This is the presentation on the second day.

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 Lesson
www.banhar.blogspot.com Hawaii, USA
Marshall Cavendish Institute
www.facebook.com/MCISingapore www.mcinstitute.com.sg

3. Number bonds which is fundamental in number sense
development is emphasized in subsequent levels
even when they are not explicit in the textbooks.
We have seen how number bonds is used in Grade
1 lesson (video). 32 is 10 + 10 + 10 + 2. 32 is also
20 and 12. 32 is also 20 + 10 + 2.

4. We have also seen how it is used in the development
of number facts.

5. Lesson 2 August 6, 2012
In Grade 3, we use it doe large number
multiplication when products are found through
partial products.

6. In the differentiated
approach to doing
long division in the
Grade 5 lesson ,
number bonds
continue to play a
prominent role.

7. visualization
bar model
multiplication
division
fractions
conceptual
understanding
mental
computations

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

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

10. FRAC
TION
the C P A
approach

11. 10
Lesson 7

15. FRAC
TION 3
teaching for 3 fourths
4
meaning

16. ??

21. St Edward’s School, Florida

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

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

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

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

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

28. Lesson 8
Another area of difficulty is equivalent fraction.

30. 2 thirds is equal to how many sixths?
2 thirds is cut into 8
equal parts. Are the
parts smaller? What is
the name of the
smaller equal parts?

31. Lesson 9
Addition and subtraction of fractions – all depends on understanding
what you can add and what you cannot.

33. Make 1 by combining 3 of
Rename as fourths the fourths with 1 half.

36. Additional Example
Addition and subtraction of fractions – all depends on understanding
what you can add and what you cannot.

38. Lesson 10
Visualization is the emphasis when students learn, say, multiplications
involving fractions.

42. 1 2 1
   2 thirds
4 3 4
1 2 1
   4 sixth
4 3 4

43. 1 2 1
   8 twelfths
4 3 4
1 2
  2 twelfths
4 3
1 2
  1 sixth
4 3

44. 1 2 1
 
4 3 6

45. 1 2 1 1 2 1 1 1
     
4 3 6 4 3 2 3 6

46. 1 2 1 1 2 1 1 1
     
4 3 6 4 3 3 2 6

47. Moanalua Middle School, Honolulu

48. Moanalua Middle School, Honolulu

49. Lesson 11
How do we help students develop the method to multiply and divide
fraction by a fraction?

54. Additional Example
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.

55. Lesson 12 August 7, 2012
Grade Grade
6 Grade
4
5
240

56. Lesson 12 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

57. Lesson 12 August 3, 2012
240 + 120
Grade Grade
6 Grade
4
5
240

58. Lesson 12 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

60. Additional Example for Secondary

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

62. x
x x 1
x x 1

63. x
x x x x 1
x x x x

64. x
x x x 2
x x x

65. x
x x 5
x x

66. King Solomon Academy, London