Maths on the Go
Also available Maths on the Go
2
Book
i t ivi
r o f es
a
ct
mat Rob Vingerhoets
ISBN 1420209310 ISBN 9781420209310
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 30 minute
! r e l l e s t s Be
1 1
Book
Book 1
The activities in Maths on the Go Book 1: • 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 four main content strands: Number, Chance and Data, Measurement and Space • can be readily used as part of any maths program • are perfect for revision or extension.
y r a l e m v 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
Rob Vingerhoets MathsOnTheGo_Bk1_78808_cvr_prs.indd 1
10/19/20 4:57 PM
5Book 1
5 to 30 minute activities for all primary levels • Space • Number • Measurement • Chance and Data
Rob Vingerhoets
803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 1
14/07/15 9:47 AM
Dedication To my wonderful wife Margaret for providing enough space and time for me to get this book finished. To Garry Chapman for his help in developing some of the worksheets contained in this book. To Mick Ymer for helping develop some of the activities contained in this book. To my eldest daughter Maddie for pestering me sufficiently to mention her in this book.
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 2001 by Macmillan Science and Education Australia Pty Ltd Copyright © Rob Vingerhoets 2001 National Library of Australia Cataloguing-in-Publication data Vingerhoets, Rob. Maths on the go teacher resource book ISBN 978 0 7329 7880 8 ISBN 0 7329 7880 7. 1. Mathematics – Study and teaching (Primary). 2. Mathematics – Problems, exercises, etc. I. Title. 372.7044 Text design by Domenic Lauricella Cover design by Cliff Watt Illustration on page 65 by Boris Silvestri Printed in Australia by Courtney Brands 1 2 3 4 5 6 7 25 24 23 22 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 Copyright Act 1968 of Australia (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.
MathsOnTheGo_Bk1_78808_imp_prs.indd 2
10/22/20 2:22 PM
Contents Introduction 5 Activity Focus Level
Duration (minutes)
Equipment/ Worksheet
Page
Number Activities 1 Tell Me Something
Numbers in everyday life
Years 0–6
5–15
✗
7
2 Number Mastermind
Logic, place value, numeration
Years 0–6
10–30
✓
8
3 What’s My Number?
Logical thinking
Years 4–6
5–15
✗
10
4 Four-move Wipe-out
Place value
Years 2–6
10–30
✓
11
5 The Calculator Versus
Mental calculation
Years 2–6
10–30
✓
13
6 Maths with a
Fractions, operations, measurement
Years 3–6
10–15
✓
15
Metre Ruler
7 Just Gridding
Place value, numeration
Years 2–6
20–30
✓C
17
8 Equator
Equations
Years 4–6
15–30
✓
21
9 Order Order
Place value
Years 3–6
20–30
✓C
23
10 BTs (Brain Teasers)
Logic, working mathematically
Years 3–6
10–30
✗C
27
11 Probability Lines
Probability
Years 1–6
20–30
✗C
31
12 Deal a Diamond
Probability
Years 3–6
15–30
✓C
35
13 Ninny Ninny
Probability
Years 2–6
20–30
✓C
37
14 The Tough 6
Probability
Years 0–3
20–30
✓C
40
15 Greedy Pig
Probability and luck
Years 2–6
20–30
✓
43
16 Venn Diagrams
Representing data
Years 0–6
15–30
✓
44
About…
the Computator
Chance and Data Activities
803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 3
14/07/15 9:47 AM
Activity Focus Level
Duration (minutes)
Equipment/ Worksheet
Page
Measurement Activities 17 Beat the V
Estimation of length, capacity,
Years 4–6
30–45
✓C
46
18 Take 10 Seconds
Time, decimals
Years 4–6
10–30
✓C
49
19 Grab the Ruler
Measurement of distance
Years 4–6
5–10
✓
52
20 Be There in a Minute
Judging time
Years 2–5
1–10
✓C
53
21 Where’s the Letter?
Geometry, spatial terminology
Years 4–6
20–30
✗C
56
22 Back to Back
Shape, spatial terminology
Years 2–6
10–30
✓
59
23 Hear the Shape
Shape recognition
Years 0–6
10–30
✓
60
24 Give Me Some
Directions, shape
Years 0–6
10–30
✓
62
25 I Hate Maths!
Number, space, measurement in everyday life
Years 0–6
15–30
✗C
64
26 Word Football
Adding, dividing, spelling
Years 3–6
15–30
✓
66
27 0s and Xs—With
Logic, grid referencing
Years 1–6
10–30
✓
68
28 Who Wants to be
Mental computation
Years 3–6
10–30
✗
70
volume, time
Space Activities
Direction
General Activities
a Difference
a Mathematician?
803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 4
14/07/15 9:47 AM
Introduction After we have given daily lessons in society and the environment, science, technology, English, sex education and drug education, conducted P.E. sessions and rehearsals for the school concert, incorporated an integrated curriculum, watched for declining spelling and numeracy skills, done peer tutoring, developed personal programs and written reports, how are we as teachers expected to deliver a balanced maths program that allows for Measurement, Space, Number, and Chance and Data as well? How can we possibly fit it all in? I don’t have the answer to meeting the myriad of curriculum demands made upon teachers, but I do know it is possible to squeeze a little more maths into the same amount of time. It is all a matter of efficiency. Is it efficient to teach multiplication followed by area/perimeter/volume work? Is it efficient to teach division and then do work on averages? Why revise addition and subtraction and then have your students collect and tally data and analyse it? With the amount of content we are expected to deliver to our students, we simply have to become more efficient teachers of mathematics. This means that the days of teaching four days of pure number and making Friday the day we do applied should be long gone. For example, teaching children how to multiply and then finding contexts or applications of that algorithm is not efficient. However, it is efficient to do area work as part of your Measurement program and then have the children see the need to use multiplication to solve interesting and relevant problems. I can’t remember the last time I taught any of the algorithms out of a suitable context (apart from games). When working on averages (one of the few very good applications of division), I may note a number of students experiencing difficulty with division. In this case I take them for a pure number session dealing with some methods they can try. Generally, this works well as the children feel challenged to resolve their difficulties and are keen to learn any method that may help them. Apart from Term 1, when I concentrate strongly on place value, I rarely conduct pure number sessions more than once a week. By Term 2, I generally only devote an hour per fortnight to pure number sessions. These are usually logic problem-solving, cooperative problem-solving tasks and pattern/sequence problems where more than one method or answer occurs and where the correction of the problems is the real teaching. All other pure number sessions occur in context. Measurement, and Chance and Data are the two content strands that allow you to teach a significant percentage of your Number program. This is part of the beauty of the Chance and Data strand. Don’t dismiss this strand as being narrow. It does have depth and substance and it is frequently a very enjoyable and challenging strand to teach and learn.
5 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 5
14/07/15 9:47 AM
Children love the work and the meaningful and relevant contexts for mental computation, written algorithms, calculator work, fractions/ decimals/percentages and pattern work are all there. Get into your Measurement, and Chance and Data programs and much of your Number program will look after itself. You will teach number as you are engaging the children in activities and experiences that motivate them. So if we genuinely want to be more efficient teachers of mathematics, we need to make spare moments worthwhile and productive.
Maths on the Go Activities There are often times when you think: ‘Now what can I do with the kids that’s productive? Every minute of the teaching day is precious, so I need to make the most of these occasions.’ It may be the 30 minutes between school assembly and morning recess, the 20 minutes between Library and lunch or the 5 minutes at the end of the day. Whenever the time, the activities in this book are very worthwhile and relevant maths activities that are a real alternative to the perennial hang-man or 20 questions. The activities require a minimum of equipment, and in some cases none at all. Where a worksheet is required it is given after the activity. The activities themselves range from Years 0 to 6 (or beyond) and cover the four main content strands of Number, Chance and Data, Space, and Measurement. The activities are not simply one-offs. Hopefully, you and your students will want to do them again and again because they are enjoyable and beneficial. The activities can be used as part of your current maths program or as revision or simply as enjoyable and worthwhile challenges that are easy to organise and implement. The book is divided into the four content strands. For each activity there is a brief summary at the top of the page giving the focus, age level, duration and equipment needed. There is then a description of the objectives, how the activity is organised, the procedure and then alternative ideas for follow-up. Some of the activities also include photocopiable worksheets. Enough banter. Here’s the book––enjoy it!
6 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 6
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Tell Me Something About...
Activity 1
FOCUS AGE LEVEL DURATION EQUIPMENT
Numbers in everyday life Years 0 to 6 (5- to 12-year-olds) 5 to 15 minutes None
Objectives 5 5
To encourage students to be aware of numbers in their everyday lives and to think of numbers in ways other than as a means for counting. To think beyond the obvious and look for the special attributes or connections to do with particular numbers.
Organisation A whole-class activity.
Introduction Begin with something like: ‘I want you to think about the number 8. In one minute I am going to ask each of you to tell me something that is special about the number 8.’
Procedure I tend to work randomly around the class so the children don’t know when their turn will be. I appreciate and encourage any response but I particularly praise efforts that are creative and reflect some thought. Here are some responses you are likely to receive:
‘It is 1 more than 7.’ ‘It is my lucky number.’ ‘4 plus 4 equals 8.’ ‘My brother/sister is 8.’ ‘It’s hard to spell.’ ‘It’s the body of a snowman.’
‘It’s 2 circles on top of one another.’ ‘It is the square root of 64.’ ‘It is symmetrical.’ ‘It’s half of 16.’ ‘It is a backwards 3 and a forwards 3 put together.’ ‘There are eight 8s in 64.’
I have used this activity with 5- to 12-year-olds. The procedure is fundamentally the same and the responses tend to be similar, though the younger students are often more creative. Encourage this creativity while acknowledging all responses. I tend to use the numbers 1 to 10 for the activity, although numbers from 11 to 20 or specific ones such as 100 or 99 work well with the older classes.
Variations This simple activity can also be used for shapes. For example: ‘Tell me something special about a circle.’ ’Tell me something special about a triangle.’
7 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 7
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Number Mastermind
Activity 2 FOCUS AGE LEVEL DURATION EQUIPMENT
Logic, place value, numeration Years 0 to 6 (5- to 12-year-olds) 10 to 30 minutes A board with a grid drawn on it. Some children need their own grid to help work out the most likely combinations; others simply follow it on the board. This may be a grid for Years 4 to 6:
Number Mastermind Tens of thousands
Thousands
Hundreds
Tens
Ones
Objectives 5 5
To encourage children to think logically, learning from information already gathered. To provide a context for children to read and say large numbers.
Organisation A whole-class activity.
Introduction Tell the children that this is a game like Mastermind except with numbers. They try to work out the number that you have thought of in a given number of attempts.
Procedure 5
5
Assuming you have a middle primary year, think of a 4-digit number (for example, 5803), then write it down on a piece of paper or on the palm of your hand (this may not set the best of examples but it adds a little to the drama and mystique!). Now draw up a grid such as this: Thousands
Hundreds
Tens
Ones
Guess No. 1 Guess No. 2 Guess No. 3 Guess No. 4 Guess No. 5
This means the children have five guesses in which to work out the number. Five guesses work extremely well whether the children are guessing a hundreds or hundreds of thousands number.
8 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 8
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
5 5
5
Inform the class that your number is made up of the digits 0 to 9 but that none is repeated. There won’t be, for example, two 5s or two 9s in your number. Tell the students that if they guess a number correctly, it means it is in the exact matching place value position and you will place a tick (✓) next to the number. The message is that this number should not be moved. If they have guessed any other numbers b ut not in the correct matching place value position, place o next to those numbers. The message is to try that number in a different position. Finally, if a number they have chosen is not in your number at all then place ✘ next to that number. The message is simple: don’t bother trying that number again. Encourage someone to have the first guess. This guess should be the least threatening as there is nothing to lose. If some of the numbers are incorrect, the individual or the class may be disappointed but point out that this is very helpful because you now know which numbers not to try.
A sample game The secret number is 5803. The first student tries 7543. Write the number in the grid alongside Guess No. 1. Place a cross next to the 7 because there is no 7 in your number. Place a circle next to the 5 because there is a 5 in your number but it is not in the correct place value position. The number 4 is not in your number so place a cross next to it. The 3 receives a tick because it is in the precise place value position. Guess No. 1
Thousands
Hundreds
Tens
Ones
7✘
5o
4✘
3✓
After some thinking time, choose someone to volunteer the second guess. This person should realise that there is no point including a 7 or 4 in their number but that they should leave the 3 where it is and move the 5 to a new position. The game then proceeds with you encouraging the students to think logically until five guesses are complete. The complete game might look something like this: Thousands
Hundreds
Tens
Ones
Guess No. 1
7✘
5o
4✘
3✓
Guess No. 2
6✘
2✘
5o
3✓
Guess No. 3
5✓
1✘
8o
3✓
Guess No. 4
5✓
8✓
9✘
3✓
Guess No. 5
5✓
8✓
0✓
3✓
Variations This game can be played with all years. In the lower years, where you may be playing it in hundreds or perhaps thousands, it is wise to give the students an indication of the numbers that the chosen number comes from. For example, if you choose 751 you may either increase the number of guesses or restrict the number of digits from, say, 1 to 7. With the upper primary years make Number Mastermind more challenging by playing in the tens of thousands or hundreds of thousands in four guesses.
9 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 9
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Activity 3 FOCUS AGE LEVEL DURATION EQUIPMENT
What’s My Number? Logical thinking Years 4 to 6 (9- to 12-year-olds) 5 to 15 minutes None
Objective For students to think logically and to use questioning strategies, such as bigger than/ smaller than, odd/even, or divisible by 5, to ascertain a goal number.
Organisation A whole-class activity.
Introduction This game encourages students to ask logical questions to deduce the number you have chosen. Seven to 10 guesses seem to be the most appropriate for a range of numbers between 1 and 100, and 12 to 15 guesses for numbers between 1 and 1000.
Procedure Explain to the class that it has to guess a particular number that you have chosen. Tell the students the number of guesses that they are allowed. Now encourage them to think of questions that will immediately eliminate a whole range of numbers in a single try.
Example Pick number 33, tell the class your number is between 1 and 100 and then ask the students if they can think of a question that gets rid of half of the numbers in one go. If your hints have not worked, tell the students that the number can only be an odd or an even number and then ask them what question they could ask knowing this. At this point, depending on the age group, keep encouraging questions that eliminate large groups of numbers in one go. If not forthcoming, indicate that they could ask questions to do with smaller than (<) or bigger than (>). Knowing that the number is odd and between 1 and 100 may provide the logical prod for someone to ask:
‘Is the number smaller than or larger than 50?’ This should prove the catalyst for a host of ‘is it smaller than’ or ‘is it bigger than’ questions. The quality of the questions will depend on the logical grasp the students have of the activity. Encourage them to think not just of ‘smaller or bigger than’ questions but of the most efficient or effective questions. For example, if the students listen carefully and the questions are logically thought out, such as ‘Is it smaller or bigger than 25?’, it will not be long before they discover the number is between 25 and 50. And from there they can quickly whittle it down to 33.
Variations Ensure you try numbers that are suitable for your year. With the older years choose numbers between 1 and 1000, or between 1 and 50 where the number is a decimal into tenths, or a number that is a decimal/fraction into the hundredths between 3 and 4.
10 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 10
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Activity 4 FOCUS AGE LEVEL DURATION EQUIPMENT
Four-move Wipe-out Place value Years 2 to 6 (7- to 12-year-olds) 10 to 30 minutes A calculator per person, or a calculator per pair
Objective To reinforce and extend place value concepts and skills.
Organisation A whole-class activity.
Introduction This activity has been around for longer than I’d like to admit. Nonetheless, it is a valid and relevant activity to revise and develop place value skills and concepts. I have played this game with students from Years 2 to 6. The object is to try to keep up with the teacher for four distinct moves and attempt to be up with the teacher’s number at the end of the activity.
Procedure 5 5 5
If possible, all students should have a calculator. If not, try to have one calculator between two. Write your initial number on the board, for example, 7863. Ask the students to enter this number into their calculators.
Move 1
7863 0
Ask the class to wipe out the number 6 so that there is a 0 where the 6 was. Depending on the students’ level, you may need to provide clues such as: ‘If I am getting rid of the number 6 will I be adding or taking away?’ ‘If I am taking away, which button does the taking away or subtracting?’. Invariably some will press the minus key then the 6. I always like the look on their faces when they see that not only have they not wiped out the 6, but there is now a 5 in its place, and the 3 that was on the end is now a 7. This is why I write the number on the board, because there is usually a chorus of ‘What was the number again?’. Ask those who went directly to the minus 6 to look at the place value position of the 6 so they realise it is in the tens column and so has the value of 6 tens or 60. Therefore minus 60 is what is required to make it 0. Or encourage the students to read the number aloud: ‘It’s seven thousand eight hundred and sixty-three.’ The delight they display when they minus 60 and see that there is a 0 where the 6 was is usually quite evident. This immediate reinforcement or correction of their own work is one of the positive aspects of this activity.
11 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 11
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Move 2
7803 0
Now ask the class to wipe out the 8. Tell them to work out its value first. The students will then realise the 8 is in fact 800, so minus 800 will give 7003.
Move 3
7003 0
or
7003 7100
For the lower years, ask them to wipe out the 3. This is an easy one. For the middle and upper years, ask the students to use just one move to wipe out the 3 and to replace the 0 next to the 7 with a 1. You may need to tell the class that by adding a 1 next to the 7, they are making the number larger. So this time they won’t be using the minus button but the addition button. The 1 next to the 7 will be plus 100 and the wipe-out of 3 means they must add 97. The answer is 7100.
Move 4
7000 0
7100 or 3550
For the lower years, tell them to wipe out the number 7 in 7000. Explain that it is 7000, which means minus 7 and three 0s. For the middle and upper years, their fourth move could be to wipe out the 1 in 7100 and at the same time turn the 7 into a 9. The 9 would be 9000; from 7100 to 8000 is plus 900. From 8000 to 9000 is plus 1000, so plus 1900 should wipe out the 1 and make the 7 a 9. The result is 9000. An alternative may be to turn the 7100 into 3550 in one move. Some children will realise that this is half the original number, so they simply divide 7100 by 2. Others may recognise that 3550 + 3550 = 7100 so they will start with 7100 and subtract 3550. Others may multiply 7100 × .5.
Variations 5 5
5
With the older classes, you can start with numbers such as 7 832 534 and play five-move wipe-out. 1. Wipe out the 5. 2. Wipe out the 8. 3. Wipe out the 2. 4. Wipe out both 3s in one move. 5. 7 000 004 remaining, so wipe out the 4 and turn the 7 into an 8. With the younger classes, start with a 3-digit number, such as 786, and ask them to wipe out the 7. Then pick another number and so on. Alternatively, place them in pairs and ask them to take it in turns to make up a 3- or 4-digit number and to ask their partner to wipe out a number. You can make this version competitive by making the first partner to earn 5 points the winner. One point is earned each time a nominated number is wiped out on the first attempt. Add on (as opposed to wipe out). For middle to upper years, start with the number 10 000. Ask the students to replace the second zero from the right with a 5 (10 050), and then the fourth zero from the right with a 7 (plus 7000 = 17 050) and so on.
12
803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 12
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Activity 5
FOCUS AGE LEVEL DURATION EQUIPMENT
The Calculator Versus the Computator Mental calculation Years 2 to 6 (7- to 12-year-olds) 10 to 30 minutes A calculator
Objective To reinforce and extend automatic response and mental calculation skills.
Organisation A whole- or part-class activity.
Introduction This is a worthwhile activity for sharpening mental computation and automatic responses and it also regularly proves that the human brain is quicker than the manufactured device. In the end this is the battle—the proficient computator versus the reliable calculator. Initially it may appear that the person using the calculator has the advantage. This is true when the problems are straightforward, such as 5 × 9. However, with more complex problems, such as what is half of 256 or how many hours in a week, the person using the calculator must also do some logical mathematical thinking to feed the appropriate information into the calculator.
Procedure 5
Choose two students to come to the front of the room. Give one a calculator or let them toss a coin for it.
5
Tell the combatants that you are going to ask some mental computation-type questions and whoever is first to reach three points will be the winner. The first person to answer the question correctly wins the point.
5
Tell the person with the calculator that they must enter every relevant number and command, including the equals button, and wait till the answer appears on the screen before calling out an answer.
5
When I do this activity I have the competitors at the front of the room, the children seated at their tables/desks and I ask the questions from the rear of the room.
5
I usually have another student keep score on the board, so the class can keep track of the contest.
13 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 13
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Here is a sample of some questions for both middle and upper primary.
5
MIDDLE
1.
What is 6 groups of 7?
2.
How many 6s are there in 36?
3.
What is half of 48?
4.
What is 24 plus 26?
5.
How many centimetres in 1 metre?
6.
How many seconds in 3 minutes?
7.
How many days are there in 4 weeks?
8.
What is 8 lots of 8?
9.
What is 40 divided by 5?
10.
If I buy 4 things that each cost 75¢, how much is that altogether?
UPPER
1.
How many 9s are there in 72?
2.
7 times what number equals 56?
3.
What is half of 270?
4.
How many millilitres in 5 litres?
5.
How many days are there in winter?
6.
What is one-quarter of 88?
7.
How many hours in a week?
8.
6x7=?
9.
What is 2000 minus 999?
10.
What is my change from $10, if I buy 4 items that each cost $1.20?
Variations Variations on this activity can be made by changing the type of questions asked to suit your particular year level. You can also ask both students to write the answers on a piece of paper. However, you do not wait for either person to complete a problem before asking the next question. This will get each competitor to write their answers as quickly as possible. After the questions are completed, correct the answer sheets. Discuss the results.
14
803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 14
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
Activity 6
FOCUS AGE LEVEL DURATION EQUIPMENT
Maths with a Metre Ruler Fractions, operations, measurement Years 3 to 6 (8- to 12-year-olds) 10 to 15 minutes A metre ruler for Years 5 and 6 A metre ruler per group of four or five students for Years 3 and 4
Objective To relate number situations to measurement, particularly length, ask a range of related questions and draw observations from the students that revise and extend number skills.
Organisation A whole-class activity. Students should be seated in small groups of four or five at their tables/desks or on the floor.
Introduction Apart from measuring, there are many uses for your metre ruler. The fact that it is 100 cm long means that your students have a wealth of number situations to work with.
Procedure 5
Tell the students that they have a set amount of time (between 10 and 20 minutes works well) to produce as many statements or facts about the metre ruler as possible.
5
Designate one person from each group to record the group’s facts.
5
Provide two or three examples so that each group is aware of your expectations. Examples may include: one-quarter of a metre is 25 cm; 4 × 25 = 100; 10 × 10 cm = 100 cm; 50 cm + 50 cm = 1 m; 500 mm = 50 cm = .5 m; 3/4 of a metre + 25 cm = 1 m; 4 × 15 = 60. The depth and quantity of examples will depend on year level, work completed in maths to this stage and general ability of the group.
5
With the Years 5 and 6 students I go from group to group displaying the ruler. However, they should be able to make conclusions and recall facts about the ruler without actually having it in front of them. (This is essentially a revisional activity.) I have found that Years 3 and 4 students need to have the ruler in front of them so they can actually touch/find/see the facts they wish to record.
15 803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 15
14/07/15 9:47 AM
Maths on the Go NUMBER ACTIVITIES
5
Give clues or hints to any group that is struggling to record facts or is running out of ideas. Clues may take the form of comments such as, ‘Have you thought of some different ways you can make 50?’ or ‘One-quarter is one name for 25 cm; I wonder if you can think of any others?’ or ‘Four groups of how many centimetres would equal 60 cm?’.
5
At the conclusion I ask a representative (not necessarily the recorder) from each group to read out and/or demonstrate on the ruler the best discovery they have made. You may do this for two or three rounds. Don’t be perturbed by laments of ‘But we had that one!’ and reinforce those discoveries that are creative and display some depth of thought.
Variations 5
Use a 1000 mL measuring jug instead of the metre ruler.
5
Set each group a specific target, such as finding at least 10 facts about the ruler. Avoid setting the challenge of being the first group to obtain 10 facts as this invariably leads to facts or discoveries that are very superficial or simplistic.
5
I often simply walk among the students and randomly ask them questions for 5 to 10 minutes as a warm-up session. For example, with my finger on 75 cm I may ask a student to tell me what it is as a percentage or a decimal.
16
803732 Maths on the Go Bk1_Text_OnD_Repr2015 REV.indd 16
14/07/15 9:47 AM