doss fast 010710

DossFASTDoss Fast Addition and Subtraction Technique

for ‘instant’ mental addition and subtraction of numbers.

without Counting Fingers or Any Paper work

Age 8yrs; No upper limit

Prof. M. A. ThiruthuvadossChennai, India

We use DossFAST techniqueThis avoids carry-overs and borrowing

© M A Thiruthuvadoss (Since 2003 ... 2010)All Rights Reserved

No part of this publication may be reproduced, in any form, without the priorpermission of the author.

Graphics & DTP: AuthorCover Design: AuthorPublished by: Author

Author: M A Thiruthuvadoss [email protected]/6 Indiranagar I Avenue [email protected] - 600 020, India. http://www.magicmaths.org

Telephone: 044-24423524Cell: 94452 04774

PREFACE

Juggle Numbers also called Mental Addition and Subtraction has, now, beencompletely re-written from scratch in an endless pursuit of continuous improvementand upgradation.

This now becomes DossFAST

DossFAST - Doss Fast Addition and Subtraction Technique

which makes mental addition and subtraction of any two numbers possible and easy.

DossFAST assumes the ability to instantly add / subtract two single digit numbers.

Those who DO NOT possess this ability, but is determined to acquire it, can use oneof the two alternative methods in Appendix I or Appendix II, to learn and hone theirbasic skills and abilities.

One has to have a firm will, set time, work daily until you master the skill.

Prof. M. A. Thiruthuvadoss1 July, 2010

JUGGLE NUMBERS iii

The Magic Maths project started in late 2001.

WRITE A MATHS BOOK - IT WILL COME TO YOUSometime in November, 2001 Sri Mathurakali# told me, “You write a maths book.”For me, ‘maths book’ meant school text-book and I was 62 then. I did not take itseriously. After about three weeks “Why have you not started?”, She asked andcontinued, “Leave all other work; write the maths book. It is my order.”

“What shall I write?” “Write anything; just start. ‘You will get’ [cdf;Fj; NjhZk;].Always keep a paper and pencil handy. Note everything you get; because, you willnot remember after half-an-hour.”

So the Magic Maths project is a gift from the Divine for Universal use. M. A.Thiruthuvadoss is not the ‘author’ but just an ‘instrument, link or channel’, like thecomputer on which all this is being typed.

QUICK MATHSI started compiling a few short-cut calculation techniques, which I thought, mighthelp students. In March 2002, a 24 pages book, Quick Maths - a collection of 1-stepcalculation techniques - with about 15 techniques was printed. Today (July, 2010)Quick Maths runs into about 230 pages with innumerable techniques/methods*.

MAGIC MATHS PROJECT

# Sri Mathurakali is one of the numerous forms of Parvathi - the Universl Shakthi that drives theentire Universe - is the presiding deity of the temple in Siruvachur (Trichy District), 48km from Trichy(Tamilnadu, India) on the GST Rd, to Chennai. This is an unusual temple which opens only on twodays (Monddays and Fridays) of the week and a few other special days in the year.

* You may visit http://www.magicmaths.org/

iv JUGGLE NUMBERS

JUGGLE NUMBERSI conducted numerous free workshops all over and taught these techniques to children,teachers and parents. During these workshops I realised that most children do nothave the required mastery over the basic arithmetic operations (+, –, x, ÷) of evensingle-digit numbers and and so Quick Maths was really of no use to them. So Iwrote Juggle Numbers - mental addition and subtraction, in 2003. After a few avatars,Juggle Numbers is now DossFAST - a compact, easy and effective program.

MAGIC MATHSWhen two girl students came to me for help with their CAT entrance preparation(even though they had enrolled with two popular coaching institutions) I got a glimpseof the dull formal high-school material dished out to them. It had nothing to do withskill developement or aptitude. This prompted me to write the Magic Maths book,solving aptitude problems in under 10 seconds by lateral methods. A part-I of thebook was printed in January, 2004 followed by a complete book later. Now a finalversion of Magic Maths is getting ready and will be out in a couple of months.

GANITHAIn around 2005 a book was litterally thrust on me in a shop by its owner in Mylapore.The book was, Classics of Indian Mathematics - Algebra, with Arithmetic and Mensuration,from the Sanskrit of Brahmagupta and Bhaskara, by Henry Thomas Colebrooke, firstpublished in 1817 A.D. The shop was the Indological Book Shop on Appar SwamiKoil St. (Opp to Sanskrit College, Mylapore, Chennai). The result, I wrote the Lilavatiof Shri Bhascaracharya (1150 A.D.) in today’s English as Ganitha.

BRAHMA’S OWN NUMBERSWorking for Ganitha lead me to look into the numbers and number systems etc. andas a result, the next book in the line is Brahma’s Own Numbers.

ALL BOOKS ON THE WEBI had been writing, modifying and updating the books on a continuous basis for thepast 8+ years, as and when I was ‘getting’ new material and ideas. Now I am in theprocess of redoing all the books into their ‘final’ shapes. As and when the books getready, they will be put on the net - http://www.magicmaths.org/ - for the free use ofeveryone. Hope these reach more and more people, for whom they are meant.

JUGGLE NUMBERS v

MATHS-PHOBIAMathematics is natural to humans. Everyone in the world, even the vegetable vendorwho, perhaps, never went to school, counts, calculates, compares, handles moneyand materials and so on. No one is ‘troubled by’ or ‘scared of’ maths. So mathsphobiais not a natural fear. It is a Frankenstein monster; it is our own creation

BASIC NUMERACY SKILLSAddition of two numbers is the basis of all mathematics, science and life itself.Subtraction is the reverse of addition; multiplication is extended addition and divisionis the inverse of multiplication. A thorough fluency in these basic arithmetic operationsalone can save our children from this fear of maths. Answers must be instant as ifthe question was, “What is your name?”

THE WORLD DOES NOT KNOW HOW TO TEACH ADDITION .....We inherited excellent, easy and effective methods to teach basic mental arithmeticcomputations. But the world, including us, the anglicised lot, destroyed all that andnow no one seems to know how to teach even addition of two single digits.

INDIANS EXCELLLED IN ITAncient Indians, down to our grandfathers, excelled in numbers, logic and aptitude.After all it was India that gave today’s numbers, number system, calculation techniquesand the arithmetic. They were taught the tables - Addition, Subtraction andMultiplication (including table of fractions like: ,,,,,,etc.)

How can any other method become as effective? Perhaps, future generations willplant a tables-chip in the brain.

TEACH THE TABLESIf you are genuinely interested in the child, teach Mathematical Tables, mainly additionand multiplication tables. Any other method like Counting Fingers or ‘Five in themind .....’, is meant for weaker children and not for us.

MATHS-PHOBIA AND MATHS TEACHING

vi JUGGLE NUMBERS

JUGGLE NUMBERS vii

Contents

PREFACE .............................................................................................................................. 9 : 3

MAGIC MATHS PROJECT ..................................................................................................... 9 : 4

MATHS-PHOBIA AND MATHS TEACHING ........................................................................... 9 : 6

ABOUT THIS BOOK ............................................................................................................. 9 : 8

HOW TO USE THIS BOOK? .................................................................................................. 9 : 9

1 ADDITION USING DOSSFAST ...................................................................................... 9 : 12Add Any number (without Carryover) ........................................................................................ 9 : 12Add A Single Digit Number (to Double Digit) with Carryover ............................................ 9 : 14Add A Double Digit Number (with Carryover) ........................................................................ 9 : 16Add Any Number ............................................................................................................................ 9 : 18Actual Mental Addition .................................................................................................................. 9 : 19

2 SUBTRACTION USING DOSSFAST ................................................................................ 9 : 22Simple case ...................................................................................................................................... 9 : 22Just Subtract ..................................................................................................................................... 9 : 24

APPENDIX I: ADDITION USING TABLES ............................................................................ 9 : 28Addition Tables ................................................................................................................................ 9 : 28Teach Addition Tables ................................................................................................................. 9 : 29

APPENDIX II: ADDITION WITHOUT TABLES .................................................................... 9 : 33What is 10? ..................................................................................................................................... 9 : 33What is 5? ........................................................................................................................................ 9 : 35What is 3? ........................................................................................................................................ 9 : 37What is 4? ........................................................................................................................................ 9 : 37What is 6? ........................................................................................................................................ 9 : 39What is 9? ........................................................................................................................................ 9 : 41What is 7? ........................................................................................................................................ 9 : 43What is 8? ........................................................................................................................................ 9 : 45Add Single Digit (to Single Digit) with Carryover ................................................................. 9 : 47

APPENDIX III: EXTRA TABLES ........................................................................................... 9 : 49Subtraction Tables .......................................................................................................................... 9 : 49Multiplication Tables ....................................................................................................................... 9 : 50

ABOUT THIS BOOK

THE BOOK (ONLY 2 CHAPTERS)The book is only the first TWO chapters (pages 12 to 25). This introduces a simpletechnique called DossFAST which makes the job easier by avoiding the carryoversand borrowings that are very essential part of our school learning.

THE REST (3 Appendices)Obviously, I ‘assume’ mastery over the basic ability to add and subtract two singledigit numbers, mentally and instantly, as if the question was, “What is your name?”You can not run a race without legs!

But I do know the reality is very different and pathetic. So you get the 3 Appendiceswhich are for the ones who do not have this ability.

FOR WHOM IS THIS BOOK?How many of us, children or adults (including people who teach maths to children),can add three hundred and eighty seven and two hundred and forty five mentally,without any writing, in under 10 seconds? Congrats if you can do it; else this bookcould be for you.

DossFAST could be very useful for children and even for adults.

WHAT CAN THE BOOK DO?This simple and short course (13 pages only) will show you how even a 8 year oldwill add 387 and 245 in just three mental steps;The child will rattle:

three eight sevenfive eight sevensix two seven

answer is: six three two i.e. 632

SELF-TEACHING BOOKGuru’s personal guidance and teaching is like ‘Coke’ - the real thing. Anything else,either the audio, video, DVD, electronic interfaces including interactive white boardswith chat are nothing but inferior compromises. This fact has well-established itself,with the advent of each and every gadget, right from radio, TV, ... What I am givingis (just) a self-teaching book.

viii JUGGLE NUMBERS

JUGGLE NUMBERS ix

HOW TO USE THIS BOOK?

1) Follow any and every insruction, note or suggestion, method, writing or step,etc. diligently and litterally. DO NOT CHANGE OR DROP ANYTHING; EVEN A SMALLTHING. Obviously students will grow out of this book’s language andconcepts as they grow. For now, to start with, make the material andmethods your own. Do not deviate.

2) Start from the beginning.

3) Master every idea on a page.

4) Answer all the problems of the Exercise.

5) Confirm your ability, accuracy and speed of response every time.

6) The speed of response is ‘instant’; as fast as if you were asked your name.

7) Have a reasonable limit for the work you learn in a day. You have to assimilateeverything you learn; this takes time. Simply doing a lot at one time is of noreal use.

8) Everyday when you start, make sure that you are thorough with all theprevious methods and techniques.

9) Our goal is mental work.

10) If necessary, write and do the work in the beginning. Once you master theconcept, in the following days try to do them mentally.

11) Do not rush through. This skill is so basic and so fundamental for mathsand aptitude developement, mastering is important and not the time spent.Take your time. Remember the foundation, including every brick and everylayer of bricks, needs to be strong.

1ADDITION

USING


12 JUGGLE NUMBERS

ADD ANY NUMBER (without Carryover)This is extremely simple and fast (assumes mastery of single digit addition).

• Read 1st number, digit by digit; from left to right.• Add any digit from the 2nd number if in the corresponding place.

EXAMPLES01) Take 624 + 35

As you read six two four, you will notice6 has no digit to be added;2 has 3 to be added;4 has 5 to be added.

So you will read 6 ‘2+3’ ‘4+5’ [and not six two four]which is six five nine.

624 + 35 = 659 [In one step]

02) 813 + 52 = 865 [8 ‘1+5’ ‘3+2’]

03) 42 + 56 = 98 [‘4+5’ ‘2+6’]

04) 543 + 321 = 864 [‘5+3’ ‘4+2’ ‘3+1’]

05) 254 + 31 = 285

06) 54 + 23 = 77

07) 35 + 24 = 59

08) 2314 + 32 = 2346 [2 3 ‘1+3’ ‘4+2’]

09) 8124 + 53 = 8177

10) 3261 + 35 = 3286

11) 4321 + 567 = 4888

12) 5124 + 2315 = 7439

We all know it is6 hundred and twentyfour.

We better read digit by digitSix, Two, Four

1 ADDITION USING DossFAST

JUGGLE NUMBERS 13


01) 34 + 3 = ________

02) 23 + 41 = ________

03) 13 + 45 = ________

04) 547 + 21 = ________

05) 821 + 43 = ________

06) 742 + 43 = ________

07) 531 + 265 = ________

08) 1623 + 51 = ________

09) 3624 + 143 = ________

10) 7825 + 42 = ________

11) 8804 + 194 = ________

12) 1052 + 6514 = ________

13) 834 + 53 = ________

14) 7153 + 26 = ________

15) 137 + 12 = ________

16) 5472 + 214 = ________

17) 8215 + 463 = ________

18) 7402 + 243 = ________

19) 5318 + 2051 = ________

20) 1623 + 5142 = ________

21) 3624 + 1430 = ________

22) 7025 + 931 = ________

23) 8004 + 573 = ________

EXERCISE (9)

24) 64 + 23 = ________

25) 531 + 25 = ________

26) 713 + 213 = ________

27) 3000 + 498 = ________

28) 5002 + 83 = ________

29) 7000 + 275 = ________

30) 4000 + 2000 = ________

31) 5000 + 3541 = ________

32) 8275 + 1523 = ________

33) 502 + 71 = ________

34) 3456 + 5121 = ________

35) 6093 + 1804 = ________

36) 57 + 21 = ________

37) 524 + 141 = ________

38) 713 + 243 = ________

39) 3524 + 241 = ________

40) 8210 + 403 = ________

41) 7042 + 435 = ________

42) 8765 + 1234 = ________

43) 1623 + 6154 = ________

44) 3624 + 5264 = ________

45) 7005 + 423 = ________

46) 4030 + 424 = ________

14 JUGGLE NUMBERS


ADD A SINGLE DIGIT NUMBER (to Double Digit) with Carryover

01) 38 + 7 = ?The 38 takes 2 from 7; becomes 40 (and 5 is left); so 45

02) 87 + 5 = 92 [cut 3 from 5]03) 59 + 8 = 67 [cut 1 from 8]04) 46 + 5 = 51 [cut 4 from 5]

In actual work, we can do this in two steps.46 becomes 50 and then becomes 51We shall write it like: 46 50 51

VERIFY

01) 58 + 7 = 65 [58 60 65]

02) 78 + 7 = 85 [78 80 85]

03) 38 + 7 = 45 [38 40 45]

04) 57 + 8 = 65 [57 60 65]

05) 18 + 7 = 25 [18 20 25]

06) 8 + 56 = 64 [56 60 64]

07) 5 + 26 = 31 [26 30 31]

08) 5 + 47 = 52 [47 50 52]

09) 4 + 69 = 73 [69 70 73]

10) 7 + 34 = 41 [34 40 41]

11) 16 + 7 = 23 [16 20 23]

12) 75 + 7 = 82 [75 80 82]

13) 56 + 6 = 62 [56 60 62]

14) 78 + 8 = 86 [78 80 86]

JUGGLE NUMBERS 15


EXERCISE (10)

01) 36 + 7 = ____

02) 23 + 8 = ____

03) 79 + 4 = ____

04) 47 + 5 = ____

05) 18 + 7 = ____

06) 59 + 4 = ____

07) 78 + 5 = ____

08) 16 + 8 = ____

09) 36 + 4 = ____

10) 25 + 9 = ____

11) 88 + 4 = ____

12) 15 + 6 = ____

13) 56 + 8 = ____

14) 77 + 7 = ____

15) 49 + 6 = ____

16) 37 + 4 = ____

17) 97 + 6 = ____

18) 32 + 9 = ____

19) 18 + 5 = ____

20) 78 + 9 = ____

21) 24 + 8 = ____

22) 19 + 9 = ____

23) 89 + 8 = ____

24) 95 + 6 = ____

25) 128 + 7 = ____

26) 84 + 6 = ____

27) 35 + 8 = ____

28) 22 + 8 = ____

29) 57 + 4 = ____

30) 73 + 9 = ____

31) 49 + 7 = ____

32) 52 + 8 = ____

33) 17 + 6 = ____

34) 14 + 7 = ____

35) 97 + 5 = ____

36) 76 + 6 = ____

37) 89 + 5 = ____

38) 37 + 7 = ____

39) 28 + 5 = ____

40) 15 + 9 = ____

41) 67 + 6 = ____

42) 14 + 7 = ____

43) 88 + 4 = ____

44) 46 + 5 = ____

45) 27 + 8 = ____

46) 19 + 3 = ____

16 JUGGLE NUMBERS


ADD A DOUBLE DIGIT NUMBER (with Carryover)We avoid carry-overs and borrowing as they interfere with speed and flow.The technique is better explained by examples.

We shall learn to go slow to GO FAST!.Let us take the example on the earlier page

624 + 35 = ?

We take 624, the left side (L.S.) number;Modify it by adding digits from right side (R.S.) number one by one.We shall do only one addition (of one digit) in one step.

We read:Step 1: 6 2 4 [the L.S. number as it is]Step 2: 6 5 4 [ ‘2+3’ ]Step 3: 6 5 9 [ ‘4+5’ ]So 624 + 35 = 659

Consider 684 + 35 = ?Now step 2 will be a problem as ‘8+3’ gives a carryover.

Step 1: 6 8 4 [the L.S. number as it is]‘8+3’ is a problem; take ‘68+3’ [That is all the trick!]

68 4Step 2: 71 4 [ ‘68+3’ ]Step 3: 7 1 9 [ ‘4+5’ ]So 684 + 35 = 719

ACTUAL WORKING6 8 4 + 3 5 = ?

step 1: 6 8 4step 2: 68 4

71 4step 3: 7 1 9

So 6 8 4 + 3 5 = 7 1 9

JUGGLE NUMBERS 17


EXAMPLES

01) 2 7 6 + 5 2 = ________27 632 63 2 8

02) 5 7 6 + 8 3 = 6 5 957 665 66 5 9

After practice, cut the 3rd step(!).03) 8 5 1 + 7 6 = 9 2 7

85 192 1

Cut the fist step also.04) 3 6 8 + 9 1 = 4 5 9

45 8

Cut the remaining step also.05) 4 8 3 + 6 2 = 5 4 5

NOTEThe ‘student’ must practice many times like each of the examples above and moveto the next model when you are thorough and comfortable.

18 JUGGLE NUMBERS


ADD ANY NUMBER

Examples01) 6 7 8 + 5 6 = 7 3 4

72 87 287 34

02) 9 7 3 + 5 2 1 = 1 4 9 414 7 3

03) 6 7 8 + 2 5 6 = 9 3 48 7 892 89 289 34

04) 5 7 8 + 3 8 1 = 9 5 98 7 8 87 8 95 8

05) 2 4 7 + 3 1 6 = 5 6 35 4 75 5 75 575 63

06) 9 7 8 + 6 5 6 = 1 6 3 4 15 7 81 5 7 81 57 81 62 81 6 281 6 34

NOTEThe final level is to do just to write the answer (without any other writing).

JUGGLE NUMBERS 19


ACTUAL MENTAL ADDITION

THE BEST APPROACHThe enthusiastic and energetic parent / teacher may get the idea of theDossFAST method from the past few pages; and then teach the ‘student’only this page.

In the previous few pages the DossFAST method was explained. If the idea isgrasped then the actual working by the student is given below.

Using underlining instead of ‘grouping’ is much simpler and easier.The previous page will look like this.

The student must be encouraged to WRITE these steps, as they are, withoutany change. Once they understand the method thoroughly, they will hate towrite any steps and they will just write the answer only.

Examples01) 6 7 8 + 5 6 = 7 3 4

7 2 8

02) 9 7 3 + 5 2 1 = 1 4 9 41 4 7 3

03) 6 7 8 + 2 5 6 = 9 3 48 7 89 2 8

04) 5 7 8 + 3 8 1 = 9 5 98 7 89 5 8

05) 2 4 7 + 3 1 6 = 5 6 35 5 7

06) 9 7 8 + 6 5 6 = 1 6 3 41 5 7 81 6 2 8

20 JUGGLE NUMBERS


01) 74 + 15 = ________

02) 258 + 53 = ________

03) 574 + 247 = ________

04) 300 + 5498 = ________

05) 468 + 327 = ________

06) 543 + 728 = ________

07) 374 + 586 = ________

08) 2479 + 152 = ________

09) 2932 + 5347 = ________

10) 215 + 7049 = ________

11) 305 + 1020 = ________

12) 5378 + 57 = ________

13) 57 + 21 = ________

14) 524 + 141 = ________

15) 713 + 243 = ________

16) 3524 + 241 = ________

17) 8210 + 403 = ________

18) 7042 + 435 = ________

19) 8765 + 1234 = ________

20) 1623 + 6154 = ________

21) 3624 + 5264 = ________

22) 7005 + 423 = ________

23) 4030 + 424 = ________

01) 34 + 8 = ________

02) 23 + 49 = ________

03) 17 + 45 = ________

04) 547 + 24 = ________

05) 828 + 45 = ________

06) 746 + 47 = ________

07) 537 + 265 = ________

08) 1278 + 551 = ________

09) 3624 + 735 = ________

10) 7869 + 423 = ________

11) 4527 + 1356 = ________

12) 5147 + 6485 = ________

13) 527 + 65 = ________

14) 1528 + 734 = ________

15) 4075 + 846 = ________

16) 72 + 14 = ________

17) 258 + 173 = ________

18) 5216 + 3074 = ________

19) 2608 + 3751 = ________

20) 56 + 78 = ________

21) 1234 + 5678 = ________

22) 9876 + 1234 = ________

23) 3408 + 249 = ________

EXERCISE (11)

2SUBTRACTION

USING


2 SUBTRACTION USING DOSSFAST

SIMPLE CASE

Go over all the subtraction problems that you may find from Exercise (1) onwards.Go through the following also and pick up any method, if you like.

Few simple methods; see the notes around each sum.

01) 70 – 26 50 44 [First subtract 20 and then 6]or Jump from 26 to 30; get 4 and 30 to 70 is 40. So 44

02) 300 – 62 = 238From 300, keep 200 and 100 – 62 is 38 [To subtract 62, 100 is enough]

or 300 – 60 = 240; 240 – 2 = 238 [Take away 60 and then 2]

03) 800 – 162 = 638 [Keep 600; 200–162=38]or 800 – 100 = 700; 700 – 62 = 638i.e. 800 – 162 700 640 638 [First subtract 100, then 60, finally 2]

04) 54 – 9 = 45 [Subtract 10 and then add 1]

05) 754 – 48 = 706 [Subtract 50 and then add 2]

06) 13 – 7 = ?Subtracting 3 from 13 is easy; So split 7as 3 & 413 – 3 is 10; 10 – 4 = 6So 13 – 7 = 6

i.e. 13 10 6 [Take away 3 and then 4]

07) 57 – 9 = ? [Take away 7 and then 2]So 57 – 9 50 48

08) 45 – 8 = ? [Take away 5 and then 3]So 45 – 8 40 37

09) 64 –12 = 52 [Take away 4 and then 8]i.e. 64 60 52

10) 76 – 15 = 61 [Take away 6 and then 9]i.e. 76 70 61

JUGGLE NUMBERS 23


01) 10 – 6 = ________

02) 30 – 6 = ________

03) 40 – 6 = ________

04) 70 – 6 = ________

05) 90 – 6 = ________

06) 120 – 6 = ________

07) 430 – 6 = ________

08) 100 – 6 = ________

09) 50 – 6 = ________

10) 50 – 8 = ________

11) 50 – 5 = ________

12) 50 – 3 = ________

13) 8 – 6 = ________

14) 38 – 6 = ________

15) 78 – 6 = ________

16) 578 – 6 = ________

17) 29 – 5 = ________

18) 54 – 3 = ________

19) 69 – 7 = ________

20) 78 – 4 = ________

21) 58 – 8 = ________

22) 23 – 1 = ________

23) 34 – 3 = ________

EXERCISE (12)

01) 43 – 3 = ________

02) 58 – 6 = ________

03) 50 – 7 = ________

04) 70 – 9 = ________

05) 100 – 3 = ________

06) 320 – 4 = ________

07) 720 – 5 = ________

08) 1000 – 2 = ________

09) 58 – 1 = ________

10) 55 – 4 = ________

11) 51 – 1 = ________

12) 50 – 1 = ________

13) 80 – 2 = ________

14) 30 – 3 = ________

15) 47 – 5 = ________

16) 79 – 3 = ________

17) 95 – 2 = ________

18) 48 – 7 = ________

19) 83 – 3 = ________

20) 29 – 4 = ________

21) 159 – 5 = ________

22) 99 – 3 = ________

23) 39 – 7 = ________

24 JUGGLE NUMBERS


JUST SUBTRACT

This is extremely simple and fast (assumes mastery of single digit subtraction).

• Read 1st number, digit by digit; from left to right.• Subtract any digit from the 2nd number if in the corresponding place.

This is exactly the same as the corresponding work on DossFAST addition. So weshall follow the underlining pattern on last page of Section 3.

Examples01) 6 7 8 – 5 6 = 6 2 2

6 2 2

02) 6 5 9 – 7 6 = 5 8 35 8 9

03) 9 2 3 – 5 6 1 = 3 6 24 2 33 6 3

04) 6 4 2 – 3 5 6 = 2 8 63 4 22 9 2

05) 2 5 7 8 – 7 8 1 = 1 7 9 71 8 7 81 7 9 8

06) 2 4 7 5 – 8 1 6 = 1 6 5 91 6 7 51 6 6 5

07) 7 5 0 3 – 6 8 4 6 = 6 5 71 5 0 3 7 0 3 6 6 3

A F T E RS U F F I C I E N TPRACTICE THISCAN BE DONE INJUST ONE LINE!

JUGGLE NUMBERS 25


EXERCISE (13)

01) 48 – 6 = _______

02) 25 – 7 = _______

03) 534 – 213 = _______

04) 725 – 43 = _______

05) 354 – 78 = _______

06) 572 – 285 = _______

07) 3214 – 547 = _______

08) 500 – 73 = _______

09) 342 – 29 = _______

10) 700 – 99 = _______

11) 237 – 152 = _______

12) 450 – 51 = _______

13) 84 – 68 = _______

14) 538 – 62 = _______

15) 738 – 69 = _______

16) 5728 – 666 = _______

17) 293 – 50 = _______

18) 320 – 30 = _______

19) 2691 – 91 = _______

20) 2691 – 691 = _______

21) 5008 – 358 = _______

22) 2345 –1678 = _______

01) 53 – 27 = _________

02) 359 – 74 = _________

03) 903 – 276 = _________

04) 7032 – 547 = _________

05) 978 – 345 = _________

06) 128 – 67 = _________

07) 436 – 163 = _________

08) 1092 – 637 = _________

09) 457 – 163 = _________

10) 38 – 5 = _________

11) 729 – 310 = _________

12) 670 – 258 = _________

13) 98 – 72 = _________

14) 173 – 57 = _________

15) 736 – 274 = _________

16) 927 – 158 = _________

17) 2856 – 362 = _________

18) 7419 –6391 = _________

19) 5307 –2983 = _________

20) 938 – 543 = _________

21) 4242 –4040 = _________

22) 574 – 308 = _________

23) 2407 – 968 = _________

END

OF

THE BOOK

ADDITION(of 2 single digit numbers instantly)

USING

ADDITION TABLES

APPENDIXI

YOU CAN CHOOSE BETWEEN APPENDIX I OR II

28 JUGGLE NUMBERS

1 + 1 = 2 1 + 2 = 3 1 + 3 = 4 1 + 4 = 5 1 + 5 = 62 + 1 = 3 2 + 2 = 4 2 + 3 = 5 2 + 4 = 6 2 + 5 = 73 + 1 = 4 3 + 2 = 5 3 + 3 = 6 3 + 4 = 7 3 + 5 = 84 + 1 = 5 4 + 2 = 6 4 + 3 = 7 4 + 4 = 8 4 + 5 = 95 + 1 = 6 5 + 2 = 7 5 + 3 = 8 5 + 4 = 9 5 + 5 =10

6 + 1 = 7 6 + 2 = 8 6 + 3 = 9 6 + 4 =10 6 + 5 = 117 + 1 = 8 7 + 2 = 9 7 + 3 =10 7 + 4 = 11 7 + 5 =128 + 1 = 9 8 + 2 =10 8 + 3 = 11 8 + 4 = 12 8 + 5 =139 + 1 =10 9 + 2 = 11 9 + 3 = 12 9 + 4 = 13 9 + 5 =14

10 + 1 = 11 10 + 2 = 12 10 + 3 = 13 10 + 4 = 14 10 + 5 =15

1 + 6 = 7 1 + 7 = 8 1 + 8 = 9 1 + 9 =10 1 + 10 = 112 + 6 = 8 2 + 7 = 9 2 + 8 =10 2 + 9 = 11 2 + 10 =123 + 6 = 9 3 + 7 =10 3 + 8 = 11 3 + 9 = 12 3 + 10 =134 + 6 =10 4 + 7 = 11 4 + 8 = 12 4 + 9 = 13 4 + 10 =145 + 6 = 11 5 + 7 = 12 5 + 8 = 13 5 + 9 = 14 5 + 10 =15

6 + 6 =12 6 + 7 = 13 6 + 8 = 14 6 + 9 = 15 6 + 10 =167 + 6 = 13 7 + 7 =14 7 + 8 = 15 7 + 9 = 16 7 + 10 =178 + 6 = 14 8 + 7 = 15 8 + 8 =16 8 + 9 = 17 8 + 10 =189 + 6 = 15 9 + 7 = 16 9 + 8 = 17 9 + 9 =18 9 + 10 =19

10 + 6 = 16 10 + 7 = 17 10 + 8 = 18 10 + 9 = 19 10 +10 =20

ADDITION TABLES

• The ‘one’ and ‘ten’ tables are easy; the results in bold in the tables (compiledbelow) form nice patterns which children love and can be taught independently.

• Tell (encourage) them everyday how much they havelearnt and how little is left to be learnt. This gives thema sense of achievement and gives them a comfortablefeeling that they already know quite a bit of additionand addition is not difficult after all.

• Now take up the remaining tables taking half a blockof 5 lines (shaded) at a time, for a week or so for thechild to learn it thoroughly. If the children take time itdoes not matter; just encourage them and be positive.

APPENDIX I: ADDITION USING TABLES

1 + 1 = 22 + 2 = 43 + 3 = 64 + 4 = 85 + 5 = 106 + 6 = 127 + 7 = 148 + 8 = 169 + 9 = 18

10 +10 = 20

9 + 1 = 108 + 2 = 107 + 3 = 106 + 4 = 105 + 5 = 104 + 6 = 103 + 7 = 102 + 8 = 101 + 9 = 10

JUGGLE NUMBERS 29

APPENDIX I: ADDITION USING TABLES

TEACH ADDITION TABLES

TEACH AS RHYMESChildren love rhymes even without knowing (‘understanding’) who is ‘Jack’ or whatis ‘Jill’. Tables also are to be taught just as rhymes. It is rote learning and blind andunconcious recital that we need.

HOW?NO DISTRACTIONSTurn off the electronic gadgets that distract the child. Help the child to concentrate.

ReciteThe child repeatedly recites the chosen (5) lines, say 5 to 10 times.

Write ...In case of a doubt we write an English word to get the correct spelling. So there issome sort of ‘memory’ in writing apart from oral, aural and visual memories. Thechild recites a line of the table loud and at the same time writes the line. This waythe learning process takes place through the mouth, ear, hand and eyes. (Childrenhave a tendency to ‘fill’ the tables by vertical columns; do not allow it as it is a totalwaste of time and energy.)

RepeatThis process, reciting and writing, may be repeated morning and evening for a fewdays until fluency is achieved. Start with the first block. Only when the child isthorough with this, move on to the next block.

KEEP UPDATINGEach time you start, check earlier blocks learnt. When you test the child for additionof 2 single-digit numbers, the response must be instant (not starting from the 1st lineetc.) as if the question was, ‘What is your name?’.

TEACH VERY EARLY

To avoid confusing the child, teach tables before the (education) ‘system’ startsmessing up with numbers and, more importantly, calculations.

MAIL MEYou can always mail me for any consultations or [email protected] [email protected]

ADDITION(of 2 single digit numbers instantly)

WITHOUT

ADDITION TABLES

APPENDIXII

YOU CAN CHOOSE BETWEEN APPENDIX I OR II

JUGGLE NUMBERS 33

Split 10 (in all possible ways)

10 is 9 & 1 or 1 & 98 & 2 2 & 87 & 3 3 & 76 & 4 4 & 65 & 5

10 is

5 & 5

4 & 6

7 & 3

6 & 4

3 & 7

1 & 9

8 & 2

9 & 1

2 & 8

WHAT IS 10?

APPENDIX II: ADDITION WITHOUT TABLES

34 JUGGLE NUMBERS


10 is 01) 5 & ___02) 7 & ___03) ___ & 204) 9 & ___05) 3 & ___06) 8 & ___07) ___ & 408) 1 & ___09) 6 & ___10) ___ & 511) 4 & ___12) ___ & 813) 2 & ___14) ___ & 1015) ___ & 716) ___ & 317) ___ & 918) ___ & 619) 10 & ___

01) 10 – 7 = ____02) 10 – 5 = ____03) 10 – 1 = ____04) 10 – 8 = ____05) 10 – 6 = ____06) 10 – 3 = ____07) 10 – 9 = ____08) 10 – 4 = ____09) 10 – 0 = ____10) 10 – 2 = ____11) 10 – 10 = ____12) 10 – 3 = ____13) 10 – 7 = ____14) 10 – 5 = ____15) 10 – 1 = ____16) 10 – 6 = ____17) 10 – 5 = ____18) 10 – 8 = ____19) 10 – 4 = ____

EXERCISE (1)

JUGGLE NUMBERS 35


5 is

___ & ___

___ & ___

___ & ___

___ & ___

WHAT IS 5?

PRACTICE (1)

10 is 5 & ___ 5 is 4 & ___ 5 is 2 & ___ 5 is 1 & ___ 10 is 7 & ___ 5 is 3 & ___ 10 is 8 & ___ 5 is 4 & ___ 10 is 3 & ___ 5 is 1 & ___ 10 is 4 & ___ 5 is 2 & ___ 10 is 6 & ___ 5 is 4 & ___

PRACTICE (2)

5 is ___ & 3 10 is ___ & 6 5 is ___ & 1 10 is ___ & 8 5 is ___ & 2 5 is ___ & 5 10 is ___ & 9 5 is ___ & 4 10 is ___ & 7 10 is ___ & 8 5 is ___ & 2 5 is ___ & 5 10 is ___ & 9 5 is ___ & 4

36 JUGGLE NUMBERS


01) 10 is ___ & 202) 5 is ___ & 003) 5 is 0 & ___04) 10 is 8 & ___05) 10 is ___ & 406) 5 is 2 & ___07) 10 is 7 & ___08) 10 is ___ & 609) 10 is ___ & 910) 5 is 1 & ___11) 10 is 9 & ___12) 10 is 4 & ___13) 5 is ___ & 314) 5 is ___ & 415) 10 is 6 & ___16) 10 is ___ & 517) 5 is 3 & ___18) 10 is ___ & 0

01) 5 – 3 = ____02) 5 – 5 = ____03) 5 – 1 = ____04) 10 – 3 = ____05) 10 – 5 = ____06) 10 – 10 = ____07) 10 – 7 = ____08) 5 – 2 = ____09) 5 – 0 = ____10) 5 – 3 = ____11) 10 – 0 = ____12) 5 – 3 = ____13) 5 – 4 = ____14) 10 – 8 = ____15) 5 – 1 = ____16) 10 – 2 = ____17) 10 – 9 = ____18) 10 – 6 = ____

EXERCISE (2)

JUGGLE NUMBERS 37


WHAT IS 3?3 is 2 & 1 or 1 & 2

WHAT IS 4?4 is 3 & 1 or 1 & 3

2 & 2 or 2 & 2

PRACTICE (1)

3 is 2 & ___ 4 is 3 & ___ 4 is 1 & ___ 3 is 1 & ___ 4 is 4 & ___ 3 is 3 & ___ 4 is 2 & ___ 5 is 3 & ___ 10 is 8 & ___ 4 is 3 & ___ 5 is 2 & ___ 10 is 2 & ___ 10 is 3 & ___ 5 is 1 & ___ 4 is 2 & ___ 3 is 2 & ___ 10 is 3 & ___

PRACTICE (2)

2 & ___ is 4 1 & ___ is 3 7 & ___ is 10 3 & ___ is 5 4 & ___ is 10 ___ & 3 is 5 ___ & 6 is 10 ___ & 2 is 5 ___ & 8 is 10 ___ & 2 is 10 ___ & 3 is 4 ___ & 4 is 5 ___ & 4 is 10 ___ & 2 is 10 ___ & 1 is 5 ___ & 1 is 3 ___ & 2 is 5

38 JUGGLE NUMBERS


EXERCISE (3)

01) 6 + 4 = ____02) 3 + 2 = ____03) 2 + 1 = ____04) 1 + 4 = ____05) 2 + 8 = ____06) 2 + 3 = ____07) 3 + 7 = ____08) 8 + 2 = ____09) 2 + 2 = ____10) 1 + 3 = ____11) 4 + 1 = ____12) 7 + 3 = ____13) 16 + 4 = ____14) 43 + 2 = ____15) 72 + 1 = ____16) 21 + 4 = ____17) 32 + 8 = ____18) 92 + 3 = ____19) 23 + 7 = ____20) 58 + 2 = ____21) 23 + 2 = ____22) 61 + 4 = ____23) 57 + 3 = ____

1) 10 – 4 = ____2) 5 – 2 = ____3) 3 – 1 = ____4) 5 – 4 = ____5) 10 – 8 = ____6) 3 – 3 = ____7) 10 – 7 = ____8) 4 – 2 = ____9) 2 – 2 = ____10) 2 – 1 = ____11) 10 – 3 = ____12) 5 – 3 = ____13) 45 – 3 = ____14) 95 – 3 = ____15) 20 – 3 = ____16) 40 – 2 = ____17) 5 – 4 = ____18) 25 – 4 = ____19) 7 – 7 = ____20) 27 – 7 = ____21) 23 – 3 = ____22) 68 – 8 = ____23) 74 – 2 = ____

JUGGLE NUMBERS 39


WHAT IS 6?

PRACTICE (1)

5 is 2 & ___ 6 is 2 & ___ 4 is 2 & ___ 6 is 1 & ___ 6 is 4 & ___ 6 is 6 & ___ 4 is 1 & ___ 10 is 3 & ___ 6 is 3 & ___ 4 is 3 & ___ 3 is 2 & ___ 5 is 3 & ___ 10 is 2 & ___ 10 is 6 & ___ 8 is 2 & ___ 7 is 2 & ___ 9 is 2 & ___ 3 is 1 & ___ 4 is 1 & ___

PRACTICE (2)

2 & ___ is 7 1 & ___ is 9 1 & ___ is 6 2 & ___ is 5 2 & ___ is 8 ___ & 3 is 5 ___ & 2 is 10 ___ & 2 is 9 ___ & 2 is 8 ___ & 2 is 5 ___ & 3 is 5 ___ & 3 is 6 ___ & 4 is 6 ___ & 1 is 9 ___ & 2 is 6 ___ & 4 is 6 ___ & 5 is 6 4 & ___ is 6 2 & ___ is 6

6 is 5 & 1 or 1 & 54 & 2 or 2 & 43 & 3 or 3 & 3

40 JUGGLE NUMBERS


01) 10 – 4 = ____02) 5 – 2 = ____03) 3 – 1 = ____04) 6 – 4 = ____05) 10 – 8 = ____06) 4 – 3 = ____07) 10 – 7 = ____08) 4 – 2 = ____09) 6 – 2 = ____10) 5 – 3 = ____11) 3 – 1 = ____12) 4 – 1 = ____13) 10 – 3 = ____14) 20 – 3 = ____15) 40 – 3 = ____16) 6 – 4 = ____17) 26 – 4 = ____18) 96 – 3 = ____19) 6 – 6 = ____20) 26 – 6 = ____21) 56 – 6 = ____22) 68 – 8 = ____23) 76 – 2 = ____

01) 2 + 4 = ____02) 3 + 7 = ____03) 2 + 3 = ____04) 1 + 5 = ____05) 4 + 6 = ____06) 1 + 4 = ____07) 1 + 9 = ____08) 4 + 2 = ____09) 5 + 5 = ____10) 65 + 5 = ____11) 5 + 1 = ____12) 8 + 2 = ____13) 3 + 2 = ____14) 13 + 2 = ____15) 2 + 1 = ____16) 12 + 1 = ____17) 2 + 11 = ____18) 8 + 2 = ____19) 18 + 2 = ____20) 4 + 2 = ____21) 14 + 2 = ____22) 54 + 2 = ____23) 94 + 2 = ____

EXERCISE (4)

JUGGLE NUMBERS 41


WHAT IS 9? 9 is 8 & 1 or 1 & 87 & 2 or 2 & 76 & 3 or 3 & 65 & 4 or 4 & 5

PRACTICE (1)

9 is 2 & ___ 6 is 3 & ___ 5 is 1 & ___ 8 is 1 & ___ 9 is 4 & ___ 9 is 3 & ___ 4 is 2 & ___ 9 is 7 & ___ 9 is 5 & ___ 5 is 3 & ___ 8 is 1 & ___ 8 is 2 & ___ 6 is 2 & ___ 9 is 1 & ___ 9 is 6 & ___ 10 is 7 & ___ 6 is 4 & ___ 9 is 8 & ___

PRACTICE (2)

2 & ___ is 9 1 & ___ is 9 1 & ___ is 8 2 & ___ is 6 2 & ___ is 10 ___ & 3 is 9 ___ & 2 is 12 ___ & 2 is 9 ___ & 2 is 6 ___ & 7 is 9 ___ & 3 is 9 ___ & 3 is 5 ___ & 4 is 9 ___ & 1 is 9 ___ & 8 is 9 ___ & 5 is 9 ___ & 6 is 9 2 & ___ is 9

42 JUGGLE NUMBERS


01) 9 – 3 = ____02) 6 – 2 = ____03) 4 – 3 = ____04) 3 – 1 = ____05) 9 – 4 = ____06) 2 – 1 = ____07) 10 – 3 = ____08) 5 – 2 = ____09) 6 – 3 = ____10) 5 – 3 = ____11) 10 – 7 = ____12) 9 – 5 = ____13) 10 – 8 = ____14) 68 – 8 = ____15) 59 – 2 = ____16) 95 – 4 = ____17) 36 – 4 = ____18) 79 – 3 = ____19) 29 – 7 = ____20) 49 – 6 = ____21) 17 – 1 = ____22) 65 – 5 = ____23) 65 – 60 = ____

01) 26 + 3 = ____02) 37 + 2 = ____03) 52 + 1 = ____04) 14 + 4 = ____05) 22 + 8 = ____06) 83 + 6 = ____07) 42 + 7 = ____08) 91 + 8 = ____09) 65 + 4 = ____10) 18 + 2 = ____11) 48 + 1 = ____12) 76 + 3 = ____13) 35 + 4 = ____14) 43 + 3 = ____15) 67 + 2 = ____16) 4 + 35 = ____17) 21 + 8 = ____18) 22 + 3 = ____19) 32 + 7 = ____20) 83 + 2 = ____21) 24 + 2 = ____22) 1 + 38 = ____23) 4 + 12 = ____

EXERCISE (5)

JUGGLE NUMBERS 43


WHAT IS 7? 7 is 6 & 1 or 1 & 65 & 2 or 2 & 54 & 3 or 3 & 4

PRACTICE (1)

7 is 3 & ___ 7 is 5 & ___ 10 is 4 & ___ 9 is 5 & ___ 13 is 3 & ___ 7 is 4 & ___ 3 is 2 & ___ 9 is 3 & ___ 6 is 2 & ___ 15 is 10 & ___ 7 is 1 & ___ 6 is 2 & ___ 4 is 2 & ___ 11 is 1 & ___ 7 is 6 & ___ 7 is 7 & ___ 5 is 3 & ___ 7 is 1 & ___ 7 is 4 & ___

PRACTICE (2)

2 & ___ is 7 5 & ___ is 7 4 & ___ is 8 2 & ___ is 6 7 & ___ is 10 ___ & 3 is 7 ___ & 2 is 7 ___ & 6 is 16 ___ & 2 is 4 ___ & 7 is 7 ___ & 3 is 5 ___ & 3 is 4 ___ & 4 is 7 ___ & 1 is 7 ___ & 8 is 18 ___ & 5 is 25 ___ & 6 is 76 2 & ___ is 92 3 & ___ is 7

44 JUGGLE NUMBERS


01) 6 – 2 = ____02) 26 – 3 = ____03) 10 – 4 = ____04) 9 – 4 = ____05) 39 – 4 = ____06) 5 – 3 = ____07) 89 – 5 = ____08) 4 – 3 = ____09) 3 – 2 = ____10) 50 – 7 = ____11) 7 – 3 = ____12) 5 – 3 = ____13) 10 – 6 = ____14) 25 – 3 = ____15) 9 – 2 = ____16) 29 – 2 = ____17) 39 – 2 = ____18) 56 – 4 = ____19) 37 – 7 = ____20) 17 – 5 = ____21) 6 – 3 = ____22) 7 – 4 = ____23) 6 – 2 = ____

01) 26 + 1 = ____02) 35 + 2 = ____03) 2 + 145 = ____04) 132 + 4 = ____05) 271 + 8 = ____06) 23 + 3 = ____07) 32 + 7 = ____08) 81 + 2 = ____09) 23 + 2 = ____10) 12 + 3 = ____11) 49 + 1 = ____12) 57 + 3 = ____13) 63 + 4 = ____14) 3 + 24 = ____15) 2 + 15 = ____16) 1 + 431 = ____17) 2 + 804 = ____18) 2 + 312 = ____19) 342 + 7 = ____20) 85 + 2 = ____21) 28 + 2 = ____22) 16 + 3 = ____23) 405 + 1 = ____

EXERCISE (6)

JUGGLE NUMBERS 45


WHAT IS 8?

8 is 7 & 1 or 1 & 76 & 2 or 2 & 65 & 3 or 3 & 54 & 4 or 4 & 4

PRACTICE (1)

8 is 3 & ___ 12 is 2 & ___ 10 is 6 & ___ 8 is 7 & ___ 8 is 4 & ___ 19 is 9 & ___ 8 is 2 & ___ 8 is 7 & ___ 5 is 5 & ___ 5 is 2 & ___ 8 is 6 & ___ 8 is 3 & ___ 8 is 4 & ___ 19 is 1 & ___ 38 is 8 & ___ 10 is 5 & ___ 6 is 2 & ___ 7 is 4 & ___

PRACTICE (2)

2 & ___ is 8 5 & ___ is 8 1 & ___ is 8 6 & ___ is 8 3 & ___ is 8 ___ & 4 is 8 ___ & 8 is 18 ___ & 1 is 28 ___ & 2 is 8 ___ & 7 is 8 ___ & 3 is 8 ___ & 3 is 7 ___ & 4 is 6 ___ & 1 is 3 ___ & 8 is 10 ___ & 6 is 8 ___ & 2 is 9 7 & ___ is 10

46 JUGGLE NUMBERS


01) 600 + 8 = ____02) 3 + 25 = ____03) 2 + 126 = ____04) 124 + 4 = ____05) 271 + 8 = ____06) 200 + 3 = ____07) 370 + 7 = ____08) 803 + 2 = ____09) 42 + 8 = ____10) 7 + 73 = ____11) 49 + 1 = ____12) 75 + 3 = ____13) 9 – 3 = ____14) 39 – 3 = ____15) 59 – 2 = ____16) 8 – 6 = ____17) 28 – 6 = ____18) 43 – 3 = ____19) 37 – 7 = ____20) 56 – 2 = ____21) 32 – 1 = ____22) 88 – 1 = ____23) 47 – 2 = ____

01) 671 + 4 = ____02) 3 + 382 = ____03) 2 + 41 = ____04) 31 + 4 = ____05) 53 + 7 = ____06) 1 + 39 = ____07) 341 + 7 = ____08) 6 + 2 = ____09) 25 + 3 = ____10) 1 + 37 = ____11) 4 + 14 = ____12) 75 + 3 = ____13) 8 – 2 = ____14) 5 – 3 = ____15) 3 – 2 = ____16) 8 – 5 = ____17) 10 – 3 = ____18) 7 – 3 = ____19) 9 – 7 = ____20) 5 – 2 = ____21) 6 – 4 = ____22) 7 – 2 = ____23) 8 – 1 = ____

EXERCISE (7)

JUGGLE NUMBERS 47


01) 8 + 5 = ?The 8 needs a 2 to make 10; Take this 2 from 5; we are left with 38 10; 5 3;So 8 + 5 = 10 & 3 = 13

02) 7 + 5 = ?7 takes 3 from 5 leaving behind 2; so 7 + 5 = 12

03) 9 + 8 = ?9 takes 1 from 8 leaving behind 7; so 9 + 8 = 17

Now that we understand the method, we shall cut the steps.01) 8 + 3 = 11 [cut 2 from 3]02) 9 + 6 = 15 [cut 1 from 6]03) 7 + 5 = 12 [cut 3 from 5]

Starting with the larger number may be easier!

04) 4 + 8 = 12 [cut 6 from 8] or 03) 8 + 4 = 12 [cut 2 from 4]05) 6 + 9 = 15 [cut 4 from 9] or 04) 9 + 6 = 15 [cut 1 from 6]06) 2 + 9 = 11 [cut 8 from 9] or 06) 9 + 2 = 11 [cut 1 from 2]07) 3 + 9 = 12 [cut 7 from 9] or 07) 9 + 3 = 12 [cut 1 from 3]08) 5 + 8 = 13 [cut 5 from 8] or 08) 8 + 5 = 13 [cut 2 from 5]09) 7 + 9 = 16 [cut 3 from 9] or 09) 9 + 7 = 16 [cut 1 from 7]

Fill the blanks:01) 7 + 6 = ______ 02) 8 + 6 = ______

03) 9 + 5 = ______ 04) 8 + 4 = ______

05) 2 + 9 = ______ 06) 6 + 5 = ______

07) 3 + 8 = ______ 08) 4 + 7 = ______

09) 6 + 8 = ______ 10) 7 + 9 = ______

11) 5 + 7 = ______ 12) 8 + 5 = ______

ADD SINGLE DIGIT (to Single Digit) with Carryover

48 JUGGLE NUMBERS


01) 5 + 6 = ____02) 8 + 7 = ____03) 4 + 6 = ____04) 5 + 8 = ____05) 2 + 8 = ____06) 7 + 4 = ____07) 3 + 9 = ____08) 9 + 7 = ____09) 2 + 8 = ____10) 7 + 6 = ____11) 4 + 7 = ____12) 7 + 5 = ____13) 6 + 6 = ____14) 9 + 5 = ____15) 7 + 7 = ____16) 8 + 5 = ____17) 5 + 9 = ____18) 7 + 6 = ____19) 4 + 7 = ____20) 8 + 4 = ____21) 6 + 5 = ____22) 7 + 8 = ____23) 9 + 3 = ____

EXERCISE (8)

01) 6 + 7 = ____02) 3 + 8 = ____03) 9 + 4 = ____04) 7 + 5 = ____05) 8 + 7 = ____06) 9 + 4 = ____07) 8 + 5 = ____08) 6 + 8 = ____09) 6 + 4 = ____10) 5 + 9 = ____11) 8 + 4 = ____12) 5 + 6 = ____13) 6 + 8 = ____14) 7 + 7 = ____15) 9 + 6 = ____16) 7 + 4 = ____17) 7 + 6 = ____18) 2 + 9 = ____19) 8 + 5 = ____20) 8 + 9 = ____21) 4 + 8 = ____22) 9 + 9 = ____23) 9 + 8 = ____

Starting with the larger number may be easier!

APPENDIX III: EXTRA TABLES

SUBTRACTION TABLES

• One can learn these subtraction tables; but it is not a must.If one knows addition (tables) well then subtraction (addition’s reverse process)is pretty easy, like division is easy if you are thorough with multiplication tables.

• All the dotted lines indicate easy results.

1 – 1 = 0 2 – 2 = 0 3 – 3 = 0 4 – 4 = 0 5 – 5 = 02 – 1 = 1 3 – 2 = 1 4 – 3 = 1 5 – 4 = 1 6 – 5 = 13 – 1 = 2 4 – 2 = 2 5 – 3 = 2 6 – 4 = 2 7 – 5 = 24 – 1 = 3 5 – 2 = 3 6 – 3 = 3 7 – 4 = 3 8 – 5 = 35 – 1 = 4 6 – 2 = 4 7 – 3 = 4 8 – 4 = 4 9 – 5 = 4

6 – 1 = 5 7 – 2 = 5 8 – 3 = 5 9 – 4 = 5 10 – 5 = 57 – 1 = 6 8 – 2 = 6 9 – 3 = 6 10 – 4 = 6 11 – 5 = 68 – 1 = 7 9 – 2 = 7 10 – 3 = 7 11 – 4 = 7 12 – 5 = 79 – 1 = 8 10 – 2 = 8 11 – 3 = 8 12 – 4 = 8 13 – 5 = 8

10 – 1 = 11 11 – 2 = 9 12 – 3 = 9 13 – 4 = 9 14 – 5 = 911 – 1 = 10 12 – 2 = 10 13 – 3 = 10 14 – 4 = 10 15 – 5 = 10

6 – 6 = 0 7 – 7 = 0 8 – 8 = 0 9 – 9 = 0 10 – 10 = 07 – 6 = 1 8 – 7 = 1 9 – 8 = 1 10 – 9 = 1 11 – 10 = 18 – 6 = 2 9 – 7 = 2 10 – 8 = 2 11 – 9 = 2 12 – 10 = 29 – 6 = 3 10 – 7 = 3 11 – 8 = 3 12 – 9 = 3 13 – 10 = 3

10 – 6 = 4 11 – 7 = 4 12 – 8 = 4 13 – 9 = 4 14 – 10 = 411 – 6 = 5 12 – 7 = 5 13 – 8 = 5 14 – 9 = 5 15 – 10 = 512 – 6 = 6 13 – 7 = 6 14 – 8 = 6 15 – 9 = 6 16 – 10 = 613 – 6 = 7 14 – 7 = 7 15 – 8 = 7 16 – 9 = 7 17 – 10 = 714 – 6 = 8 15 – 7 = 8 16 – 8 = 8 17 – 9 = 8 18 – 10 = 815 – 6 = 9 16 – 7 = 9 17 – 8 = 9 108 – 9 = 9 19 – 10 = 916 – 6 = 10 17 – 7 = 10 18 – 8 = 10 19 – 9 = 10 20 – 10 = 10

APPENDIX III: EXTRA TABLES

• The 1-table and 10-table are easy.• The 5-table is an interesting pattern and easy to learn. Children love them.• The 10 results with bold letter also form a nice pattern and so these could be

taught as a separate set. Children love these too.• Now take up the remaining tables taking half a block of 5 lines at a time. If the

children take time it does not matter; just encourage them and be positive.

MULTIPLICATION TABLES

1 x 1 = 1 1 x 2 = 2 1 x 3 = 3 1 x 4 = 4 1 x 5 = 52 x 1 = 2 2 x 2 = 4 2 x 3 = 6 2 x 4 = 8 2 x 5 = 103 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12 3 x 5 = 154 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 =16 4 x 5 = 205 x 1 = 5 5 x 2 = 10 5 x 3 = 15 5 x 4 = 20 5 x 5= 25

6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 307 x 1 = 7 7 x 2 = 14 7 x 3 = 21 7 x 4 = 28 7 x 5 = 358 x 1 = 8 8 x 2 = 16 8 x 3 = 24 8 x 4 = 32 8 x 5 = 409 x 1 = 9 9 x 2 = 18 9 x 3 = 27 9 x 4 = 36 9 x 5 = 45

10 x 1 = 10 10 x 2 = 20 10 x 3 = 30 10 x 4 = 40 10 x 5 = 50

1 x 6 = 6 1 x 7 = 7 1 x 8 = 8 1 x 9 = 9 1 x 10 = 102 x 6 = 12 2 x 7 = 14 2 x 8 = 16 2 x 9 = 18 2 x 10 = 203 x 6 = 18 3 x 7 = 21 3 x 8 = 24 3 x 9 = 27 3 x 10 = 304 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36 4 x 10 = 405 x 6 = 30 5 x 7 = 35 5 x 8 = 40 5 x 9 = 45 5 x 10 = 50

6 x 6 =36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 607 x 6 = 42 7 x 7 =49 7 x 8 = 56 7 x 9 = 63 7 x 10 = 708 x 6 = 48 8 x 7 = 56 8 x 8 =64 8 x 9 = 72 8 x 10 = 809 x 6 = 54 9 x 7 = 63 9 x 8 = 72 9 x 9 =81 9 x 10 = 90

10 x 6 = 60 10 x 7 = 70 10 x 8 = 80 10 x 9 = 90 10 x10 =100

doss fast 010710

Documents