Masterclass Utrecht MAP101

Welkom Master Class
Singapore Math
Dr.Yeap Ban Har Marshall Cavendish Institute
2011alt/ HCO R
MAP101 Fundamentals in Singapore Mathematics

Masterclass
Singapore Rekenen
Rotterdam  Utrecht
DrYeap Ban Har
banhar@sg.marshallcavendish.com
Marshall Cavendish Institute Singapore
Presentation slides are available at www.banhar.blogspot.com

what
is singapore
mathematics

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

110 g
180 g
110 g
Bella puts 180 g brown sugar on the dish.
290 g

on an identical dish
110 g
2 units = 180 g
1 unit = 90 g
110 g
180 g
3 units = 270 g
Bella puts 270 g brown sugar on the dish.
290 g

Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.

Singapore Math
Visualization

C H E R Y L

C H E R Y L
1

C H E R Y L
2

C H E R Y L
3

C H E R Y L
4

C H E R Y L
5

C H E R Y L
6

C H E R Y L
7

C H E R Y L
8

C H E R Y L
9

C H E R Y L

C H E R Y L
Which letter is 99?

Method 1
The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located.
Method 4
The position for 99 can be found by writing out all the numbers but this is not efficient method.
Method 3
Numbers ending with 9 are at E. So, 99 is at E too.
Method 2
The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.

D A V I D

Method 1
The letters under A and I are even. So 99 cannot be there.
Method 2
The positions of numbers ending with 9 form a diagonal pattern.
Method 3
The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out.
Method 4
The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out.
Method 5
Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.

Method 2
The positions of numbers ending with 9 form a diagonal pattern.
The methods were the ones that participants in Chile came up with.

Another Method
In a course done in December 2010 with a group of Chilean teachers, there was a method that involves division. For Cheryl, it was 99 : 10.
For David, it was 99 : 8. Are you able to figure out that method?

Singapore Math
Patterns & Generalization

Singapore Mathematics: Focus on Problem Solving

CPA Approach based on Jerome Bruner was used to learn division of fractions – using paper folding and subsequent drawing.

Singapore Math
Learn New Concept Through
Problem Solving

Singapore Math
Drill-and-Practice Through
Problem Solving

Singapore Math
Applying Knowledge in
Problem Solving

Learning Theories

How many 4s are there in 12?
12 ÷ 4 = 3

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Masterclass Utrecht MAP101

by Jimmy Keng on Oct 04, 2011

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