E X P L O R I N G. M A T H S. N U M B E R. L O W E R. P R I M A R Y. Activities, blackline masters & assessment page
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EXPLORING
Calculators Bev Dunbar Activities, blackline masters & assessment pages that are fun and easy to use N U M B E R
L O W E R
P R I M A R Y
8
Introduction Exploring Calculcators
Calculators are an inexpensive, fun tool for mathematical discovery in our classrooms. Young students no longer need to be limited by the size of numbers they can manipulate. They can appreciate the joys of exploring a wide range of mathematical concepts and patterns at an early age. The focus here is on mathematical thinking and problem solving, not just the mechanics of calculation. Using calculators will improve your students’ confidence, as well as assist the development of place-value understanding and operations. This book is a companion to the other Number books in the Exploring Maths series. Here, there are over 60 exciting teaching ideas for developing skills in estimation, numeration and addition and subtraction in particular. The activities will integrate easily with your current numeration and operations activities. Although free exploration and discovery is encouraged, there are sets of 8 workcards for more structured activities for pairs, small groups or even the whole class. These cards can be used by parent helpers or fluent readers. They are written in clear, easy-to-understand language. The many ideas presented here are starting points for further mathematical discoveries. They encourage your students to think for themselves, to be creative and to search for patterns. In other words, your students will become active mathematicians, independent of formal worksheets or textbooks. The activities also cater for a wide range of student abilities. They begin with just pressing buttons to see what happens and end with solving complex “number crunching”. Look forward to exploring the joys of calculators with your students.
Copyright Bev Dunbar Maths Matters 2000 Exploring Calculators ISBN 186509 2207 Published by Blake Education Locked bag 2022 Glebe NSW 2037 Series editor: Garda Turner Illustration and design by Janice Bowles Printed by Printing Creations The blackline masters in this book may be reproduced by the original purchaser for use with their class(es) only.
Contents How to use this book
2
First Explorations
3
Exploring to 20 and beyond
31
Exploring to 99 and beyond
57
Answers
93
Outcome Indicators Record
94
◆ Teaching Ideas
How to use this Book
More than 60 exciting teaching ideas have been placed into 3 sections to assist your planning for individuals and small groups. Each activity provides a clear learning outcome and Teaching Ideas easy-to-follow instructions.
More than 60 exciting teaching ideas have been placed into 3 sections to assist your planning for individuals and small groups. Each activity provides a clear learning outcome and easy-to-follow ◆ Calculators instructions.
For younger students, large, inexpensive calculators are available from a wide range of educational suppliers, Calculators supermarkets, newsagents and post offices. Ideally needfrom a a wide range of educational For younger students, large, inexpensive calculators are you available calculator for each student or at least for Ideally a smallyou need a calculator for each student or suppliers, supermarkets, newsagents and enough post offices. at least one each small group. Most in the same way but be aware that group. Mostforsimple calculators work simple in the calculators same way work but be some do follow different programming rules. Check each suggested program before actively working aware that some do follow different programming rules. with your students. Check each suggested program before actively working with your students. e.g. To take away the same number each time (e.g. - 2): Identify a starting number (e.g. 20) then press 2 0 - - 2 then continue to press = . (Some calculators only require 20 - 2).
Blackline Masters
There are three types of blackline masters.
1. Sample worksheets
Pattern? ... ... What s My ... ... 5 ... 7
3
11 1
Pattern? ... ... What s My ... ... 3 ... 17 2 5 11
e.g. What’s My Pattern? (page 59) These provide structured examples of activities to support your free exploration.
Pattern? ... ... What s My ... ... 9 ... 4
14 1
9
Pattern? ... ... What s My ... ... 3 ...
2. Multi-use worksheets e.g. Guess What’s Next (page 30) These can be used over and over again. Your students can create their own activities with these.
25 3 9 17
Pattern? ... ... What s My ... ... 6 ... 35 4 13 24 2
4
8
Outcomes Indicator Record
The complete list of learning outcomes is available on page 94. Use this to record individual student progress.
2
Exploring Calculators
Guess Wh at s Nex t Find 1 les s. My Gu ess
s Calculator Exploring
59
Guess Wh at s Nex t Fin
3. Workcards e.g. Race Me (pages 80 - 83) The cards are generally graded from 1 - 8. The language is simple and easy to follow. Parent helpers or fluent readers can use these for group work.
d 1 mo re.
My Gu ess
... ... ... ... ...
Pattern? What s My 1
Guess Wh at s Nex t Fin
d 1 mo re.
My Gu ess
Guess Wh at s Nex t Fin d 1 less.
My Gu ess
30
Exploring Calculator s
Three in a Row What are you trying to do?
◆ Recognise and name calculator numerals 0 - 9 (C3). ◆ Recognise the position of each numeral 0 - 9 on a calculator (C3).
How many can play? ◆ 2 players.
What do you need?
◆ Two large pictures of a calculator (BLM p.5). ◆ Two sets of small calculator digit cards (BLM p.14 - cut into 20 cards). ◆ A small pile of counters. ◆ A calculator (face down to one side).
How do you play?
◆ Shuffle the cards and place them face down in the centre.
◆ Take the top card in turn and place it on your calculator picture in the correct position. ◆ Try to be the first player to get 3 cards in a row, column or diagonal in the matching positions as on a calculator. ◆ Use the hidden calculator to check.
e.g.
◆ Repeat until someone has won five counters.
Variations
◆ Snap Shuffle 4 sets of calculator digit cards (2 copies of BLM p.14). Deal them out to each player. In turn, reveal your top card. Call out ‘Snap’ if 2 cards match. ◆ Largest Shuffle 2 sets of calculator digit cards. Deal them out to each player. In turn, reveal your top card. Win a token if your card is the largest number.
◆ Get in Order Shuffle 2 sets of calculator digit cards. Select any 3 cards at random. Sort into order from the smallest to the largest number. Repeat using 4 or more cards. Exploring Calculators
13
0 2 4 6 8 14
Exploring Calculators
0 2 4 6 8
1 3 5 7 9
1 3 5 7 9
Beat the Calculator What are you trying to do?
◆ Practise +/- quick recall facts to 10 (C10).
How many can play?
◆ Pairs, up to the whole class.
What do you need?
◆ A calculator for each pair. ◆ Identical ‘Beat the Calculator’ workstrips for each partner (BLM p.48, cut into 8 strips). (NB: The top 4 strips show facts to 5. The bottom 4 strips show facts to 10). ◆ Pencils.
How do you play?
◆ Calculators can help you practise adding and taking away. ◆ Make sure you have the same Beat the Calculator strip as your partner. ◆ One player uses a calculator to work out the answers. The other player uses his/her head. On a signal, you both start together. ◆ When you have finished, check your answers together. ◆ Who was the fastest?
Circle this if you used your head and finished first.
Underline this if the player using the calculator finished first. Circle this if you used the calculator and finished first.
Underline this if the player using his/her head finished first.
◆ Try another number strip. Does the player with the calculator always win?
Variation
◆ Write your own 10 questions for another pair to answer.
Exploring Calculators
47
2 1 5 2 4 0 1 3 4 1
Beat the calculator
+ + + + + + + + + +
3 2 0 2 1 3 3 2 0 1
/10
Number correct
5 1 4 2 3 0 4 3 9 7
Beat the calculator
+ + + + + + + + + +
Number correct
3 7 6 5 4 8 4 6 0 1
/10
5 4 5 3 1 5 2 5 3 4
Beat the calculator
-
0 2 3 2 0 5 2 4 1 3
/10
Number correct
Beat the calculator
10 8 6 7 9 6 10 9 6 8
-
Number correct
0 2 4 5 4 5 3 6 5 4
/10
0 4 2 3 5 2 4 5 3 4
Beat the calculator
+4 -1 +3 -0 +0 -2 +1 -3 +1 -2
Number correct
6 8 2 9 5 6 7 7 9 8
/10
Beat the calculator
+3 -1 +7 -4 +3 -2 +3 -4 +1 -8
Number correct
/10
Beat the calculator
1 5 2 4 5 3 1 5 2 3
+3 -5 +2 -3 +0 -2 +4 -3 +3 -0
Number correct
1 8 3 8 7 9 1 6 2 8
/10
Beat the calculator
+7 -5 +4 -6 +0 -5 +8 -6 +7 -0
Number correct
/10
Can You Make It? What are you trying to do?
◆ Use a calculator to solve mixed number problems (C16).
How many can play? ◆ Pairs, or small groups.
What do you need?
◆ Calculators. ◆ ‘Can You Make It?’ workcards (BLMs p.68 - 71, each cut into 2 cards and laminated).
How do you play?
◆ Sometimes it can be faster to calculate the answers to number problems in your head.
◆ Work with a partner. You need one workcard between you. One player will use a calculator, the other player will use his/her head. ◆ Challenge each other to make it to the final answer first. Is the player with the calculator always the fastest? ◆ Compare answers. How do you know which answer is correct?
Variations
◆ Write your own Can You Make It? instructions for another team to use.
◆ Use one of the cards as a Class Challenge. Ask everyone to close their eyes while you read out the steps. Can they work out their answer just using their head? Check with a calculator.
Exploring Calculators
67
68
Exploring Calculators
5
2
x
=
1
Press
-
5
4
+
-
6
+
-
2
+
0
0
0
0
5
1
2 6
+
Press
+
-
-
=
4
3
1
2
x
-
3
+
1
0
0
0
0
0
0
0
Press
5
Press
7
Can you make it?
Can you make it?
2
Exploring Calculators
69
2
1
3
+
+
Press
-
-
=
5
4
6
+
-
3
+
5
0
0
0
0
0
3
2
Press
+
-
+
-
=
2
3
6
5
5
x
-
7
+
1
0
0
0
0
0
0
0
Press
0
Press
5
Can you make it?
Can you make it?
4
70
Exploring Calculators
2
1
6
+
+
Press
-
-
=
2
4
1
+
-
3
+
0
5
5
5
5
5
5
5
5 3
1
+ + Press
-
-
=
2
3
7
+
-
6
+
3
5
5
5
5
5
5
0
Press
0
Press
2
Can you make it?
Can you make it?
6
Exploring Calculators
71
3
2
5
+
+
Press
-
-
=
3
4
1
+
-
2
+
0
4
0
0
2
0
2
7
2 4
+
Press
+
-
-
=
1
3
5
2
x
-
5
+
6
0
5
5
0
0
0
Press
0
Press
4
Can you make it?
Can you make it?
8
Race Away
What are you trying to do? ◆ Practise extended +/- quick recall facts to 99 (C15).
How many can play?
◆ The whole class in teams of up to 5 players.
What do you need for each team?
◆ One calculator. ◆ One race caller. ◆ ‘Race Away’ cards (BLM p.85, cut into 8 cards). ◆ Teacher’s Answers (BLM p 93). ◆ A start and finish line 10 m apart.
How do you play?
◆ Play outdoors or in a large hall. Divide the class into teams. Give each team leader a calculator. The Race Callers stand at the finish line with the Race Away cards, while the teams line up behind the 10 m line. ◆ On the word “Go”, the first person from each team races down to the Callers. The Callers say the first problem to be solved with the calculator (eg. from Set 1: 17 + 20). The first person then races back to his/her team, calculates the answer, passes the calculator to the second person, then runs to the back of the team. ◆ Repeat for each player, until all Caller’s instructions have been calculated.
◆ At the end of the race the last player reports their team’s final answer to the teacher. This answer should match the final answer on the teacher’s sheet. ◆ Try to be the fastest team to have the correct finishing answer.
Variation
◆ Make up your own Race Away questions.
84
Exploring Calculators
Exploring Calculators
85
- 42
- 50
+ 14
x2 + 22
x2
+ 25
Press 16 + 40
Press 12 + 28
+ 39
SET 6
-27
SET 5
+ 16
x2 x2
- 47
- 40
+ 33
Press 14 + 26
Press 17 + 20
+ 35
SET 2
SET 1 +9
SET 7
- 16
x2
- 32
Press 13 + 33 + 14
+ 19
-59
x2
Press 13 + 28
SET 3 + 35
SET 8
+ 23
x2
- 74
Press 18 + 50 + 32
- 25
+ 13
- 30
Press 15 + 37
SET 4
ANSWERS Page 59
3
5
4
9
13 1
7
11
9
17
24
2
What’s my Pattern?
11
17
14
25
35
4
15
23
19
33
46
8
19
29
24
41
57
16
23
35
29
49
68
32
27
41
34
57
79
64
Page 62
Beat the calculator
Page 63
Beat the calculator
Page 64
Beat the calculator
10 - 7 = 3 10 - 5 = 5 10 - 10 = 0 10 - 8 = 2 10 - 4 = 6 10 - 6 = 4 10 - 0 = 10 10 - 1 = 9 10 - 9 = 1 10 - 3 = 7
2 + 9 = 11 7 + 4 = 11 5 + 6 = 11 10 + 7 = 17 8 + 5 = 13 9+0=9 1+8=9 6 + 7 = 13 4 + 9 = 13 10 + 3 = 13
15 + 9 = 24 12 + 8 = 20 17 + 6 = 23 18 + 3 = 21 12 + 9 = 21 14 + 8 = 21 11 + 5 = 26 13 + 7 = 20 18 + 7 = 25 17 + 9 = 26
20 - 7 = 13 20 - 5 = 15 20 - 10 = 10 20 - 8 = 12 20 - 4 = 16 20 - 6 = 14 20 - 0 = 20 20 - 1 = 19 20 - 9 = 11 20 - 3 = 17
3x2=6 6 x 2 = 12 0x2=0 5 x 2 = 10 2x2=4 8 x 2 = 16 4x2=8 7 x 2 = 14 1x2=2 9 x 2 = 18
Page 68-71
Can you make it? 1. 50 2. 100 3. 40 4. 60 5. 70 6. 25 7. 80 8. 60
10 x 10 = 100 3 x 10 = 30 8 x 10 = 80 2 x 10 = 20 4 x 10 = 40 7 x 10 = 70 1 x 10 = 10 5 x 10 = 50 9 x 10 = 90 6 x 10 = 60
31
47
39
65
90
35
53
44
73
101
128 256
Page 60
(add 4)
(add 6)
23
21
19
17
15
13
11
9
(minus 2)
81
78
75
72
69
66
63
60
57
(minus 3)
74
(add 5)
(add 8)
66
(add 11)
92
(double the number)
What’s my Pattern?
25
45
69
58
83
41
64
50
74
37
59
42
65
33
54
34
56
29
49
26
47
25
44
18
38
21
39
10
29
17
34 2
20
13
(minus 5)
(minus 8)
(minus 9)
(minus4 )
17 - 7 = 10 12 - 5 = 7 19 - 10 = 9 13 - 8 = 5 11 - 4 = 7 15 - 6 = 9 20 - 10 = 10 14 - 7 = 7 16 - 9 = 7 12 - 3 = 9
6 + 5 = 11 15 - 5 = 10 9 + 4 = 13 14 - 8 = 6 5 + 6 = 11 16 - 9 = 7 8 + 5 = 13 15 - 6 = 9 2 + 9 = 11 13 - 8 = 5
1 + 10 = 11 4 + 9 = 13 7 + 8 = 15 10 + 5 = 15 8 + 3 = 11 0 + 10 = 10 6 + 9 = 15 8 + 4 = 12 5 + 7 = 12 10 + 10 = 20
19 - 9 = 10 14 - 5 = 9 17 - 10 = 7 15 - 6 = 9 14 - 4 = 10 13 - 5 = 8 18 - 10 = 8 15 - 9 = 6 11 - 8 = 3 13 - 7 = 6
8 + 8 = 16 17 - 9 = 8 5 + 6 = 11 18 - 9 = 9 6 + 5 = 11 14 - 7 = 7 10 + 3 = 13 15 - 8 = 7 8 + 9 = 17 17 - 8 = 9
4 + 9 = 13 16 - 7 = 9 9 + 8 = 17 14 - 5 = 9 8 + 6 = 14 15 - 7 = 8 8 + 7 = 15 16 - 6 = 10 10 + 9 = 19 15 - 6 = 9
26 + 6 = 32 25 + 5 = 30 29 + 3 = 32 24 + 7 = 31 25 + 9 = 34 26 + 6 = 32 28 + 8 = 36 27 + 5 = 32 22 + 9 = 31 23 + 7 = 30
30 - 3 = 27 30 - 8 = 22 30 - 1 = 29 30 - 9 = 21 30 - 2 = 28 30 - 5 = 25 30 - 4 = 26 30 - 0 = 30 30 - 7 = 23 30 - 6 = 24
36 + 5 = 41 35 + 5 = 40 39 + 4 = 43 34 + 8 = 42 35 + 6 = 41 36 + 9 = 45 38 + 5 = 43 35 + 6 = 41 32 + 9 = 41 33 + 8 = 41
40 - 6 = 34 40 - 9 = 31 40 - 0 = 40 40 - 4 = 36 40 - 5 = 35 40 - 2 = 38 40 - 8 = 32 40 - 3 = 37 40 - 7 = 33 40 - 10 = 30
43 + 5 = 48 47 + 7 = 54 48 + 3 = 51 44 + 9 = 53 41 + 5 = 46 40 + 0 = 40 47 + 6 = 53 45 + 8 = 53 42 + 7 = 49 49 + 8 = 57
50 - 5 = 45 50 - 3 = 47 50 - 1 = 49 50 - 6 = 44 50 - 9 = 41 50 - 0 = 50 50 - 10 = 40 50 - 2 = 48 50 - 8 = 42 50 - 7 = 43
2 x 5 = 10 0x5=0 8 x 5 = 40 4 x 5 = 20 9 x 5 = 45 1x5=5 3 x 5 = 15 7 x 5 = 35 10 x 5 = 50 5 x 5 = 25
2 x 10 = 20 2 x 7 = 14 2x1=2 2x0=0 2 x 8 = 16 2 x 5 = 10 2x3=6 2 x 9 = 18 2 x 6 = 12 2x2=4
4x2=8 2 x 10 = 20 6 x 2 = 12 5 x 10 = 50 1x2=2 7 x 10 = 70 2x2=4 8 x 10 = 80 3x2=6 9 x 10 = 90
3 x 5 = 15 2 x 7 = 14 4 x 5 = 20 2 x 9 = 18 8 x 5 = 40 2 x 6 = 12 6 x 5 = 30 2x1=2 7 x 5 = 35 2x0=0
2 x 10 = 20 6 x 2 = 12 8 x 5 = 40 3x2=6 7 x 10 = 70 9 x 2 = 18 2x4=8 9 x 5 = 45 10 x 2 = 20 4 x 10 = 40
4 x 10 = 40 2 x 8 = 16 6 x 2 = 12 5 x 5 = 25 1 x 10 = 10 7 x 2 = 14 2 x 9 = 18 7 x 5 = 35 4x2=8 9 x 10 = 90
Page 73-76
What’s your Answer? 1. 619 (big) 2. 663 (egg) 3. 5637 (legs) 4. 8078 (blob) 5. 7738 (bell) 6. 77345 (shell) 7. 5514 (hiss) 8. 3045 (shoe)
Page 85
Race Away Set 1 80 Set 2 25 Set 3 60 Set 4 45 Set 5 50 Set 6 100 Set 7 40 Set 8 75
Exploring Calculators
93
EXPLORING CALCULATORS
NUMBER
LOWER PRIMARY
The Exploring Maths series is designed to provide busy teachers with practical resources that are mathematically up-to-date, fun and easy to use. Each book contains a wealth of activities, blackline masters and assessment tasks for a whole life-time of teaching. These activities encourage your children to think mathematically by exploring, experimenting, being creative and taking risks. By asking questions and active discovery, children learn to enjoy using mathematics as part of their everyday lives.
Exploring Calculators includes: • Three carefully sequenced units to develop skills with 5, 6 and 7 year olds • Over 60 activity-based, easy-to-use teaching ideas • Over 60 blackline masters • Useful activity cards for independent small group work
• An outcomes indicators record to help you record individual progress. In fact, almost everything you need to take full advantage of a calculator’s potential for mathematics in your classroom.
About the author Originally a primary school teacher, Bev Dunbar is now actively involved in teacher education as a Mathematics Consultant and University Lecturer in Mathematics Education working in both the State and Catholic Education systems. Bev is a passionate believer in fun, practical resources which help teachers make maths lessons a highlight of the day.
Titles in the Exploring Maths series ISBN 1-86509-220-7
NUMBER Exploring 1 - 5 Exploring 6 - 10 Games and Activities for 0 - 10
Numbers to 50 Picture Pack Exploring 0 - 100 Numeration Exploring 0 - 100 Operations Exploring Calculators Exploring Fractions Exploring Money
Exploring 0 - 50 Numeration Exploring 0 - 50 Operations
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