These were the materials covered in last year's professional development. This year's session is a follow-up with revisiting of core ideas and extension of others.

1. marshallcavendishinstitute
S I N G A P O R E
professionaldevelopment
i n s i n g a p o r e m a t h
Weston Public Schools Yeap Ban Har
8.00 a.m. to 9.30 a.m.
yeapbanhar@gmail.com 
www.banhar.blogspot.com 
https://sites.google.com/site/yeapbanhar 
www.facebook.com/MCISingapore 

2. 2 | P a g e
CONTENTS
Session 1
Fractions Grades 6 – 7 ………………………...……………… Page 3
Session 2
Problem Solving Grades K – 2 and 5 – 7 ………………...…… Page 7
Session 3
Whole Numbers Addition & Subtraction Grade 2 …………… Page 11
Session 4
Number Bonds & Early Mathematics Grades K – 1 …………… Page 13
Session 5
Word Problems in Fractions and Ratio Grades 5 – 7 ………… Page 15
This professional development program aims to provide participants with an
understanding of the fundamentals of Singapore Math. Participants teaching
middle school will also learn about the bar model method. This course can be
done for credits in MAP101 Fundamentals in Singapore Mathematics
Curriculum and MAP111 Bar Models in Primary Mathematics.

3. 3 | P a g e
Session 1
Fractions  Grades 6 – 7
Students typically learn multiplication and division in middle school. This
session helps you understand the main causes of difficulties with
fractions and how to help students learn fraction multiplication and
division in a way that it relates to whole number operations.
 Students need to develop a conceptual understanding of fraction as part of a whole.
When 1 is divided into equal parts, each part can be named. For example, these are
named as halves, thirds, fourths and eighths. They should appreciate the meaning of
numerator (‘number’) and denominator (‘noun’). Thus, 3 fifths is in the same language
structure as 3 lions.
 Students need to understand what can be counted, added and subtracted, and what
cannot. For example, 2 boys and 3 girls do not add up to 5 boys nor 5 girls. Put simply,
different ‘nouns’ cannot be counted, added or subtracted. Thus, it is impossible to take
away 2 boys from a group of 5 girls. It is, however, possible to take away 2 children
from a group of 5 children.
 Students need to be fluent in finding equivalent fractions.
 Students must understand the two meanings of division – as sharing and as grouping.

4. 4 | P a g e
Example 1
Find the values of

5
1
5
2


10
1
5
2


2
1
3
1


2
1
1
3
1
4 

5. 5 | P a g e
Example 2
Let the square piece of paper stand for 1.
Show
4
3
.
Share
4
3
equally among 3.
What is the value of 3
4
3
 ?
Show these using a rectangular strip of paper which stands for 1.
What is the value of 2
4
3
 ?
What is the value of 4
4
3
 ?

6. 6 | P a g e
Example 3
 How many
4
1
s are there in 2?
 How many
4
3
s are there in 2?
 How many
2
1
s are there in
4
3
?
 How many
4
3
s are there in
2
1
?
Key Ideas
The ability to visualize is emphasized in Singapore Math.
Students learn concepts and skills through the CPA
Approach where they have initial concrete experiences,
which are followed by the use of visuals and pictorial
representations to eventually deal with concepts and skills
in an abstract way.

7. 7 | P a g e
Session 2
Problem Solving  Grades K – 2 and 5 – 7
Problem solving is central in Singapore Math. In this session we look at
how Singapore textbook is written to promote teaching through
problem solving where every lesson begins with an anchor problem.
There is some expectations that students can do tasks that are different
from the ones taught and tasks more complex than the one taught. This
is after all the essence of problem solving.
Example 4
This square tile stands for 1.
Show 4 in different ways.
Show 5 in different ways.

8. 8 | P a g e
Example 5
Arrange in either a square or rectangular arrangement.

9. 9 | P a g e
Example 6
Amy has 8 cookies.
Billy gives her 6 more.
How many cookies does Amy have now?
Example 7
Divide the square into 4 equal parts.

10. 10 | P a g e
Example 8
Change each into a rectangle but cutting and rearranging.
Example 9
Cheryl has $1950.
She has $250 less than David.
How much money do they both have altogether?

11. 11 | P a g e
Session 3
Addition and Subtraction  Grade 2
How do we balance mastery of a skill and problem solving?
Example 10
Mr. Lee has 381 boxes of cookies in his shop.
How many boxes will there be after he sells 198 boxes?

12. 12 | P a g e
Example 11
Use one set of digit tiles to make a correct addition sentence.

13. 13 | P a g e
Session 4
Number Bonds & Early Numeracy  Grades K – 1
What are the essential elements of early mathematics?
Example 12
Put the bears into two boxes.
How many bears in each box?
Study two consecutive lessons in Kindergarten from a Singapore
textbook. Think about how number bonds is introduced.
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________
_____________________________

14. 14 | P a g e

15. 15 | P a g e

16. 16 | P a g e
Example 13
Use a tangram set to make a rectangle.
Look at the rectangle you made.
Trace the rectangle on a sheet of paper.

17. 17 | P a g e
Example 14
Use two different digits to make two different two-digit numbers.
Subtract the smaller number from the larger number.
Look for a pattern.
Study a lesson video on how this lesson is conducted in a Grade 1
class.
Observation Question Notes
Example 15
Use numbers 1 to 5 so that the total of the three numbers in the vertical
column is equal to the total of the three numbers in the horizontal row.

18. 18 | P a g e
Session 5
Bar Models  Grades 5 – 7
Example 16
Larry and Maria share $300 in the ratio 1 : 3.
How much does Maria get?
Example 17
A bottle of syrup was
4
3
full.
After Mrs. Chan used 100 ml of syrup from the bottle, it became
12
5
full.
What was the capacity of the bottle?
Source: Ai Tong School Semestral Assessment 2011 (Primary 4)

19. 19 | P a g e
Example 18
May and Chris had 550 bookmarks altogether.
May had
4
1
as many bookmarks as Chris.
How many bookmarks must Chris give to May so that they have an equal number of
bookmarks?
Source: Kong School Semestral Assessment 2011 (Primary 4)

20. 20 | P a g e
Example 19
In a test consisting of Sections A, B and C, Ben spent
5
1
of his time on Section A,
3
1
of the
remaining time on Section B and the rest of the time on Section C. If he spent 48 minutes
on Section C, how much time did he take to complete the whole test?
Source: My Pals Are Here! Maths 5A (Second Edition)

21. 21 | P a g e
Example 20
34 of a group of 88 students wear spectacles.
3
1
of the boys and
7
3
of the girls wear spectacles.
How many girls wear spectacles?

22. 22 | P a g e
Example 21
A man is now 3 times as old as his son. In 10 years’ time, the sum of their ages will be 76.
How old was the man when his son was born?
Source: New Syllabus Mathematics (Sixth Edition)

23. 23 | P a g e
Example 22
Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The
ratio of Edward’s money to Sam’s money was 4 : 3 at first. Jason and Edward each spent
of their money. Given that the three boys had $648 left, how much did Jason have at
first?
Source: Anglo Chinese Schools Preliminary Examination 2011 (Primary 6)

24. 24 | P a g e
Example 23
Nurul and Peili went shopping together with a total sum of $60. Nurul spent twice as much
as Peili. The amount Peili had left was $7 more than what she had spent. She had twice as
much money left as Nurul?
(a) How much money did Peili spend?
(b) How much money did Nurul have at first?
Source: Primary School leaving Examination 2007 – 2011