The document summarizes discussions from breakout sessions at the 4th Singapore Math Institute on teaching mathematics using Singapore's approach. It provides tasks and problems from Singapore classrooms related to practicing skills through problem-solving, using anchor tasks to structure lessons, and teaching geometry in grades 4-6. The goals are to emulate Singapore's emphasis on problem-solving and multi-step word problems to develop students' mathematical thinking.

1. 1
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Practice Lessons Using the Problem-Solving Approach
Presenter: Yeap Ban Har
Singapore’s national mathematics curriculum is a problem-solving one. Lessons
to teach new concepts, lessons to consolidate recently learnt concepts, as well as
lessons to apply learnt concepts, can all be taught through a problem-solving
approach.
This session is on doing practice lessons using the problem-solving approach.
Task 1
Make a correct division equation. All the five digits are different.
Complete instruction.
Make a correct division equation such a two-digit number when divided by a 1-digit
number gives a two-digit quotient.
All the five digits are different.
Grade Level
What is the skill that students are practicing?

2. 2
Task 2
Start with a certain number of beans / counters / paper clips. Take turns to remove
either one or two beans / counters / paper clips. The winner is the player who
removes the last beans / counters / paper clips.
Is there a way to always win in this game?
Grade Level
What is the skill that students are practicing?

3. 3
Task 3
Use any five consecutive numbers. Arrange them such that the vertical sum equal
the horizontal sum.
Grade Level
What is the skill that students are practicing?

4. 4
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Anchor Tasks in Singapore Math
Presenter: Yeap Ban Har
Singapore textbooks are written with the main learning task being an anchor task.
Anchor task is the single tasks used over a prolonged period of instructional time.
It embodies the idea of Teach Less, Learn More – a philosophy of the Singapore
education system.
In Primary Mathematics, anchor tasks are the one that opens the chapter (un-
numbered tasks) or the ones which follow a previous day independent Workbook
Practice. These tasks are often solved completely for the students. In Math in
Focus, anchor tasks are the boxed-up Learn tasks. Typically, a mathematics
lesson begin with about 15 minutes or so doing and discussing the anchor task,
before moving on to Guided Practice and Independent Practice (if any).
Key Questions
 What is the research base for Anchor Tasks?
 How does a teacher implement Anchor Tasks?
 What is the purpose of Anchor Tasks?
Task 1
Find the value of 9 x 6.
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5. 5
Board Plan
Journal 1 Date
Problem
9 x 8
Method 1 Method 2 Method 3
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What is the learning outcome for this anchor task? Grade Level

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Task 2
3
2
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What is the learning outcome for this anchor task? Grade Level
Board Plan
Journal 2 Date
Problem
Method 1 Method 2

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Task 3
Show 4 tiles. Make a shape.
Show 5 tiles. Make a shape. Make another one.
What is the learning outcome for this anchor task? Grade Level
Board Plan
Journal Date

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Board Plan
Journal Date
Board Plan
Journal Date

9. 9
Board Plan
Journal Date
Board Plan
Journal Date

10. 10
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Challenging Word Problems from Singapore Classrooms
Presenter: Yeap Ban Har
Singapore schools provide significant opportunities for all students to deal with
challenging problems – problems that are more complex than (and sometimes new
/ novel compared to) textbook problems. This is because the state test includes
significant number of such problems.
Problem 1
This problem is based on one used by a Primary 3 Lesson Study done by a Professional Learning
Team in Kong Hwa School, Singapore.
Mr Lee had 3 durians more than Mr Kim.
Mr Kim then gave Mr Lee 2 durians.
Who had more durians in the end? How many more?
Primary 3
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Problem 2
This problem is based on one given on a state test for Primary 6 students in a recent examination.
This particular problem is new to the group of Singapore students who took that test.
Han arranged 110 squares and circles in a straight line. There are at least 3 circles
between any 2 squares. What is the largest possible number of squares among
the 110 squares and circles?
Primary 5 – 6
Based on Primary 3 Content
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Problem 3
This problem is from Catholic High School (Primary). It was given to its Primary 6 students during
a Preliminary Examination in preparing them for the national Primary School Leaving Examination,
PSLE.
A total of 325 boys and girls attended a performance in the school hall.
5
4
of the
boys and
4
3
of the girls left the hall after the performance ended. There were 29
more boys than girls who remained in the hall.
How many girls attended the performace?
Primary 5 – 6
Based on Primary 4 Content
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13. 13
Problem 4
This problem is based on one given on a state test for Primary 6 students in a recent examination.
This particular problem is new to the group of Singapore students who took that test.
Indra was packing a batch of cookies into some containers she had in her kitchen.
She tried to pack 11 cookies into each container but the last one contained only 6
cookies. When she packed 8 cookies into each container, there were 25 cookies
left over.
How many cookies were there altogether?
Primary 5 – 6
Based on Primary 4 Content
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14. 14
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Teaching Geometry in Grades 4 – 6
Presenter: Yeap Ban Har
Students in Grade 4 are expected to be on van Hiele Level 2 of Geometric Thought.
Task 1
 Cut out a triangle.
 Investigate the three (interior) angles of the triangle.

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Task 2
Find the sum of the angles in each polygon.

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Task 2
Find the sum of the angles in each polygon.
Number of sides Method 1 Method 2
What if … ?

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Task 3
Is it possible to calculate the sum of the angles at the corners of the star?

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 Please cut these out.