The document discusses the bar model method for teaching primary mathematics. It begins with an introduction to the presenter and includes links to additional resources. It then provides examples of using bar models to represent and solve word problems involving ratios, equations, and systems of equations. The examples are from primary classrooms in Singapore, New York, Chile, and Guatemala. The document demonstrates how bar models can help students learn abstract mathematical concepts through concrete, visual representations.

1. Bar Model Method in Primary Mathematics
5 Dec 2013 | MAV Annual Conference
Dr Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute
Slides are available at
www.banhar.blogspot.com
The Merlion by Yeap Ken Min

2. | Hanusek, Jamison, Jamison & Woessmann 2008

3. “Upon separation from Malaysia in 1965, Singapore
was faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate. “

4. Seely Place Elementary School, New York
 Using concrete and
pictorial representations
help students acquire
abstract ideas

5. Escuela de Guetamala, Chile
6
6
6
6

6. Example 0
Typical Word Problems
Let’s warm up with a typical textbook problem.
Sumin has 1135 local coins.
He has three times as many foreign coins as
local coins.
Sumin puts the coins equally into 5 boxes.

7. Sumin has 1135 local coins.
He has three times as many foreign coins as
local coins.
number of
local coins
1135
number of
foreign coins
number of foreign coins
=
3 x 1135
=
3300 + 105
=
3405

8. Sumin puts the coins equally into 5 boxes.
number of
local coins
number of
foreign coins
3405

9. Sumin puts the coins equally into 5 boxes.
4540  5 = 
There are  coins in each box.

10. Example 1
Learning Basic Ideas
1 2

3 3

11. Seely Place Elementary School, New York

12. Seely Place Elementary School, New York

13. Example 2
2x 1  5
Learning Basic Ideas
1
5

14. Example 2
2x 1  5
2x  5 1
Learning Basic Ideas
1
5

15. Example 3
The ratio of the number of boys to the
number of girls in a school is 6 : 5 .
There are 1353 children in the school.
What questions can we answer?

16. Example 4

17. Box B contains twice as many books as Box A. Box C contains 20
more books than Box A. Together, the three boxes contains 116
books.

18. Box B contains twice as many books as Box A. Box C contains 20
more books than Box A. Together, the three boxes contains 116
books.

19. Box B contains twice as many books as Box A. Box C contains 20
more books than Box A. Together, the three boxes contains 116
books.

20. B
A
C
116
20

21. B
4 units = 116 - 20
4 units = 96
1 units = 96  4
A
116 - 20
1 units = 20 + 4 = 24
What questions can we answer?
C
20

22. Box B contains twice as many
books as Box A. Box C
contains 20 more books than
Box A. Together, the three
boxes contains 116 books.
Edgewood Elementary School, New York

23. x + 2x + x + 20 = 116
4x = 116 – 20 = 96
x = 96  4 = …
x
A
x
C
Edgewood Elementary School, New York
B
x
x
116
20

24. Example 5 Homework
A challenging problem for Primary 5.

25. Lesson 
Date //

26. Lesson 
Date //
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