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

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

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Abacus-To understand the numeration-

Regional Office for In-service Training in ThiesJICA Volunteer

MITSUNAGA Norito

Page 2: 1 Abacus -To understand the numeration- Regional Office for In-service Training in Thies JICA Volunteer MITSUNAGA Norito

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1. Counting numbers (2weeks)Objects Let’s count numbers exactly

Let’s confirm numbers with moving the ball

1st stage Numbers until 10

Methode1 Always 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

Page 3: 1 Abacus -To understand the numeration- Regional Office for In-service Training in Thies JICA Volunteer MITSUNAGA Norito

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2nd stage Numbers until 20Methode1 With 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

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Development1. Place the cards from 1 to 20 in the paper bag. 2. Take one card and ask the students to copy this number3. Initially count the number 16 of card.Make the same number 16 with ball

StrategyLet’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

Page 5: 1 Abacus -To understand the numeration- Regional Office for In-service Training in Thies JICA Volunteer MITSUNAGA Norito

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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 10Methode1 Increase 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

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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 ?

One, two, tree, four, five. This is five !

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2nd stage Number zero « 0 »When there is nothing, we explain it zero with showing the card nothing

3rd stage Numbers until 20Ask 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

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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.

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3. Count ordinal number (2 weeks)object Let’s understand how to count ordinal number

1st stage Count ordinal number simplya) 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

Enveloppe3

Enveloppe

5

Page 10: 1 Abacus -To understand the numeration- Regional Office for In-service Training in Thies JICA Volunteer MITSUNAGA Norito

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2nd stage Count with 2 directiona) 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

26

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3rd stage conclusion of ordinal numberAsk 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?

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4. Compare the numbers (2 weeks)object Let’s compare two numbers and tree numbers.1st stage Which 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

DevelopmentComparer numbers with two figure

StrategyIt 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

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5. Compositions (2 month)

object understand the composition until 10

1st stage Let’s compose 5a) 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

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2nd stage Let’s compose 10a) 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»

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3rd stage Let’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

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5. Addition (1mois)

object Let’s understand additions with formula

1st stage Addition until 10with moving balls from right to left.

0+2=2 0+3=3 0+4=4 0+5=5 0+6=61+2=3 1+3=4 1+4=5 1+5=6 1+6=72+2=4 2+3=5 2+4=6 2+5=7 2+6=83+2=5 3+3=6 3+4=7 3+5=8 3+6=94+2=6 4+3=7 4+4=8 4+5=9 4+6=105+2=7 5+3=8 5+4=9 5+5=106+2=8 6+3=9 6+4=107+2=9 7+3=108+2=10

0+7=7 0+8=8 0+9=9 0+10=101+7=8 1+8=9 1+9=102+7=9 2+8=103+7=10

0 + 1=1

1 + 1=2

2 + 1=3

3 + 1=4

4 + 1=5

5 + 1=6

6 + 1=7

7 + 1=8

8 + 1=9

9 + 1=10

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2nd stage Addition with carrying overEx. 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

82

1

9 1

2

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7. Subtraction (1 month)

object Let’s understand subtraction with formula

1st stage Subtraction until 10 with moving balls from left to right.

2-2=0 3-3=0 4-4=0 5-5=0 6-6=03-2=1 4-3=1 5-4=1 6-5=1 7-6=14-2=2 5-3=2 6-4=2 7-5=2 8-6=25-2=3 6-3=3 7-4=3 8-5=3 9-6=36-2=4 7-3=4 8-4=4 9-5=4 10-6=47-2=5 8-3=5 9-4=5 10-5=58-2=6 9-3=6 10-4=69-2=7 10-3=710-2=8

7-7=0 8-8=0 9-9=0 10-10=08-7=1 9-8=1 10-9=19-7=2 10-8=2

10-7=3

1-1=02-1=13-1=24-1=35-1=46-1=57-1=68-1=79-1=810-1=9

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2nd stage Subtraction with carrying overEx. 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=10+3-9

=10-9+3

=1+3

=4

e)

14-8

=10+4-8=

=10-8+4

=2+4

=6

f) Practice with other numbers

10

482

4

10

3

91

3

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8. Numbers until 100 (2 weeks)object understand to count number every 10

1st stage Numbers until 100a) 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 stage Count numbers with 10a) Ask the students «There are 5 piece of 10 pencils. How many are there totally ? »

2 4 5 10

10

15

20

30

5 piece of 10 pencils. How many are there totally ?

50

10 10 10 10 10

10

10

10

10

10

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3rd stage Addition with 10Ex. 20+30=50

a) «20+30= ? With showing 2 pieces de 10pencils and 3 piece »

b) Prepare 20 pencils first and add 30 next

20+30= ?

50102030

1020

?

10 10 10 10 10

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4th stage Subtraction with 10Ex. 50-30=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= ?

102030

1020304050

20

?

10 10 10 10 10

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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 × 13

459×5= ?

12 ( 10+2 ) balls

13 ( 10+3 ) coloms

100 20

30 6

10 2

10

3

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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