practise and perfect subtraction
DESCRIPTION
This workbook provides handy strategies to teach skills that students need to perform subtractions in the range of 1 to 21. There is no regrouping. Students are encouraged to master basic subtraction facts by learning simple computations techniques. The application of correct strategies will give the students confidence and encouragement to apply this knowledge and skills to solve simple problems and to develop a positive attitude towards mathematics.TRANSCRIPT
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Publisher JAYS' EDUCATION 704 Old Cleveland Rd East Wellington Point Queensland 4160 phone 07 3822 1813 [email protected]
Practise and Perfect Subtraction
Author Hana Jay
Cover design Dana Sundgren
Illustrations Dana Sundgren
Compilation and layout Tom Jay
1st DIGITAL edition 2015
Jays Education
ISBN 978-1-921622-81-6
Reproduction and communication for educational purposes The Copyright Act 1968 allows a maximum one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced etc. by an educational institution for its own purposes, provided that the institution has given a notice to CAL Australia (in other countries notice must be given to the national copyright agency of that state).
However the publisher is here with granting the right to reproduce 100% of this book to the original purchaser for classroom or personal use. Commercial use is prohibited and expressly forbidden.
Electronic copying, storage or transmission is permitted only for the use of the original purchaser. The pdf file must be left intact and in the original format and content.
Jays' Education is reserved and must be kept displayed on each sheet copied.
CAL Copyright Agency Limited Level 11 66 Goulburn Street Sydney 2000 Phone 02 9394 7600 Fax 02 9394 7601 [email protected]
Reproduction and communication for other purposes Except as permitted by the Copyright Act 1968 (for example a 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. Direct all inquiries to the publisher, see address at the top of this page.
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SUBTRACTION STRATEGIES
II Practise and Perfect Subtraction Jays Education www.jayseducation.com
It is better to count forward from left to right
and count back from right to left
or better still, to count up to add
and count down to subtract.
Counting down is for some
students much easier then
counting back from right to left.
Vertical number line.
Touch the numbers as you count from top down saying 12 and then count 11, 10, 9, 8, 7.
Use number lines to subtract.
Horizontal number line.
16 - 4 = 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Touch the numbers as you count back from the right, saying 16 and then count 15, 14, 13, 12.
12 - 5 = 7
13
14
12
11
10
9
8
7
6
5
4
3
2
1
5
Adequate numeracy provides lifelong opportunities to the fulfilment and social and workplace participation. Despite ever increasing technologies a growing number of students fail to acquire essential mathematical skills and a positive disposition towards mathematics. Mathematical problem solving is a cognitive activity requiring a reasonable level of automaticity in recalling and applying fundamental number skills. This workbook provides handy strategies to teach skills that students need to perform subtractions. Students are encouraged to master basic subtraction facts by learning simple computations techniques. The application of correct strategies will give the students confidence and encouragement to apply this knowledge and skills to solve simple problems and to develop a positive attitude towards mathematics. Many children get confused when to count forward to add and when to count back to
subtract.
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Using dot patterns to subtract.
Each number has a dot pattern the students use to count back.
III Practise and Perfect Subtraction Jays Education www.jayseducation.com
The dot strategy can be applied to single digit horizontal subtraction as well as to
vertical subtraction of multiple digit numbers.
4 6
2 3
2 3
Two digit application, no regrouping:
6 9 5
2 4 3
4 5 2
Three digit application, no regrouping:
At first the students make the dots as they count, then when they get comfortable
with the patterns, they pretend to make the dots as they count until the dots are no
longer needed and the recall of number facts becomes automatic.
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Using Fingers as a number line.
11 - 4 =
Open up 4 fingers, touch the number eleven and then
go on touching each finger as you count back 10, 9, 8, 7.
The answer is 7.
10
9 8 7
11
Somehow we have developed a negative attitude to the use of fingers. If we use the fingers as a ready made number line, the recall of number facts becomes easier and after a while the children will use the method only occasionally, when stuck.
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Count On
Put the fingers in a fist. touch the fist saying 7 and then count
on saying 8, 9, 10, 11, 12, opening one finger after another
(starting with the thumb) until the word 12, then count the open
fingers to find the answer 5.
7 + 5 = 12 therefore 12 - 7 = 5
8
9 10 11
12
7
5 fingers are open, the answer is 5.
15 - 8 =
8 + 7 = 15 therefore 15 - 8 = 7
8
9
10 11 12
13 14
15
7 fingers are open, the answer is 7.
Count Back
15 - 8 =
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6 7 10
1 3 9 8 4 1
15 11 2
4 5 6
10 3 8 9 2 12
1 2 1
4 5 6
10 7 8 9 11 12
4 5 6
10 7 8 9 11 12
1 2 3
1 2 3 4 5 6
10 7 8 9 11 12
or
Students who are slow to recall the numbers to write are doing well using the
LUK system, just working out the answer and placing the tile on the correct number.
The advantage of the LUK system is that the students can work independently,
check their answers and correct their mistakes.
The students like to work with the tiles, searching for the numbers and looking
forward to be rewarded by a pattern. They think of LUK as a game.
How to use the miniLUK System. The lid of the mini LUK tray (box) is divided into 12 blank squares, the base is divided into 12 numbered squares. There are 12 numbered tiles to work with.
Step 1. Place the 12 tiles in sequence from 1 to 12 on
the blank squares on the lid of the miniLUK box.
or
Place the 12 tiles in sequence from 1 to 12
on the table ready to be used.
Step 2.
Choose your worksheet (page).
Step 3.
Pick up tile number 1 and place it under or next to
the number 1 subtraction sentence. Work out the problem and write the answer (number). Find this number on
the base of the miniLUK box. Place the tile number 1
onto that number. Continue in the same way until all 12 problems are solved and the 12 tiles are transferred
from the lid to the bottom of the miniLUK box.
Step 4. When finished and all tiles are placed on the correct
squares, the task is completed. Close the lid of the
box and turn the Mini LUK over sideways. Open the lid and a geometrical pattern will be formed by the
back of the tiles.
Step 5.
Match the pattern in the box with the pattern on the bottom of the page and colour match the pattern.
miniLUK Self Checking System
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1
2
3
4
5
6
7
8
9
10
11
12
6 4 =
7 4 =
8 3 =
5 4 =
15 3 =
6 2 =
10 2 =
14 4 =
9 3 =
10 3 =
13 2 =
12 3 =
15
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1
2
3
4
5
6
7
8
9
10
11
12
12 3 =
16 5 =
12 4 =
15 5 =
7 5 =
14 2 =
8 4 =
10 5 =
9 2 =
6 3 =
5 4 =
8 2 =
16
15
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1
2
3
4
5
6
7
8
9
10
11
12
10 3 =
15 4 =
7 3 =
12 4 =
15 5 =
16 4 =
5 3 =
9 4 =
6 3 =
5 4 =
12 3 =
10 4 =
14
15
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1
2
3
4
5
6
7
8
9
10
11
12
6 5 =
9 4 =
8 4 =
7 5 =
15 5 =
9 3 =
12 5 =
15 3 =
8 5 =
12 4 =
13 4 =
14 3 =
14
15
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15 6 =
13 6 =
18 6 =
16 6 =
12 6 =
8 6 =
10 6 =
7 6 =
11 6 =
9 6 =
17 6 =
14 6 =
7
8
9
10
11
12
1
2
3
4
5
6
18
17
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9 6 =
7 6 =
12 6 =
10 6 =
18 6 =
8 6 =
16 6 =
13 6 =
11 6 =
15 6 =
17 6 =
14 6 =
7
8
9
10
11
12
1
2
3
4
5
6
18
17
-
16
15
1
2
3
4
5
6
7
8
9
10
11
12
12 5 =
14 3 =
9 6 =
12 4 =
16 6 =
15 3 =
8 6 =
10 5 =
9 5 =
7 6 =
15 6 =
12 6 =
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1
2
3
4
5
6
7
8
9
10
11
12
6 5 =
9 4 =
16 6 =
8 6 =
10 6 =
12 6 =
12 4 =
16 5 =
12 3 =
13 6 =
9 6 =
16 4 =
16
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1
2
3
4
5
6
7
8
9
10
11
12
19 7 =
10 7 =
14 7 =
18 7 =
8 7 =
11 7 =
12 7 =
17 7 =
15 7 =
13 7 =
9 7 =
16 7 =
19
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1
2
3
4
5
6
7
8
9
10
11
12
19 7 =
10 7 =
8 7 =
12 7 =
14 7 =
11 7 =
18 7 =
16 7 =
15 7 =
13 7 =
9 7 =
17 7 =
19
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9 7 =
10 6 =
12 7 =
8 7 =
16 4 =
10 7 =
15 7 =
14 5 =
12 6 =
12 5 =
18 7 =
17 7 =
7
8
9
10
11
12
1
2
3
4
5
6
18
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10 7 =
12 7 =
9 7 =
10 6 =
15 7 =
12 6 =
15 6 =
18 7 =
8 7 =
17 7 =
13 6 =
18 6 =
7
8
9
10
11
12
1
2
3
4
5
6
18
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1
2
3
4
5
6
7
8
9
10
11
12
12 3 =
7 5 =
11 6 =
17 7 =
16 4 =
8 7 =
10 6 =
14 7 =
13 7 =
9 6 =
15 4 =
14 6 =
17
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20
1
2
3
4
5
6
7
8
9
10
11
12
16 8 =
20 8 =
12 8 =
15 8 =
18 8 =
19 8 =
9 8 =
14 8 =
11 8 =
10 8 =
17 8 =
13 8 =
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20 1
2
3
4
5
6
7
8
9
10
11
12
14 8 =
10 8 =
12 8 =
13 8 =
18 8 =
9 8 =
19 8 =
16 8 =
11 8 =
20 8 =
17 8 =
15 8 =
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20
1
2
3
4
5
6
7
8
9
10
11
12
12 8 =
10 3 =
20 8 =
10 7 =
12 6 =
10 8 =
15 6 =
8 7 =
12 7 =
18 8 =
15 4 =
15 7 =
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1
2
3
4
5
6
7
8
9
10
11
12
10 7 =
14 7 =
20 8 =
12 8 =
15 9 =
10 8 =
15 6 =
9 8 =
13 8 =
16 6 =
19 8 =
16 8 =
20
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10 9 =
20 9 =
19 9 =
17 9 =
13 9 =
15 9 =
11 9 =
14 9 =
18 9 =
16 9 =
12 9 =
21 9 =
7
8
9
10
11
12
1
2
3
4
5
6
21
-
10 9 =
12 9 =
15 9 =
19 9 =
21 9 =
16 9 =
13 9 =
18 9 =
7
8
9
10
11
12
1
2
3
4
5
6
21
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20 9 =
14 9 =
17 9 =
11 9 =
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1
2
3
4
5
6
7
8
9
10
11
12
13 9 =
10 9 =
12 6 =
10 7 =
16 5 =
10 8 =
18 8 =
16 8 =
14 9 =
15 6 =
20 8 =
14 7 =
20
-
1
2
3
4
5
6
7
8
9
10
11
12
19 9 =
8 7 =
12 6 =
14 5 =
20 8 =
6 4 =
12 9 =
14 7 =
11 6 =
12 8 =
16 5 =
15 7 =
20
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22 Practise and Perfect Subtraction Jays Education www.jayseducation.com
1
2
3
4
5
6
7
8
9
10
11
12
14 10 =
12 10 =
13 8 =
13 10 =
17 6 =
17 10 =
19 10 =
18 10 =
19 7 =
20 10 =
15 9 =
11 10 =
20
-
1
2
3
4
5
6
7
8
9
10
11
12
16 8 =
12 6 =
19 9 =
10 9 =
14 10 =
21 10 =
14 7 =
20 8 =
18 9 =
10 8 =
11 8 =
15 10 =
21
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20 10 =
14 7 =
20 8 =
18 9 =
12 6 =
16 8 =
10 7 =
9 8 =
20 9 =
12 8 =
15 10 =
10 8 =
7
8
9
10
11
12
1
2
3
4
5
6
20
-
12 1 =
17 10 =
19 10 =
13 1 =
13 10 =
18 10 =
16 10 =
11 10 =
11 1 =
15 10 =
14 10 =
12 10 =
7
8
9
10
11
12
1
2
3
4
5
6
19
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17 10
16 10
19 10
13 10
20 10
11 10
14 10
12 10
18 10
21 10
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Practise and Perfect Subtraction Jays Education www.jayseducation.com
22 10
1
3
4
5
7
8
9
10
11
12 6
2
15 10
-
12 6
15 4
10 7
16 6
11 10
13 1
14 7
12 4
18 9
10 6
10 8
11 6
1
3
4
5
7
8
9
10
11
12 6
2
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16 8
10 9
16 4
12 6
10 7
10 8
13 3
15 6
11 6
15 4
10 6
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14 7
1
3
4
5
7
8
9
10
11
12 6
2
-
12 4
12 9
12 6
18 6
20 9
10 8
11 6
13 9
14 7
10 9
17 7
18 9
1
3
4
5
7
8
9
10
11
12 6
2
10 9 8 7 6 5 4 3 2 1
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12 10
15 4
13 7
20 8
11 6
20 10
12 3
18 10
14 7
11 10
12 8
30
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9 6
1
3
4
5
7
8
9
10
11
12 6
2
-
24 14
49 44
39 31
37 35
49 43
18 14
39 27
19 12
38 35
29 20
59 58
1
3
4
5
7
8
9
10
11
12 6
2
54 43
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56 54
49 40
36 32
60 50
49 43
49 41
24 12
59 52
34 23
68 63
25 24
32
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29 26
1
3
4
5
7
8
9
10
11
12 6
2
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54 42 26 62 13 14 11 12 44 52 31 61
2 7 10 6 1 5 3 4 11 12 8 9
Answers
LUK code
39 25
86 24
69 27
27 14
58 46
97 53
88 62
97 36
69 38
99 45
74 63
1
3
4
5
7
8
9
10
11
12 6
2
69 17
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Cross out the answers.
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15 75 33 21 42 31 35 55 54 64 43 63
8 4 2 10 11 12 6 7 3 5 1 9
Answers
LUK code
34
Practise and Perfect Subtraction Jays Education www.jayseducation.com
79 36
56 23
69 14
49 14
76 45
69 15
58 43
99 36
37 16
67 25
87 23
97 22
1
3
4
5
7
8
9
10
11
12 6
2
Cross out the answers.
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Page Pattern Date Page Pattern Date Page Pattern Date
1
13
25
2
14
26
3
15
27
4
16
28
5
17
29
6
18
30
7
19
31
8
20
32
9
21
33
10
22
34
11
23
12
24
LUK Patterns Progress Chart Students name:
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Numeracy (no LUK) Basic Number Concepts Count and Write Numbers Learn to Count and Write Numbers Mental Computation Addition to 10 Subtraction Concept of 10 The Concept of 20 Money in Coins The Concept of Money - Coins What Time Is It? Multiples of 2 & 20 Concept of 100 Multiples of 10 & 5 Multiply 2, 3, 4, 5 Fractions 2 Fractions 3 Fractions 4 Angles in Triangles Simple Steps to Algebra The Four Operations
Literacy (no LUK) Reading Readiness Teaching Reading Let's Start Read and Write Using Phonics Learn to Write Simple Sentences Simple Comprehension Activities for Emergent Readers Read About Write About Dotty Read About Write About Spotty Adventures with Dotty and Spotty Magic e Sounds are Simple Spell Well to Excel English for Everyone
Visual Literacy (Pre-Writing) Time and Behaviour Basic Pencil Skills More Pencil Skills Still More Pencil Skills Reading Readiness Drawing Workshop - Learn to Draw in Few Steps Get Smart With Art
*hIB9C1|WSSYRw ISBN 978-1-921622-81-6
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LUK Self Checking System Find the Missing Number Addition level 1 Addition level 2 Subtraction level 1 Multiplication level 1 DIVISION Halves and Quarters Concept of Money Fractions Let's Practice Subtractions Tens and Ones - Focus on Money Reading & Spelling Essentials LUK Self Check Box
Mini LUK Self Checking System Number Concept Learn to Count Simple Addition Using Add On Strategy Beginning to Subtract Practice and Perfect Subtraction Regroup and Subtract Can you tell the time? Counting Money Get Ready for Problem Solving Multiply and Divide by 3 Multiplication Activities Number Concept Learn to Count Decimal notation place value multiplication Angles in Triangles All About Angles Early Reading Intervention Reading Intervention Reading and Spelling Short Words Rhyming Words Enhance Reading Reading and Spelling Patterns Reading for Meaning Reading Simple Sentences Spelling and Reading Words with a Mini LUK Self Check Box