, they should put their hands on their heads. If they believe the answer to the problem is under 50, they should put their hands on their hips. Inform students that they will have a finite amount of time to complete the mental calculation. Vary the time according to the Year level. When about two-thirds of the class have that look in their eyes that says they know the answer, I start a 10, 9, 8, . . . countdown. Tell students that they must not place their hands on head or hips until the countdown is complete. This helps stifle the temptation to simply copy another student. Once placed, the hands cannot then move from head to hips, or vice-versa. Before giving students the first problem, explain that you know that many of them will simply watch someone they regard as being very good at maths or mental computation and copy what that person does. Explain that you will be asking a random number of students with their hands in the correct position to explain how they made their calculation. If a student can’t give an explanation, they will be asked to sit down. Students soon realise there is no way around this but to attempt the calculation. Any student with hands on the incorrect area — obviously having made the mental computation incorrectly — is asked to sit down, but sincerely invited to continue to work out all following problems.
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I usually set five or six problems, and the students who remain standing after those (usually two to three) are heartily congratulated for their effort.
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Maths on the Go Book 2 MENTAL COMPUTATION
A sample game (for year 3) Inform students that 50 is the magic number today. First problem: What is 3 x 17? Give students approximately 30 seconds, then commence the countdown. When you reach zero, they must place their hands on their hips or head. Those who have not completed the calculation should sit, as should those with their hands in the incorrect position (hips). Of those remaining, select two or three students and invite them to explain their strategy for completing the mental calculation. For example, Declan says that he multiplied 3 x 20 and got 60, then took off the 3 x 3, which is 9, and 60 – 9 = 51; or Cathie says 3 x 10 = 30 and 3 x 7 = 21 and 30 + 21 = 51. Second problem: What is half of 96 plus 3? Same procedure. You will find that the seated students will all be doing the problem — congratulate and encourage this. Continue on for one or two problems such as: What is 3 x 16 + 11? What is 5 x 14 – 22? Final problem: What is 4 x 13 – 2? When playing this game for the first time, it can be fun to finish with a problem where the answer is exactly 50, or whatever magic number you’re using. Warn students before the final problem that there are to be no questions. Watching as students’ hands move up, then down, then up, then down, as they try to work out where their hands should be can be quite amusing. I have seen some very creative responses, and it’s a great way to eliminate a number of students if there are many remaining by the final problem.
Variations Vary the magic number as students become more proficient at their mental computation. Decrease the time allowed for making the calculation (being mindful of trying to give all students a feeling of success in the activity). Give students who really struggle with mental computation a calculator. I have done this on a number of occasions, and the other students have been excellent in realising that this is a fair thing to do. I realise that this precludes the student or students from using mental computation, but for some students recalling the number and operations, pressing the correct buttons, understanding the answer and then determining where to place their hands is challenge enough.
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Maths on the Go Book 2 MENTAL COMPUTATION
Activity 4
FOCUS AGE LEVEL DURATION EQUIPMENT
What is the Question? Number, working backwards Years 2 to 6 (7- to 12-year-olds) 5 to 10 minutes None
Objectives To have students work backwards, starting with the answer and attempting to develop (mentally) a problem/question that will produce that answer. To have students appreciate that maths is not always about one correct answer.
Organisation A whole-class activity.
Introduction This is a very effective and worthwhile activity to use with students on a regular basis (say, once every one or two weeks). Each time you play it, students will become more creative and think more broadly about numbers and their applications.
Procedure Think of a number — any number! Let’s say you have some Year 4 students in front of you, and choose 24. Tell students the answer is 24. What could the question be? Before seeking responses, I tell students it’s just like working backwards: you know the answer is 24 — now think of a question that will get you to the answer. Advise students that every single person in the class is going to be asked. Be positive about all correct responses, but particularly encourage those questions that are creative and reflect broader thinking about number. Possible questions for the answer ‘24’ could be: ‘What is 6 x 4?’; ‘What is 3 x 10 – 6?’; ‘How many hours are there in a day?’; ‘What is half of 48?’. Specify that each response must begin with a question word. Make sure you ask every student. If a student does not have a question ready to go, I make no fuss and simply tell them that I’ll come back again later — and I always do. This is one of those open tasks where every student can contribute at their own level: as long as a response is mathematically accurate it is accepted and noted. Don’t worry if students are a little rusty the first time you conduct this activity. You will invariably get many a ‘What is 23 + 1?’ type question, but persevere, they do get better. By the third or fourth time — particularly if you have been very positive about those responses where students have thought broadly — you will get some very insightful and enlightening questions.
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Maths on the Go Book 2 MENTAL COMPUTATION
Activity 5
The Number Formerly Known As . . .
FOCUS AGE LEVEL DURATION
Number Years 2 to 6 (7- to 12-year-olds) All day, or as long as you can handle the pressure of not being able to say the number formerly known as . . . EQUIPMENT None
Objective To have students look for alternative ways of orally identifying a number.
Organisation A whole-class activity. No special arrangements necessary.
Introduction This activity came about one day when I was writing the numbers 1 to 9 on the board and inadvertently left out the number 6. When one of the students pointed this out, I replied that I had done it on purpose. I’d woken up this morning and decided that I really did not like the number 6 at all, and that the number formerly known as 6 was banned from being used in any classroom that I was in that day. A girl near the front of the room asked the obvious: ‘So we can’t say or write the number 6?’ I immediately covered my ears in mock horror (as did a number of students — which was really very funny), screeching ‘Don’t say that number — it’s banned!’
Procedure Simply choose a number that you are intending to ban from all use for a day or a set portion of the day. You and your students must now avoid saying or writing that number (including in calculators) and must therefore find alternative ways of saying or writing it. For example, if the banned number is 9, alternatives could be: 10 – 1; 3 x 3; the number between 8 and 10; the last single digit number; 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1; how many lives a cat is supposed to have, and so on. Each alternative can only be used in the classroom once, and cannot be repeated.
Variations You may wish to cover all manifestations of the banned number with self-stick notes, tape or paper. I have seen a room in which the number 7 was covered up on the number line, on the 1 to 100 chart, on the clock, in the date — everywhere! Postscript: The first day I banned a number — the number 6 — one of the girls from the classroom where the ban had occurred came running up behind me as I was leaving the school, tugged on my jacket and said, ‘Mr V. It’s after school, so — six, six, six, six, six’ and ran off laughing. I had a chuckle as well.
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Maths on the Go Book 2 MENTAL COMPUTATION
Date Maths
Activity 6
FOCUS AGE LEVEL DURATION EQUIPMENT
Number Years 3 to 6 (8- to 12-year-olds) 10 to 15 minutes Stopwatch (optional)
Objective To develop mental computation skills and the ability to think logically to solve problems.
Organisation A whole-class activity that can be conducted in pairs, in small groups or individually. I discourage the use of pens and paper.
Introduction This activity can effectively be used once a week or every two weeks. It can produce some frustration born of lack of success in solving some of the problems, but this frustration can be the source of some very inventive and creative solutions. Too much frustration is not a good thing, though, so be ready to give a clue or hint — but only when absolutely necessary.
Procedure Place today’s date on the board, for example 10/04/07. Set up the board so it looks like this: 10/04/07 1. =1 2. =2 3. =3 4. =4 5. =5 6. =6 7. =7 8. =8 9. =9 10. = 10
11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
= 11 = 12 = 13 = 14 = 15 = 16 = 17 = 18 = 19 = 20
Inform students that their challenge, collectively, is to make an equation for each of the numbers 1 to 20 — using only the numbers in today’s date. Students can change the order of the numbers. For example, the 4 and the 0 can be 40. The 1 and 4 can be used as 14. The 1, 0 and 0 can be 100. However, if there is only one 4, say, you can only use 4 once in any single equation — 4 ÷ 4 x 1 = 1 would not be valid. To encourage creativity, I tell Year 5/6 students that any three-number equation that is mathematically correct will earn them 1 point, but any five-number
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