This is the second day of the Advanced Singapore Math Institute, held at Houston, Texas.

1. Yeap Ban Har
Dr. Yeap Ban Har
Marshall Cavendish Institute
Marshall Cavendish Institute
yeapbanhar@gmail.com
Singapore
yeapbanhar@gmail.com
Day Two
SINGAPORE
M AT H
Beyond the Basics
St Edward’s School
Slides are available at Florida, USA
Open
www.banhar.blogspot.com Lesson
Hawaii, US
A
Marshall Cavendish Institute
www.facebook.com/MCISingapore www.mcinstitute.com.sg

3. visualizatio
bar model
n
multiplicatio
division
n
fractions
conceptual
understandin
mental
computations

4. Scroll down the page to see Second Grade Mental
Math

5. Lesson 9
Visualization is the emphasis when students
learn, say, multiplications involving fractions.

7. 1 2 1
2 thirds
4 3 4
1 2 1
4 sixth
4 3 4

8. 1 2 1
8 twelfth
4 3 4
s
1 2
2 twelfth
4 3
s
1 2
1 sixth
4 3

9. 1 2 1
4 3 6

10. 1 2 1 1 2 1 1 1
4 3 6 4 3 2 3 6

11. 1 2 1 1 2 1 1 1
4 3 6 4 3 3 2 6

12. Moanalua Middle
School, Honolulu

13. Moanalua Middle
School, Honolulu

14. Lesson 10
Some main reasons why students have difficulties learning
fractions. This lesson focuses on one of them – the naming of
fractions.

15. FRAC
TION
the C P A
approach

16. 10
Lesson 7

20. FRAC
TION 3
teaching for 3 fourths
4
meaning

22. St Edward’s School, Florida

23. St Edward’s School, Florida
Grade 2
concrete pictorial  abstract

25. It does not
FRAC
show half. What
does it show
then?
TION
opportunities for
differentiation
It does not show
fourth. What does
it show then?

26. My Pals Are Here! Mathematics (Second Edition)

27. Initial
Concrete
Experience
Subsequent
Pictorial
Representation
My Pals Are Here! Mathematics (Second Edition)

28. My Pals Are Here! Mathematics (Second Edition)
Eventual
Symbolic
Representation

29. Lesson 11
We studied the strategies to help struggling readers as well as
those weak in representing problem situations.
• Who is in the story? What is it all about?
• Is the sentence easy?
• Read a complex sentence as simple sentences.
• Leave out numbers in reading.
• Which sentence is best to start off with?
• Do as we read.
• Use paper strips.
• How does the model look like? Can you picture it? How
should the bar change?
Let’s look at a word problem involving fractions.

30. Lesson 11 August 3, 2012
Grade Grade
6 Grade
4
5
240

31. Lesson 11 August 3, 2012
1 third of all is the same
as one third of the
children and one third of
the adults (120)
Grade Grade
6 Grade
4
5
240

32. Lesson 11 August 3, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

33. Lesson 11 August 3, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

34. Lesson 11 August 3, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

35. Lesson 11 August 3, 2012
c = 720
1 1 1 1
(a c) a c 120 c
3 3 3 3
4th Graders 5th Graders 6th Graders
1 1 1
c c c 1
c 120 240
1
c
3 6 2 3 6

37. Types of assessment tasks

38. Lesson 12
Another area of difficulty is equivalent fraction.

40. How
many
twelfths?
What is the
name of the
smaller piece

41. Lesson 13
Addition and subtraction of fractions – all depends on
understanding what you can add and what you cannot.

44. Lesson 14
Addition and subtraction of fractions – all depends on
understanding what you can add and what you cannot.

46. Lesson 15
How do we help students develop the method to divide fraction
by a fraction?

48. Open Lesson
This is an Open Lesson on Multiplication of fractions. The
lesson began with a review of basic multiplication fact through a
simple game (Salute!). This was done in Hawaii – in place of a
Lesson Video.

49. Moanalua Middle
School, Honolulu

50. Students were shown one whole which is divided into thirds, sixths, fourths as well
as two which were not yet divided into equal parts. They were asked to name the
fraction represented by each part if the strip represented 1.
Students were
given a paper
strip divided
into thirds.
Students were asked the
value of one half of 2 thirds
– they had difficulty using
the diagram although they
seemed to know the
algorithm.
They had to explain why the
value is 1 third and 2 sixth
Final tasks done
individually where they
had to explain using a
diagram the value of this
expression.

51. The main task was 1
fourth x 2 thirds.
Practice
x =
Without repeating numbers for
numerators and denominators
make correct multiplication
sentences.
Try to keep the numbers small.
The idea of ¼ x 4
sixths