Transcript Diapositive 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
Objects
(2weeks)
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
Five
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
Two
Six
One
Development
1. Make the example in first stage in he below.
2. Make the same number with copying the example
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2nd stage
Methode1
Numbers until 20
With moving ball from right to left, count from1 to 20
Fourteen
Methode2
Oppositely, with moving from left to right , deduct 20 to 1
Twenty
Fourteen
Six
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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
How many
carrot are there?
One, two,three,….
sixtreen. There are
sixteen
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
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2. Explain the numbers with figure
object
(2 weeks)
Let’s understand the relation between the numbers and the figures.
Let’s replace the numbers with the figure.
1st stage
Methode1
Numbers until 10
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
5
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 »
One, two, tree, four, five.
This is five !
How many
pineapples
are there ?
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.
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2nd stage
Number zero « 0 »
When there is nothing, we explain it zero with showing the card nothing
Nul
Zero
0
3rd stage
Numbers 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.
How many
cucumbers
are there?
One, two,
tree,……,fourteen.
It is fourteen!
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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
object
(2 weeks)
Let’s understand how to count ordinal number
1st stage
Count 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
Enveloppe
3
Indicate the 5th ball
from left
Here
Enveloppe
5
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2nd stage
Count 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»
Enveloppe
６
２
Indicate the ball
2nd from top and
6th from left
Here
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3rd stage
conclusion of ordinal number
Ask the students « Where is the 48th ball?»
«5th from top and , 8th from left»
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
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4. Compare the numbers
object
1st stage
(2 weeks)
Let’s compare two numbers and tree numbers.
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
Which is
biggger?
down
!
How much is the
difference of balls?
Two
Development
Comparer numbers with two figure
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18
Strategy
It is necessary to count every ball..
What is important is to compare the number of the ball in second stage
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5. Compositions
object
(2 month)
understand the composition until 10
1st stage Let’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»
1 and 4 are 5
2 and 3 are 5
3 and 2 are 5
4 and 1 are 5
5 and 0 are 5
To make 5, How
many balls are
necessaire ?
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2nd stage
Let’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»
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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
8 and 0 are 8
Compose
8
7 and 1 are 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
Strategy
Composition help understanding addition and subtraction
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5. Addition
(1mois)
object
Let’s understand additions with formula
1st stage
Addition until 10
with moving balls from right to left.
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
0+2=2
1+2=3
2+2=4
3+2=5
4+2=6
5+2=7
6+2=8
7+2=9
8+2=10
0+3=3
1+3=4
2+3=5
3+3=6
4+3=7
5+3=8
6+3=9
7+3=10
0+4=4
1+4=5
2+4=6
3+4=7
4+4=8
5+4=9
6+4=10
0+5=5
1+5=6
2+5=7
3+5=8
4+5=9
5+5=10
0+7=7
1+7=8
2+7=9
3+7=10
0+8=8
1+8=9
2+8=10
0+9=9
1+9=10
0+10=10
0+6=6
1+6=7
2+6=8
3+6=9
4+6=10
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2nd stage
Addition 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
8
1
9
e)
9+3
=9+1+2
=10+2
=12
2
1
2
f) Practice with other numbers
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7. Subtraction
object
(1 month)
Let’s understand subtraction with formula
1st stage
Subtraction until 10
with moving balls from left to right.
11=0
21=1
31=2
41=3
51=4
61=5
71=6
81=7
91=8
10-1=9
2-2=0
3-2=1
4-2=2
5-2=3
6-2=4
7-2=5
8-2=6
9-2=7
10-2=8
3-3=0
4-3=1
5-3=2
6-3=3
7-3=4
8-3=5
9-3=6
10-3=7
4-4=0
5-4=1
6-4=2
7-4=3
8-4=4
9-4=5
10-4=6
5-5=0
6-5=1
7-5=2
8-5=3
9-5=4
10-5=5
7-7=0
8-7=1
9-7=2
10-7=3
8-8=0
9-8=1
10-8=2
9-9=0
10-9=1
10-10=0
6-6=0
7-6=1
8-6=2
9-6=3
10-6=4
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2nd stage
Subtraction 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
=10+3-9
=10-9+3
=1+3
=4
10
3
9
1
3
10
e)
14-8
=10+4-8=
=10-8+4
=2+4
=6
4
2
8
4
f) Practice with other numbers
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8. Numbers until 100
object
(2 weeks)
understand to count number every 10
1st stage Numbers 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
2
4
2nd stage
1
0
5
1
5
2
0
1
0
3
0
Count numbers with 10
a) Ask the students «There are 5 piece of 10 pencils. How many are there totally ? »
50
5 piece of 10
pencils. How
many are
there totally ?
10
10
10
10
10
10
10
10
10
10
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3rd stage
Addition with 10
Ex. 20+30=50
a) «20+30= ? With showing 2 pieces de 10pencils and 3 piece »
b) Prepare 20 pencils first and add 30 next
10
20+30=
?
10
10
10
10
10
20
10
20
30
?
50
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4th stage
Subtraction with 10
Ex. 50-30=20
a) «50-30= ? With showing 5 piece of 10pencils»
b) Prepare 50 first and move 30 left
10
10
10
10
10
50-30= ?
10 ?
20
30 10
40 20
50 30
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f ) Practice with other numbers
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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.
9×5= ?
45
If the students can get enough sense,for multiplication, they can calicle much easier the
multiplication in the below
10
12 × 13
2
12（10+2）balls
10
100
20
3
30
6
13（10+3）coloms
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Let’s play with dice.
a)Move 5 balls left in each stage.
TRIA
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
I won !
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.
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