Mental arithmetic year 2 second edition

second- Editionmay 2005Designed & Prepared By

Ragu Ramasamy & Zuraimi MahamudE X I TE N T E R

LESSON 6LESSON 7LESSON 8LESSON 9LESSON 10LESSON 1LESSON 2LESSON 3LESSON 4LESSON 5SAMPLE LESSONM E N UE X I T

Basic Knowledge Of AMA RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

BASIC KNOWLEDGE OF ABACUSmenu

PARTS OF ABACUSClearing DeviceFrameUpper BeadsLower BeadsBeamRodmenu

FINGERING POSTUREFore FingerMiddle FingerThumb( to move down the lower beads )( to move up / down upper beads )( to move up lower beads )menu

FINGERING HOLDING PENCILmenu

When using abacus, pupils must sit with both shoulders relaxed and slightly leaning forward. Picture in the next slide shows the proper sitting posture while using the abacus.menu

SITTING POSTUREmenu

While doing Mental Arithmetic, pupils must close their eyes and lay on table while visualizing the abacus. Picture in the next slide shows the posture while doing Mental Arithmetic.menu

SITTING POSTURE WHILE DOING MENTAL ARITHMETICSmenu

END OF LESSON PLEASE CLICK MENU menu

Addition (Direct) Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

32 + 12 =The question is 32 + 12,First up 32,Then plus 12,Up 12,Equals44 32 + 12 = 4412345DIRECT ADDITIONADDITION WITHIN 1000menu

DIRECT ADDITIONADDITION WITHIN 1000156 + 23 =156 + 23 = 179The question is 156 + 23,First up 156,Then plus 23,Up 23,Equals179 12345menu

625 + 273 =625 + 273 = 898DIRECT ADDITIONADDITION WITHIN 1000The question is 625 + 273,First up 625,Then plus 273,Up 273,Equals898 12345menu

DIRECT ADDITIONADDITION WITHIN 1000363 + 516 =363 + 516 = 879The question is 363 + 516,First up 363,Then plus 516,Up 516,Equals879 12345menu

56 + 23 =CALCULATE USING MENTALADDITION WITHIN 1000The question is 56 + 23,First up 56,Then plus 23,Up 23,Equals79 12345menu

PRACTICE23 + 21 =1.44219 + 30 =2.24963 + 321 =3.384114 + 75 =4.189311 + 163 =5.474471 + 6 =6.477152 + 126 =7.27892 + 101 =8.193242 + 156 =9.39884 + 205 =10.289menu

PRACTICE263 + 21 =1.284378 + 501 =2.879623 + 321 =3.944114 + 755 =4.869321 + 163 =5.484718 + 21 =6.739372 + 126 =7.498382 + 101 =8.483242 + 656 =9.898834 + 105 =10.939menu

TEST152 + 126 =1.278242 + 107 =2.349632 + 215 =3.847314 + 675 =4.989511 + 263 =5.774171 + 706 =6.877452 + 526 =7.978392 + 101 =8.493420 + 561 =9.98184 + 205 =10.289menu

Addition (Pool 5) Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

32 + 3 =The question is 32 + 3 First up 32,Then plus 3,Not enough beads at lower beads to plus 3,How to do it ? 1POOL 5 ADDITIONADDITION WITHIN 1000234567Think, the little friend of 3 is , so. Up 5, down 2 352Equals 35 82menu

143 + 252 =Up 143,Then plus 252,Up 250 and up 21POOL 5 ADDITIONADDITION WITHIN 1000234Equals395 6Then,Up 5 down 3,menu

232 + 43 =Up 232,Then plus 43,Up 50, down 101POOL 5 ADDITIONADDITION WITHIN 1000234Equals475 6And Up 5 down 2,menu

132 + 465 =Up 132,Then plus 465,Up 500, down 1001POOL 5 ADDITIONADDITION WITHIN 1000234Equals597 6And Up 65,menu

CALCULATE USING MENTALADDITION WITHIN 100032 + 3 =The question is 32 + 3First up 32,Then plus 3,Not enough beads at lower beads to plus 3,How to do it ? 1234567Think, the little friend of 3 is , so. Up 5, down 2 352Equals 35 82menu

CALCULATE USING MENTALADDITION WITHIN 10004 + 12 =The question is 4 + 12First up 4,Then plus 12,Up 10,up 5 and down 3,Equals 1234516 menu

CALCULATE USING MENTALADDITION WITHIN 1000623 + 135 =The question is 623 + 135First up 623,Then plus 135,Up 100,up 50,down 20 and up 5,Equals 12345758 menu

PRACTICE234 + 154 =1.388419 + 330 =2.749372 + 213 =3.585342 + 115 =4.457243 + 613 =5.856643 + 4 =6.647512 + 246 =7.758932 + 43 =8.975245 + 403 =9.648167 + 402 =10.569menu

PRACTICE235 + 131 =1.366415 + 242 =2.657621 + 354 =3.975852 + 124 =4.976431 + 254 =5.685645 + 120 =6.765738 + 41 =7.419 + 540 =8.959214 + 445 =9.659628 + 241 =10.869779menu

TEST456 + 300 =1.756728 + 140 =2.868125 + 420 =3.545364 + 423 =4.787459 + 200 =5.659324 + 243 =6.567512 + 243 =7.755614 + 232 =8.857222 + 433 =9.655853 + 34 =10.887menu

Addition (Carrying ) Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

162 + 28 =The question is 162 + 28First up 162,Then plus 28,up 20 and up 8Not enough beads at rod ones to plus 8,How to do it ? 1ADDITION WITH CARRYINGADDITION WITHIN 1000234567Think, the big friend of 8 is , so. Down 2 and carry 1 at tens8102Equals 190 82menu

371 + 119 =The question is 371 + 119First up 371,Then plus 119,up 110 and up 9Not enough beads at rod ones to plus 9 ,How to do it ? 1ADDITION WITH CARRYINGADDITION WITHIN 1000234567Think, the big friend of 9 is , so. Down 1 and carry 1 at tens9101Equals 490 81menu

78 + 780 =The question is 78 + 780First up 78,Then plus 780,up 700 and up 80Not enough beads at rod tens to plus 80 ,How to do it ? 1ADDITION WITH CARRYINGADDITION WITHIN 1000234567Think, the big friend of 8 is , so. Down 2 at tens and carry 1 at hundredsEquals 858 82menu

275 + 132 =The question is 275 + 132First up 275,Then plus 132,up 100 and up 32Not enough beads at rod tens to plus 32 ,How to do it ? 1ADDITION WITH CARRYINGADDITION WITHIN 1000234567Think, the big friend of 3 is , so. Down 7 at tens and carry 1 at hundreds and up 2,Equals 407 87menu

82 + 32 =The question is 82 + 32First up 82,Then plus 32,Down 7 at tens, carry 1 at hundreds and up 2 ,Equals114 12345CALCULATE USING MENTALADDITION WITHIN 1000menu

178 + 541 =The question is 178 + 541First up 178,Then plus 541,Up 500, down 6 at tens, carry 1 at hundreds and up 1,Equals719 12345CALCULATE USING MENTALADDITION WITHIN 1000menu

236 + 574 =The question is 236 + 574First up 236,Then plus 574,Up 500, down 3 at tens, and carry 1 at hundreds.Equals810 12345CALCULATE USING MENTALADDITION WITHIN 10006Then plus 4 (down 6 at ones and carry 1 at tens.)menu

PRACTICE235 + 755 =1.990415 + 559 =2.974621 + 285 =3.906652 + 124 =4.776431 + 254 =5.685645 + 260 =6.638 + 291 =7.929419 + 292 =8.711214 + 695 =9.909628 + 280 =10.908905menu

PRACTICE456 + 250 =1.706728 + 191 =2.919125 + 580 =3.705364 + 155 =4.519459 + 513 =5.972324 + 106 =6.430512 + 243 =7.755614 + 232 =8.846222 + 433 =9.655853 + 58 =10.911menu

TEST458 + 502 =1.960924 + 68 =2.992465 + 25 =3.490327 + 124 =4.451796 + 130 =5.926828 + 91 =6.454 + 508 =7.962678 + 140 =8.818285 + 140 =9.425124 + 595 =10.719919menu

Subtraction (Direct) Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

82 - 32 =The question is 82 - 32First up 82,Then minus 32,Down 32,Equals 50 82 - 32 = 5012345DIRECT SUBTRACTIONSUBTRACTION WITHIN 1000menu

179 - 23 =The question is 179 - 23First up 179,Then minus 23,Down 23,Equals156 179 - 23 = 15612345DIRECT SUBTRACTIONSUBTRACTION WITHIN 1000menu

789 - 275 =The question is 789 - 275First up 789,Then minus 275,Down 275,Equals 514 789 - 275 = 51412345DIRECT SUBTRACTIONSUBTRACTION WITHIN 1000menu

289 - 165 =DIRECT SUBTRACTIONSUBTRACTION WITHIN 1000menu

82 - 32 =The question is 82 - 32First up 82,Then minus 32,Down 32,Equals50 12345CALCULATE USING MENTALSUBTRACTION WITHIN 1000menu

179 - 23 =The question is 179 - 23First up 179,Then minus 23,Down 23,Equals 156 12345CALCULATE USING MENTALSUBTRACTION WITHIN 1000menu

435 - 215 =CALCULATE USING MENTALSUBTRACTION WITHIN 1000menu

PRACTICE346 - 21 =1.325415 - 210 =2.205328 - 115 =3.213244 - 121 =4.123678 - 355 =5.323924 - 413 =6.51188 - 35 =7.53344 - 211 =8.133964 - 510 =9.454188 - 53 =10.135menu

PRACTICE78 - 26 =1.52219 - 111 =2.108471 - 261 =3.210146 - 125 =4.21411 - 401 =5.10

385 - 175 =6.210499 - 472 =7.27392 - 271 =8.121

242 - 132 =9.110484 - 122 =10.362menu

TEST244 - 212 =1.32922 - 402 =2.520867 - 656 =3.211894 - 642 =4.252666 - 561 =5.105458 - 203 =6.255888 - 255 =7.633748 - 626 =8.122946 - 421 =9.525224 - 112 =10.112menu

Subtraction (Break 5) Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

98 - 44 =The question is 98 - 44First up 98,Then minus 44, Down 40 and 4.Not enough beads at lower beads to down 4,How to do it ? 1BREAK 5 SUBTRACTIONSUBTRACTION WITHIN 1000234567Think, the little friend of 4 is , so. Up 1, down 5 451Equals54 81menu

CALCULATE USING MENTALSUBTRACTION WITHIN 100098 - 44 =The question is 98 - 44First up 98,Then minus 44, Down 40 and 4.Not enough beads at lower beads to down 4,How to do it ? 1234567Think, the little friend of 4 is , so. Up 1, down 5 451Equals 54 81menu

CALCULATE USING MENTALSUBTRACTION WITHIN 1000783 - 143 =The question is 783 - 143First up 783,Then minus 143, (Down 100 and down 43.)Not enough beads at lower beads to down 43,How to do it ? 1234567Think, the little friend of 4 is , so. Up 10, down 50 and down 3.451Equals 640 81menu

PRACTICE435 - 123 =1.312453 - 230 =2.223348 - 214 =3.134365 - 244 =4.121352 - 122 =5.230264 - 32 =6.232452 - 141 =7.311177 - 64 =8.11398 - 44 =9.54457 - 254 =10.203menu

PRACTICE879 - 635 =1.244864 - 540 =2.324925 - 503 =3.422752 - 132 =4.620663 - 232 =5.431877 - 444 =6.433946 - 523 =7.423735 - 103 =8.632672 - 241 =9.431585 - 245 =10.340menu

TEST867 - 443 =1.424 894 - 452 =2.442666 - 444 =3.222458 - 235 =4.223888 - 435 =5.453748 - 324 =6.424346 - 213 =7.133328 - 104 =8.224964 - 344 =9.620946 - 524 =10.422menu

Subtraction (Removing) Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

367 - 289 =SUBTRACTION WITH REMOVINGSUBTRACTION WITHIN 1000The question is 367 - 289First up 367,Then minus 289, Down 200,then down 80Not enough beads to down 80,1234567Equals78 Then down 9,also not enough beads,so remove 1 at tens,up 1at ones. So remove 1 at hundreds, up 2 at tens,menu

CALCULATE USING MENTALADDITION WITHIN 1000367 - 289 =The question is 367 - 289First up 367,Then minus 289, Down 200,then down 80Not enough beads to down 80,1234567Equals78 Then down 9,also not enough beads,so remove 1 at tens,up 1at ones. So remove 1 at hundreds, up 2 at tens,menu

PRACTICE286 - 127 =1.159235 - 106 =2.129410 - 270 =3.140163 - 157 =4.6436 - 241 =5.195

622 - 113 =6.509

666 - 557 =7.109798 - 659 =8.139932 - 203 =9.729938 - 145 =10.793menu

PRACTICE346 - 217 =1.129415 - 245 =2.170328 - 181 =3.147244 - 116 =4.128678 - 188 =5.490924 - 415 =6.509488 - 295 =7.193344 - 216 =8.128964 - 272 =9.692188 - 59 =10.129menu

TEST867 - 372 =1.495 894 - 327 =2.567666 - 118 =3.548458 - 239 =4.219888 - 439 =5.449748 - 329 =6.419346 - 219 =7.127328 - 183 =8.145964 - 374 =9.590946 - 561 =10.385menu

Integrated Addition & Subtraction Within 1000 RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

PRACTICE131 + 274 =1.405 135 + 254 =2.389243 + 163 =3.406323 + 128 =4.451252 + 234 =5.486162 + 273 =6.435189 + 213 =7.402264 + 217 =8.481279 + 151 =9.430309 + 126 =10.435menu

PRACTICE447 + 382 =1.829 623 + 209 =2.832376 + 578 =3.954288 + 472 =4.760491 + 378 =5.869516 + 247 =6.763385 + 428 =7.813713 + 199 =8.912147 + 627 =9.774414 + 586 =10.1000menu

PRACTICE472 - 134 =1.338 319 - 124 =2.195357 - 213 =3.144430 - 307 =4.123422 - 289 =5.133500 - 217 =6.283408 - 239 =7.169386 - 193 =8.193462 - 179 =9.283432 - 167 =10.265menu

PRACTICE825 - 473 =1.352 877 - 549 =2.328762 - 314 =3.448884 - 677 =4.207907 - 637 =5.270525 - 376 =6.149703 - 499 =7.204870 - 473 =8.397836 - 676 =9.1601000 - 497 =10.503menu

MultiplicationRAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

MULTIPLICATION WITHIN2,3,4 AND 5menu

Understanding multiplication as a repeated addition.menu

Example 1menu

Multiplication is a repeated addition.Let us put 3 lemons in each baskets. There are 2 baskets. Group 1Group 2menu

Multiplicand Multiplier Group 1Group 2The number of lemons is :-3 + 3 = 6So, 3+3 is adding 2 groups of 3. We can write it as :- 2 x 3 = 6 multiplication is a repeated addition :- 3 + 3 = 2 x 3menu

Multiplicand Multiplier Group 1Group 2Number Sentences3 + 3 = 62 x 3 = 6menu

33Number linesWhen using number lines, skip count by threes :- 3 , 6 .3 + 3 = 62 x 3 = 6menu

2 x 3 = 6Multiplicand Multiplier Product menu

Using Abacus1 digit x 1 digit = 2 digit

2x3 =0606Display 06 on the abacusmenu

Using Mental Arithmetic1 digit x 1 digit = 2 digit

2x3 =06menu

Example 2menu

Multiplication is a repeated addition.

Let us put 4 pieces of pizza in each plates. There are 3 plates.

Group 1Group 2Group 3menu

Group 1Group 2Group 3The number of pieces of pizza are :-4 + 4 + 4 = 12So, 4+4+4 is adding 3 groups of 4. We can write it as :- 3 x 4 = 12 multiplication is repeated addition :- 4 + 4+ 4 = 3 x 4menu

Number Sentences4 + 4 + 4 = 123 x 4 = 12Group 1Group 2Group 3menu

44Number lines4 + 4 + 4 = 123 x 4 = 12 4When using number lines, skip count by fours :- 4 , 8, 12 .menu


3x4 =1212Display 12 on the abacusmenu


3x4 =12menu

Multiplication usingAbacus and Mental Arithmetic menu


5x3 =1515menu


5x3 =15menu


8x2 =1616menu


8x2 =16menu


9x3 =2727menu


8x2 =16menu


9x3 =2727menu


9x3 =27menu

Lets practice together using abacus.menu

Practice 1x2 =0202menu

Practice 7x5 =3535

Lets practice together using abacus.menu

PRACTICEINSTRUCTION :Display the product on your abacus. 2 x 3 = 2. 3 x 4 = 3. 4 x 2 =

4. 3 x 5 =5. 1 x 3 =6. 2 x 2 =

7. 7 x 4 =8. 9 x 2 =9. 6 x 3 =

10. 3 x 2 =11. 9 x 4 =12. 8 x 2 =Using abacusmenu

Lets practice together using Mental Arithmetic .menu

PRACTICEINSTRUCTION :Teacher read out the question and pupils calculate using mental and say the answer . 2 x 4 = 2. 3 x 2 = 3. 7 x 2 =

4. 3 x 3 =5. 7 x 3 =6. 2 x 5 =

7. 2 x 2 =8. 9 x 3 =9. 6 x 3 =

10. 3 x 5 =11. 9 x 5 =12. 8 x 2 =Using mentalmenu

Division RAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

Division within 2,3,4 and 5menu

Example 1menu

Understanding division as sharing equally or grouping.menu

There are 4 ice-creams. The ice-creams are shared equally among Alisa and Aiman.AlisaAimanmenu

Each kids get 2 ice-creams.We write the number sentence as :-4 2 = 2menu

Division usingAbacus menu

Division Using Abacus Step 1

4 2 = 2Understanding the division equation DividendDivisorQuotientExamplemenu

Division Using Abacus Step 2The Dividend must be placed starting from the third rod on the left side of the abacus.Third rod4 2 = menu

To find the place to up the quotient, divide the first digit of the dividend with divisor, if the digit is not less than the divisor, skip 1 rod to the left from the dividend to place the quotient. If the digit is less, place the quotient beside the dividend on the left side.

Division Using Abacus Step 3Example4 2 = 4 can be divided with 2, so skip 1 rod to the left from the dividendmenu

Division Using Abacus 4 2 = Example4 can be divided with 2,so skip 1 rod to the left from the dividend.menu

Division Using Abacus 2 = 2 Step 4ExampleMinus the Dividend with the product of Quotient Divisor.Quotient x Divisor 2 x 2 = 4So, down 4 at dividendmenu

Division Using Abacus So, down 4 at dividend Quotient x Divisor 2 x 2 = 4menu

Division Using Abacus 2 = 2Step 5ExampleTo find out number of digit for quotient,(number of digit for dividend number of digit for divisor) then plus 1 if the first digit of dividend is bigger then the first digit of divisor(number of digit for dividend number of digit of divisor) 1 digit - 1 digit (number 4 is more then 2 so, add 1 digit) = 1 1 + 1 The answer or quotient must be = 1 digitmenu

Division Using Abacus Answer is 1 digit Answer for 4 2 = 2menu

Example 2menu

Mak Minah bought 15 birds. She puts 5 birds in a basket. How many basket does she need?Group 1Group 2Group 3menu

Divide 15 birds into groups of 5.Group 1Group 2Group 3There are 3 groups15 5 3 =menu

Division usingAbacus menu

Division Using Abacus Step 1

15 5 = 3Understanding the division equation DividendDivisorQuotientExamplemenu

Division Using Abacus Step 2The Dividend must be placed starting from the third rod on the left side of the abacus.Third rod15 5 = menu

Division Using Abacus Step 3Example15 5 = 1 cannot be divided with 5, so place the quotient beside the dividend on the leftTo find the place to up the quotient, divide the first digit of the dividend with divisor, if the digit is not less than the divisor, skip 1 rod to the left from the dividend to place the quotient. If the digit is less, place the quotient beside the dividend on the left side.

menu

Division Using Abacus 15 5 = Example1 cannot be divided with 5,so place the quotient next to the left of the dividend

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Division Using Abacus 15 5 = 3 Step 4ExampleMinus the Dividend with the product of Quotient Divisor.Quotient x Divisor 3 x 5 = 15So, down 15 at dividendmenu

Division Using Abacus So, down 15 at dividend Quotient x Divisor 3 x 5 = 15menu

Division Using Abacus 15 5 = 3Step 5Example(number of digit for dividend number of digit of divisor) 2 digit - 1 digit (number 1 is less then 5 so, dont add 1 digit) = 2 - 1 The answer or quotient must be = 1 digitTo find out number of digit for quotient,(number of digit for dividend number of digit for divisor) then plus 1 if the first digit of dividend is bigger then the first digit of divisormenu

Answer is 1 digit Answer for 15 5 = 3Practice 1 menu

Lets practice using abacus.menu

QUESTION25 5 = Practice 1 menu

Practice 1 Third rod25 5 = menu

25 5 = 2 cannot be divided with 5,so place the quotient next to the left of the dividend

Practice 1 menu

So, down 25 at dividend Quotient x Divisor 5 x 5 = 25Practice 1 menu

9 3 = 9 can be divided with 3, So skip 1 rod to the left from the dividendPractice 2 menu

28 4 = 2 cannot be divided with 4,so place the quotient next to the left of the dividend

Practice 3 menu

8 2 = 8 can be divided with 2, So skip 1 rod to the left from the dividendPractice 4 menu

Lets practice using abacus.menu

PRACTICEINSTRUCTION :Solve this question using abacus. 6 2 = 2. 16 4 = 3. 4 2 =

4. 18 3 =5. 15 3 =6. 35 5 =

7. 27 3 =8. 10 5 =9. 36 4 =

10. 28 4 =11. 8 4 =12. 18 2 =Using abacusmenu

Sample LessonRAGU RAMASAMY * ZURAIMI MAHAMUDDesign & Prepared By+ - x second- Editionmay 2005menu

MoneyLearning Outcomes : Represent the value of money in RM and senmenu

RM 1.7550 senRM 120 sen5senUsing Abacus175menu

MoneyLearning Outcomes : Add money up to RM50menu

RM 5.55Using AbacusRM 2.20RM 7.75+Sample menu

Documents

Mental arithmetic year 2 second edition