This document summarizes key points from a presentation on Singapore Math. It discusses 7 lessons that focus on conceptual understanding, problem solving, and visual representations. The lessons cover topics like multiplication facts, multi-digit multiplication, setting up bar models, and using diagrams to solve equations. Singapore Math emphasizes thinking, visualization, and anchoring lessons around extended problems.

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

3. Introduction
We start the day with an overview of Singapore Math.

5. Curriculum document is available at http://www.moe.gov.sg/

6. THINKING SCHOOLS
LEARNING NATION
Singapore Ministry of Education 1997

7. what
is singapore
mathematics

9. key
of singapor
mathemati
focus
cs e

10. problem
solving

11. thinking

12. Singapore Mathematics: Focus on Thinking
an
excellent
vehicle
for the development
&improvement of
a person’s intellectual
competencies
Ministry of Education Singapore 2006

13. conceptu
understandi
al
ng

16. Lesson 1
We do a case study on multiplication facts to understand the
emphasis on visualization in learning basic materials. We also
saw the use of an anchor tasks to engage students for an
extended period of time.

17. Strategy 1
Get 3 x 4 from 2 x 4
Strategy 2
Doubling
Strategy 3
Get 7 x 4 from 2 x 4 and 5 x 4
Strategy 4
Get 9 x 4 from 10 x 4

19. Public School in Chile

20. First, equal groups –
three groups of four. Third, four multiplied
three times ….
Second, array –
Three rows of four

21. Lesson 2
Can we get the multiplication facts for, say 4, from 2 x 4 and 5 x
4?

22. Lesson 2 August 2, 2012
 Problem
2x4=8
 10 x 4 =  5 x 4 = 20
 5 x 4 = 20
9x4=
 2x4=8
 4x4=
 8x8=
7x4=
 2x4=8 6x4=
 5 x 4 = 20 3x4=
2x4=8
This Grade 2 lesson on multiplication facts of 4 centers around using doubling
strategy and adding one row strategy in addition to previewing more advanced
strategies such as using 2 x 4 and 5 x 4 to get 7 x 4 as well as ‘subtraction’ strategy.
The anchor task is to use 2 x 4 and 5 x 4 to obtain all the other facts. The anchor task
allows students to work on one task for an extended period of time.

25. Da Qiao Primary School
Singapore

26. Lesson 3
Multiplication of multi-digit numbers with emphasis on
visualization.

28. Lesson 3 August 2, 2012
30 9
39 x 6
6
 
 
 
 
 
 
Method 1 Method 2
39 x 6 = 40 x 6 = 240
30 9

29. Lesson 4
Use digits 1 to 9 to make a correct multiplication sentence
 =.

30. Open Lesson at Broomfield,
Colorado

32. Textbook Study
Study the three tasks in the Guided Practice 1 through 3 and
discuss how they are different.

33. My Pals Are Here! Maths (Third Edition)

38. Lesson 5
We studied the strategies to help struggling readers as well as
those weak in representing problem situations.

39. Lesson 7 August 2, 2012
In the end ... At first …
Alice 20
Betty 10
Charmaine
Dolly

40. Lesson 7 August 2, 2012

41. Lesson 7 August 2, 2012

42. Lesson 6
Question: How do we help students set up the model? Students
are introduced to the idea of using a rectangle to represent
quantities – known and unknown. Paper strips are used. Later,
only diagrams are used. Advanced skills like cutting and
moving are learned in Grades 4, 5 and 6. How is the idea of bar
model introduced in Grades K – 3?
Lesson 6 show a basic bar model solution in Grade 5.

43. Lesson 6 August 2, 2012
Carl
$4686
Ben

45. Differentiated instruction
for students who have
difficulty with standard
algorithms. Use number
bonds.

47. 2x + x = 4686
3x = 4686
Students in Grade 7 may use algebra to deal with such situations. Bar
model is actual linear equations in pictorial form.

48. Tampines Primary School,
Singapore

50. Lesson 7
Diagrams can be used as a remedial strategy to help students
with solving linear equations in one and two unknowns.

51. x
x x 1
x x 1

52. x
x x x x 1
x x x x

53. x
x x x 2
x x x

54. x
x x 5
x x

55. King Solomon Academy,
London

56. King Solomon Academy,
London

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

58. x x x 10
76 – 20
x 10

62. King Solomon Academy, London