1. The document is a series of slides from Dr. Yeap Ban Har about teaching mathematics concepts like fractions, word problems, and patterns. 2. It provides examples of lessons, activities, and strategies to help students who struggle with math representation and word problems. 3. The lessons demonstrate concrete, pictorial, and abstract approaches to teach fractions as well as differentiation techniques.

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. Lesson 5
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 revisit the last problem from yesterday.

4. Lesson 5 June 18, 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

5. Lesson 5 June 18, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

6. Lesson 5 June 18, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

7. Lesson 5 June 18, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

8. Lesson 5 June 18, 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

10. Lesson 6
Diagrams can be used as a remedial strategy to help students
with solving linear equations in one and two unknowns.

11. x
x x 1
x x 1

12. x
x x x x 1
x x x x

13. x
x x x 2
x x x

14. x
x x 5
x x

15. King Solomon Academy,
London

16. King Solomon
Academy, London

17. Example of Secondary
Textbook
This is how algebra is introduced in a Singapore secondary
textbook.

18. x x x 10
76 – 20
x 10

20. Lesson 7
Four main reasons why students have difficulties learning
fractions. This lesson focuses on one of them – the naming of
fractions.

21. FRAC
TION
the C P A
approach

22. Lesson 7

23. Guided Practice
Independent Practice
Differentiated Instruction
Category Criteria
Emerging
Established
Extension

28. FRAC
TION 3
teaching for 3 fourths
4
meaning

29. St Edward’s School, Florida

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

31. 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?

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

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

35. Eventual
Symbolic
Representation

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

37. Lesson 8
This is an Open Lesson on Multiplication of fractions. The
lesson began with a review of basic multiplication fact through a
simple game (Salute!).

38. Moanalua Middle
School, Honolulu

39. Moanalua Middle School,
Honolulu

40. Moanalua Middle
School, Honolulu

41. 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.

42. 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

43. Equivalent Fractions
Another area of difficulty is equivalent fraction. This was
demonstrated during the Open Lesson.

45. Further Examples
Other similar examples of drill-and-practice using the fill out the
boxes method.

47. Use the digits 2, 3, 6
and 8 to make the
difference as small
as possible when a
smaller number is
subtracted from a
larger one.
Another variation is
to use any digit
without repeating
them.

48. Lessons 9 & 10
We studied a lesson on video and round up the institute by
looking at a problem on developing the ability to see patterns
and also on visualization.
Differentiated instruction and assessment were discussed
through the sessions.

51. Homework
Try the problems in the course materials.

52. 4 eighteenths
1 fourth 8 9
+
36 36
Singapore Examination & Assessment Board
Primary School Leaving Examination

59. www.si.mcinstitute.com.sg
More information at
si.mcinstitute.com.sg