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

Outline

What is Reasoning & Communication?

How to Develop Reasoning & Communication?

Measurement & Geometry Problems

Re-looking at Reasoning & Communication

3

4

5

6

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

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

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

11

12

13

Answer: 68 cm

14

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

17

It is not given that the

angles indicated by

are equal. So they can be

or not. What if they are.

18

19

20

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

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

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

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

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

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

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

Marymount Convent School, Singapore

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

Marymount Convent School, Singapore

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

3 folds

2 folds 4 folds 6 folds

5 folds 7 folds

East Coast Primary School, Singapore

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