Abacus

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• 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 Lets count numbers exactly
• Lets 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.
• Lets start counting slowly at first and
  increase the speed later

Five
3

• 2nd stage Numbers until 20
• Methode1 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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• 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
5

• 2. Explain the numbers with figure (2 weeks)
• object Lets understand the relation between
  the numbers and the figures.
• Lets replace the numbers with the figure.
• 1st stage Numbers until 10
• Methode1 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

How many pineapples are there ?
One, two, tree, four, five. This is five !
5
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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 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.
  

Zero
Nul

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 Lets 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
3
Indicate the 5th ball from left
Here
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

2
6
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

5th from top and , 8th from left
Where is the 48th ball?
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• 4. Compare the numbers (2 weeks)
• object Lets 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

Which is biggger?
down !
How much is the difference of balls?
Two
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• 5. Compositions (2 month)
• object understand the composition until 101st
  stage Lets 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 Lets 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

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• 3rd stage Lets 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
7 and 1 are 8
4 and 4 are 8
6 and 2 are 8
Compose 8
2 and 6 are 8
1 and 7 are 8
3 and 5 are 8
5 and 3 are 8
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• 5. Addition (1mois)
• object Lets understand additions with formula
• 1st stage Addition until 10
• with moving balls from right to left.

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• 2nd stage Addition with carrying over
• Ex. 8311
• a) Prepare 8 balls left in 1st stage.
• b) Move 2 balls left in1st stage.
• c) Move 1 balls left in2nd stage.
• d)
• 83
• 821
• 101
• 11
• e)
• 93
• 912

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• 7. Subtraction (1 month)
• object Lets understand subtraction with formula
• 1st stage Subtraction until 10
• with moving balls from left to right.

1-10
2-11
3-12
4-13
5-14
6-15
7-16
8-17
9-18
10-19
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• 2nd stage Subtraction with carrying over
• Ex. 13-94
• 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)
• 13-9 103-9
• 10-93
• 13
• 4
• e)
• 14-8
• 104-8

10
4
8
2
4
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• 8. Numbers until 100 (2 weeks)
• object 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
• 2nd stage Count numbers with 10

4
10
15
20
30
2
5
10
50
5 piece of 10 pencils. How many are there
totally ?
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• 3rd stage Addition with 10
• Ex. 203050
• a) 2030 ? With showing 2 pieces de 10pencils
  and 3 piece
• b) Prepare 20 pencils first and add 30 next

10 20
?
2030 ?
10 20 30
50
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• 4th stage Subtraction with 10
• Ex. 50-3020
• a) 50-30 ? With showing 5 piece of 10pencils
• b) Prepare 50 first and move 30 left

50-30 ?
10 20 30 40 50
?
10 20 30
20
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• 9. Multiplication until 100 (2 month)
• Lets 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

10
2
12(102)balls
100
20
10
30
6
3
13(103)coloms
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• Lets 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

TRIA
I won !