This is the presentation made at the conference in Denver.

1. 1
Exploring Reasoning & Communication
with Problems from
Singapore Classrooms
St Gabriel’s Primary School, Singapore
Yeap Ban Har
Marshall Cavendish Institute
Singapore
www.facebook.com/MCISingapore

2. 2
Outline
 What is Reasoning & Communication?
 How to Develop Reasoning & Communication?
 Measurement & Geometry Problems
 Re-looking at Reasoning & Communication

3. 3

4. 4

5. 5

6. 6
 
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We can find area by counting squares.
We can find area by
transforming the figure into a
simple figure (without changing its
area) such as a rectangle.
We can use fraction to find area.

7. 7
We found squares of area 1 square unit, 2 square unit, 4 square unit, 9 square units
and 16 square units.
5 square units.
10 square units.
Someone found a square of area 13
square units. Can you find it?

8. 8

9. 9
Is it possible to draw the square we have found on a grid such as this one (4 by 4 grid)?
All the square we found have area less than 16 square units.
It seems like they should be able to fit onto this grid.
But is that true?

10. 10

11. 11

12. 12

13. 13
Answer: 68 cm

14. 14

15. 15
a
b
c
a
b
c
19 cm x 5 = 95 cm
150 cm – 95 cm = 55 cm
55 cm of the wire were left.
Answer: 55 cm

16. 16

17. 17
It is not given that the
angles indicated by 
are equal. So they can be
or not. What if they are.

18. 18

19. 19

20. 20

21. 21
31o
71o
31o
19o
19o
???
180o – 2 x 19o – 2 x 31o = …
Answer: The required angle is 80o.
Why is this a right angle?
Why is this also 31o?Why is this found by
subtracting from
180o?

22. 22
During class discussion,
some students had a
different interpretation
of the problem from
the others.
How should the problem be
phrased such that the
shaded region and
unshaded region refer to
those that are as seen on
the figure?
Or is this version already
not ambiguous?
Let’s solve this version of
the problem.

23. 23
Let’s clarify.
The figure is created by a circle overlapping a
semicircle, as shown. The region on the semicircle
not covered by the circle is shaded.

24. 24
5
4
4
R2
r2
=
9
4
½ R2
½ r2
=
9
4
If we are comparing the semicircles
…
If we are
comparing the
semicircles …
Answer: The ratio is 2 : 3 .

25. 25
Exploring Reasoning & Communication
with Problems from
Singapore Classrooms
St Gabriel’s Primary School, Singapore
Communication
- through actions
- through pictures and diagrams
- through words and symbols

26. 26
Exploring Reasoning & Communication
with Problems from
Singapore Classrooms
St Gabriel’s Primary School, Singapore
Describing what they saw
Explaining what they saw
Relational explanation
Causal explanation

27. 27
Presentation of the
Problem – A square sheet
is folded twice to form a
right triangle. When a
part is removed, it forms
a particular figure.
Lesson Study on Reasoning and Communication
Marymount Convent School, Singapore

28. 28
Marymount Convent School, Singapore

29. 29
These are the figures formed when the
square sheet is folded twice, three times
and four times. Students describe what they
see, what they think and what they wander
…
Marymount Convent School, Singapore

30. 30
Marymount Convent School, Singapore

31. 31
Students present what they think
the next figure looks like and
their reasons.
Students check if their prediction
is correct or otherwise.
Marymount Convent School, Singapore

32. 32
3 folds
2 folds4 folds 6 folds
5 folds 7 folds
East Coast Primary School, Singapore

33. 33
Exploring Reasoning & Communication
with Problems from
Singapore Classrooms
St Gabriel’s Primary School, Singapore
Yeap Ban Har
Marshall Cavendish Institute
Singapore
www.facebook.com/MCISingapore