The document summarizes lessons from a workshop on the Singapore Math approach held at St Edward's School in Florida. It provides an overview of the Singapore education system and curriculum. It then summarizes 5 lessons that were observed which demonstrate the Singapore Math approach of using visual models and thinking strategies to teach basic math concepts and solve word problems. The lessons focused on multiplication facts, bar modeling techniques, and differentiated instruction strategies to help struggling students.

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 started the day with an overview of Singapore education
system. We also watched a video on the Singapore education
system. See http://www.youtube.com/watch?v=sEn6OKsVoMs

4. General Overview of Singapore and its
Education System
 Land
 270 sq miles
 People
 4.7 million

5. General Overview of Singapore and its
Education System
 GDP per capita in current U.S. dollars
1965 $510 2010 $43 300

6. General Overview of Singapore and its
Education System
 Students
 500 000
 Teachers
 30 000
 Principals & Vice-Principals
 900
 Schools
 173 Primary Schools (Primary 1 – 6)
 155 Secondary Schools (Secondary 1 – 4)
 13 Junior Colleges (JC 1 – 2)
Canossa Convent Primary School
 15 Mixed-Level Schools Singapore
The data refers to 1-12 school system. Pre-school is not part of the formal education
system. The data excludes post-secondary education system which includes institutes
of technical education, polytechnics and universities.

7. Universities
National Examination
Institutes of
Poly
Technical
technics
Junior Education
Colleges
Integrated
National Examination
Programmes
Secondary Schools
National Examination
Primary Schools
A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest
http://www.moe.gov.sg/education/education-statistics-digest/

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

10. THINKING SCHOOLS
LEARNING NATION
Singapore Ministry of Education 1997

11. what
is singapore
mathematics

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

16. Lesson 1
We did a lesson 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. Lesson 1 June 18, 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.

19. Da Qiao Primary School
Singapore

21. Lesson 2
We continued to see the emphasis on visualization through the
use of bar models in solving word problems. This lesson was
done with a small group of Grade 3 students who have no
experience with Singapore Math. This session and the ones
after lunch focused on helping students who have difficulties
with reading word problems, representing complex situations
and doing computations. We also saw the use of the cut up
word problems in doing differentiated instruction.

22. Lesson 2 June 18, 2012
Jack $3
Jack
Kyla $2
Kyla
gave
more
had
than

23. Lesson 2 June 18, 2012
Open Lesson at Hawaii, USA

24. Lesson 2 June 18, 2012
What if Kyla
Story 1 had this
Jack had $3. amount
before?
Jack gave Kyla $2
more.
Jack Kyla
Before $3 $1 $5 $19
After $1 $3 $7 ?

25. Lesson 2 June 18, 2012
Story 2
Kyla had $3 more than Jack. Who had
more money
Jack $2 afterwards?
How much
Kyla $3 more?
Jack gave Kyla $2.

26. Kyla had $3 more than Jack.
Jack gave Kyla $2.
How much more did Kyla have than Jack?
Students in Grade 6 may use algebra to deal with Story 2.
Kyla had $(x + 3)
Jack had $x
Then, Jack had $(x – 2)
And Kyla had $(x + 5)
Kyla had $(x + 5) – $(x – 2) or $7 more than Jack.

27. Lesson 3
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? Listen out for this on Day 2.
Lesson 3 show a basic bar model solution.

28. Lesson 3 June 18, 2012
Carl
$4686
Ben

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

30. 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.

31. Lessons 4 & 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

32. Lesson 4 June 18, 2012
In the end ... At first …
Alice 20
Betty 10
Charmaine
Dolly

33. Lesson 4 June 18, 2012

34. Lesson 5 June 18, 2012
Grade Grade
6 Grade
4
5
240

35. Lesson 5 June 18, 2012

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