This is a summary of the sessions for teachers of Grades 5 through 8 conducted on the second day.

1. Professional Development
Singapore Mathematics
Seoul  9 – 11 July 2012
Dr Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute Singapore
Presentation slides are available at
www.banhar.blogspot.com
Grade 5
to
www.mcinstitute.com.sg Grade 8
www.facebook.com/MCISingapore

2. Introduction
We saw examples of how the
textbook is used as it is and also
presented with some modification.
We also saw how teachers may
supplement textbook materials.

3. Example 1
We see how this lesson is executed in a lesson.
Remember this page is not meant to be read. The
book stays closed at this point.
Seoul Foreign School

4. Example 1
You have a square piece of paper. By cutting off
parts of the square, make a trapezoid.
Why is the polygon that you have made a
trapezoid?
What makes a figure a trapezoid?
What are the minimum requirements for a figure
to be a trapezoid?
Write a paragraph to say what is a trapezoid.
Differentiation for Advanced Learners
I heard from someone that there is a competing
definition for trapezoid which states that
trapezoids are quadrilaterals that has one pair of
parallel sides. This definition makes squares and
parallelograms trapezoids. Please do a research
on the internet on this.

5. At the end of the whole-class discussion, students complete a short Guided
Practice.
Struggling students received guidance from the book “Use a ruler …”
Teacher will ask students to explain their choices and want to hear students saying
this is a trapezoid because… or this is not a trapezoid because … Do students pay
attention to the fact that it is a polygon, has four sides and has exactly a pair of
parallel sides?
Advanced students can be challenged to transform non-trapezoids into one by
moving ony one of the four vertices.

6. Example 2

7. A lesson can be done as it is.
Alternatively, it can be presented in a
more open manner.
Cut out a trapezoid. Work in your
groups to find out as many things
about the angles of the trapezoid as
you can.
For students who struggle, the teacher
may ask them to refer to the textbook
for a more guided approach.
This provides students with
independent practice.

8. Example 3
A lesson can be done as it is.
Alternatively, it can be presented in a
more open manner.
Draw a triangle on the geo-board
paper.
Find the area.
How did you do it?

9. Example 3

10. Example 3
We discussed
transforming it into a
rectangle (which is the
textbook method).
But we also discussed
other methods.

11. Example 4

12. Example 4

14. Bar Model 1
We review the bar model method
and see how it is used to teach
word problems including word
problems that can be solved using
algebraic equations.

15. Example 5
Seoul Foreign School

16. Marcus gave ¼ of his coin collection to his
sister and ½ of the remainder to his
brother.
As a result, Marcus had 18 coins.
Find the number of coins in his collection
at first.
3 units = 18
8 units = ???
Marcus had 48 coins at first.

18. The problem was changed
slightly to challenged
advanced learners and to
extend the discussion to
increase students repertoire
of strategies.

19. Example 6
Seoul Foreign School

21. 



22. Bar Model 2
We review the bar model method
and see how it is used to teach
skills like division by a fraction.

23. Example 7
Seoul Foreign School

25. Example 8
Seoul Foreign School

27. Bar Model 3
We review the bar model method
and see how it is used to teach
skills like solving linear equations.

28. Example 9
Seoul Foreign School

29. x
x x 1
x x 1

30. x
x x x x 1
x x x x

31. x
x x x 2
x x x

32. x
x x 5
x x

33. King Solomon Academy,
London

34. King Solomon Academy,
London

35. Example 10
Seoul Foreign School

44. Example 11
Seoul Foreign School

46. Example 12
Seoul Foreign School