masterclass utrecht map101

Welkom Master Class

Singapore Math

Dr.Yeap Ban Har Marshall Cavendish Institute

2011alt/ HCO R MAP101 Fundamentals in SingaporeMathematics

Dr Yeap Ban [email protected]

Marshall Cavendish Institute Singapore

Presentation slides are available at www.banhar.blogspot.com

MasterclassSingapore RekenenRotterdam Utrecht

is singaporewhat

mathematics

Singapore Mathematics: Focus on Thinking

excellentvehicle

an

for the development&improvement ofa person’s intellectual

competenciesMinistry of Education Singapore 2006

110 g

290 g

110 g180 g

Bella puts 180 g brown sugar on the dish.

110 g

290 g

110 g180 g

2 units = 180 g

1 unit = 90 g

3 units = 270 g

Bella puts 270 g brown sugar on the dish.

on an identical dish

Singapore Mathematicsfocuses on the ability tovisualize. For example,bar models are usedextensively.

Singapore Math

Visualization

C H E R Y L

C H E R Y L1

C H E R Y L2

C H E R Y L3

C H E R Y L4

C H E R Y L5

C H E R Y L6

C H E R Y L7

C H E R Y L8

C H E R Y L9

C H E R Y L

C H E R Y L

Which letter is 99?

Method 1The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located.

Method 2The 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.

Method 3Numbers ending with 9 are at E. So, 99 is at E too.

Method 4The position for 99 can be found by writing out all the numbers but this is not efficient method.

D A V I D

Method 1The letters under A and I are even. So 99 cannot be there.

Method 2The positions of numbers ending with 9 form a diagonal pattern.

Method 3The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out.

Method 4The 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 5Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.

Method 2The positions of numbers ending with 9 form a diagonal pattern.

The methods were the ones that participants in Chile came up with.

Another MethodIn 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 onJerome Bruner was usedto learn division offractions – using paperfolding and subsequentdrawing.

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