1 Abacus -To understand the numeration- Regional Office for In-service Training in Thies JICA Volunteer MITSUNAGA Norito

2 1. Counting numbers(2weeks) ObjectsLet’s count numbers exactly Let’s confirm numbers with moving the ball 1st stageNumbers until 10 Methode1Always move ball to right from left to avoid confusion With moving ball from right to left, count from1 to 10 Methode2 Oppositely, with moving from left to right, deduct 10 to 1 § We teach 0 later. § Let’s start counting slowly at first and increase the speed later Development 1. Make the example in first stage in he below. 2. Make the same number with copying the example Five Six One Two

3 2nd stageNumbers until 20 Methode1With moving ball from right to left, count from1 to 20 Methode2 Oppositely, with moving from left to right, deduct 20 to 1 Fourteen Twenty Fourteen Six

4 Development 1. Place the cards from 1 to 20 in the paper bag. 2. Take one card and ask the students to copy this number 3. Initially count the number 16 of card. Make the same number 16 with ball Strategy Let’s make the students have the image of volume visually with moving the ball. It is effective to use abacus for teacher demonstrate How many carrot are there? One, two,three,…. sixtreen. There are sixteen

5 2. Explain the numbers with figure(2 weeks) object Let’s understand the relation between the numbers and the figures. Let’s replace the numbers with the figure. 1st stage Numbers until 10 Methode1Increase the number of ball in each stage to make the stairs. Count from 1 to 10 with confirming the numbers of figures in each stage

6 Methode2 Show the cards from 1 to 10. Ex. « How many pineapple are there ?» Ask the students to move the ball Confirm the numbers with the students with counting. (With showing the card) « There are 5 » It is not necessary to count the number from 1. It is possible to count from 6 to count 6, 7, 8, 9,10. How many pineapples are there ? ５ One, two, tree, four, five. This is five !

7 2nd stageNumber zero « 0 » When there is nothing, we explain it zero with showing the card nothing 3rd stageNumbers until 20 Ask the student «How many ?» with showing the card from 0 to 20. Ask the students to move to move ball Confirm numbers with the students with counting. ZeroNul 0 How many cucumbers are there? One, two, tree,……,fourteen. It is fourteen! 14

8 Strategy Volume, Number and Figure are the different concepts. It is important to unify those three concepts in the mathematics especially in the beginning. We can find the students to use their finger to count. This is the first experience to unify the (concrete) number and figure. But teacher train the student to use their finger from 5. Also to count the number with ball, Students should count the number from 6,11,16. This technique is practical to use the ruler.

9 3. Count ordinal number(2 weeks) object Let’s understand how to count ordinal number 1st stageCount ordinal number simply a) Move every ball to right. Place the cards from 1 to 10 in the paper bag and take one. Ask the students «Indicate the3rd ball from top » Ask the students «Indicate the3rd ball from bottom» b) Move every ball to right. Ask the students «Indicate the3ed ball from right » Ask the students «Indicate the3ed ball from left» Indicate the 3rd ball from top Indicate the 5th ball from left Here Enveloppe 3 5

10 2nd stageCount with 2 direction a) Move every ball left Place the cards from 1 to 10 in the paper bag and take two. Ask the students «Indicate the ball 2nd from top and 6th from left» Here Indicate the ball 2nd from top and 6th from left Enveloppe ２ ６

11 3rd stageconclusion of ordinal number Ask the students « Where is the 48th ball?» «5th from top and, 8th from left» Strategy It is important to learn how to count from the specific point. We should repeat he exercise from top, bottom, right and left. This experience has close relation to count the number until 100 5th from top and, 8th from left Where is the 48th ball?

12 4. Compare the numbers(2 weeks) object Let’s compare two numbers and tree numbers. 1st stageWhich is bigger ? Methode1 prepare balls which show two number. Ask the students «Which is bigger ?» Confirm two numbers with moving ball left. Repeat with tree numbers Development Comparer numbers with two figure Strategy It is necessary to count every ball.. What is important is to compare the number of the ball in second stage down ! Two Which is biggger? How much is the difference of balls? 14 18

13 5. Compositions(2 month) object understand the composition until 10 1st stageLet’s compose 5 a) Show example with moving 5 balls left on top. b) Prepare the numbers des balls one and one in every stage c) Ask the students in 2nd stage «How many balls is necessary to make 5 ?» d) Ask same question in 3rd stage and others. e) Move balls with counting one by one with constant rhythm. In 2nd stage «1 and 4 are 5» In 3rd stage «2 and 3 are 5» In 4th stage «3 and 2 are 5» In 5th stage «4 and 1 are 5» In 6th stage «0 and 5 are 5» To make 5, How many balls are necessaire ? 2 and 3 are 5 3 and 2 are 5 4 and 1 are 5 5 and 0 are 5 1 and 4 are 5

14 2nd stageLet’s compose 10 a) Show one example with moving 10 balls in the center of every stage b) Move balls with counting with constant rhythm. In 1st stage «10 is 1 and 9» In 2nd stage «10 is 2 and 8» In 3rd stage «10 is 3 and 7» In 4th stage «10 is 4 and 6» In 5th stage «10 is 5 and 5» In 6th stage «10 is 6 and 4» In 7th stage «10 is 7 and 3» In 8th stage «10 is 8 and 2» In 9th stage «10 is 9 and 1» In 10th stage «10 is 10 and 0» c) Compose 10 with moving balls from right to left. In 1st stage «1 and 9 are 10» In 2nd stage «2 and 8 are 10» In 3rd stage «3 and 7 are 10» In 4th stage «4 and 6 are 10» In 5th stage «5 and 5 are 10» In 6th stage «6 and 4 are 10» In 7th stage «7 and 3 are 10» In 8th stage «8 and 2 are 10» In 9th stage «9 and 1 are 10» In 10th stage «10and 0 are 10»

15 3rd stageLet’s compose several numbers a) Prepare several numbers in each stage less than 8. b) Ask the students «Compose 8» c) Compose in each stage with moving balls from right to left. d) Try with other numbers Strategy Composition help understanding addition and subtraction Compose 8 4 and 4 are 8 6 and 2 are 8 2 and 6 are 8 1 and 7 are 8 3 and 5 are 8 5 and 3 are 8 8 and 0 are 8 7 and 1 are 8

16 5. Addition(1mois) object Let’s understand additions with formula 1st stageAddition until 10 with moving balls from right to left. 0+2=20+3=30+4=40+5=50+6=6 1+2=31+3=41+4=51+5=61+6=7 2+2=42+3=52+4=62+5=72+6=8 3+2=53+3=63+4=73+5=83+6=9 4+2=64+3=74+4=84+5=94+6=10 5+2=75+3=85+4=95+5=10 6+2=86+3=96+4=10 7+2=97+3=10 8+2=10 0+7=70+8=80+9=90+10=10 1+7=81+8=91+9=10 2+7=92+8=10 3+7= = = = = = = = = = =10

17 2nd stageAddition with carrying over Ex. 8+3=11 a) Prepare 8 balls left in 1st stage. b) Move 2 balls left in1st stage. c) Move 1 balls left in2nd stage. d) 8+3 =8+2+1 =10+1 =11 e) 9+3 =9+1+2 =10+2 =12 f) Practice with other numbers

18 7. Subtraction(1 month) object Let’s understand subtraction with formula 1st stageSubtraction until 10 with moving balls from left to right. 2-2=03-3=04-4=05-5=06-6=0 3-2=14-3=15-4=16-5=17-6=1 4-2=25-3=26-4=27-5=28-6=2 5-2=36-3=37-4=38-5=39-6=3 6-2=47-3=48-4=49-5=410-6=4 7-2=58-3=59-4=510-5=5 8-2=69-3=610-4=6 9-2=710-3=7 10-2=8 7-7=08-8=09-9=010-10=0 8-7=19-8=110-9=1 9-7=210-8=2 10-7=3 1- 1=0 2- 1=1 3- 1=2 4- 1=3 5- 1=4 6- 1=5 7- 1=6 8- 1=7 9- 1=8 10-1=9

19 2nd stageSubtraction with carrying over Ex. 13-9=4 a) Prepare 10 balls left in 1st stage. b) Prepare 3 balls left in 2nd stage. c) Move 9 balls right in first stage. d) 13-9 = = =1+3 =4 e) 14-8 =10+4-8= = =2+4 =6 f) Practice with other numbers

20 8. Numbers until 100(2 weeks) object understand to count number every 10 1st stageNumbers until 100 a) count numbers from 1 to 100 from right to left b) count numbers from 100 to 1 inversely c) count numbers every 2, 5,10 2nd stageCount numbers with 10 a) Ask the students «There are 5 piece of 10 pencils. How many are there totally ? » piece of 10 pencils. How many are there totally ? 50 10

21 3rd stageAddition with 10 Ex =50 a) «20+30= ? With showing 2 pieces de 10pencils and 3 piece » b) Prepare 20 pencils first and add 30 next 20+30= ? ? 10

22 4th stageSubtraction with 10 Ex =20 a) «50-30= ? With showing 5 piece of 10pencils» b) Prepare 50 first and move 30 left f ) Practice with other numbers 50-30= ? ? 10

23 9. Multiplication until 100(2 month) Let’s use abacus for multiplication. It is effective to grow up the sense of volume for mental calculation. If the students can get enough sense,for multiplication, they can calicle much easier the multiplication in the below 12 × ×5= ? 12 （ 10+2 ） balls 13 （ 10+3 ） coloms

24 Let’s play with dice. a)Move 5 balls left in each stage. b)Chose 2 students and ask them to throw one dice. The point of left student is 1 The point of right student is 4 The point is 2 The point is 6 The right win. c)Let’s change the students every time to motivate the participation. Through the game, students start calculation automatically. I won ! TRIA