CHIJ Our Lady of Good Counsel

Catholic High School (Primary)

Keys Grade School, Manila

Mahasarakham Rajabhat University

Transforming The

Mathematics Classroom

Dr Yeap Ban Har

PrincipalMarshall Cavendish

InstituteSingapore

Director for Curriculum & Professional

DevelopmentPathlight School

Singapore

12 – 13 August 2010

Day 1

Princess Elizabeth Primary School

Mathematics Curriculum Framework

Mathematical Problem

Solving

Attitudes

Metacognition

Proc

esse

s

Concepts

SkillsNumericalAlgebraic

GeometricalStatistical

ProbabilisticAnalytical

Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling

Numerical calculationAlgebraic

manipulationSpatial visualization

Data analysisMeasurement

Use of mathematical tools

Estimation

Monitoring of one’s own thinkingSelf-regulation of learning

BeliefsInterest

AppreciationConfidence

Perseverance

Mathematics Problems in Singapore Primary 6 National Test

Problem

John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm.

How much of the copper wire was left?

Problem

John had 1.5 m of copper wire. He cut some of the wire to bend into the shape shown in the figure below. In the figure, there are 6 equilateral triangles and the length of XY is 19 cm.

How much of the copper wire was left?

150 cm – 19 cm x 5 = 150 cm – 95 cm = 55 cm

55 cm of the copper wire was left.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Problem

In the diagram below, ABCD is a square and QM = QP = QN. MN is parallel to AB and it is perpendicular to PQ.

Find MPN.

Why Teach Mathematics

Mathematics is an “excellent vehicle to develop and improve

a person’s intellectual competence”.

Ministry of Education, Singapore 2006

Problem

Mrs Hoon made some cookies to sell. 3/4 of them were chocolate cookies and the rest were almond cookies. After selling 210 almond cookies and 5/6 of the chocolate cookies, she had 1/5 of the cookies left.

How many cookies did Mrs Hoon sell?

210

5

1

Jerome Bruner

Pictorial RepresentationSymbolic Representation

210

5

1

2105

1

8

3 xx

Problem

Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim.

Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4.

How many sweets did Ken buy?

Problem

Jim bought some chocolates and gave half of them to Ken. Ken bought some sweets and gave half of them to Jim.

Jim ate 12 sweets and Ken ate 18 chocolates. After that, the number of sweets and chocolates Jim had were in the ratio 1 : 7 and the number of sweets and chocolates Ken had were in the ratio 1 : 4.

How many sweets did Ken buy?

12Jim

Ken

Chocolates Sweets

1812121212

Bar Model Methodin Singapore Textbooks

My Pals Are Here Mathematics

My Pals Are Here Mathematics

My Pals Are Here Mathematics

My Pals Are Here Mathematics

My Pals Are Here Mathematics

My Pals Are Here Mathematics

My Pals Are Here Mathematics

Lessons toDevelop New Concepts

Teaching Place Value

Activity• Combine your sets of digit

cards. Shuffle the cards.• Take turns to draw one card

at a time.• Place the card on your place

value chart. • Once you have placed the

card in a position, you cannot change its position anymore.

• The winner is the one who makes the greatest number.

Place Value

Key Concept: The value of digits depends on its place or position.

Teaching Division

Keys Grade School, Manila

Keys Grade School, Manila

Teaching Division

Lessons to Practise Skills

National Institute of Education

The product is 12.

My number is 2!

Practising Multiplication

Practising Multiplication• Use one set of the digit cards

to fill in the five spaces.• Make a correct multiplication

sentence where a two-digit number multiplied by a 1-digit number gives a 2-digit product.

• Make as many multiplication sentences as you can.

• Are the products odd or even?

x

Practicing SubtractionActivity 4• Think of a number larger than

10 000 but smaller than 10 million.

• Jumble its digits up to make another number.

• Find their difference.• Write the difference on a piece

of paper. Circle one digit. Add up the rest of the digits.

• Tell me the sum of the rest of the digits and I will tell you the digit you circled.

Example

• 72 167

• 27 671

• 72 167 – 27 671 = 44 496

• 44 496

• 4 + 4 + 4 + 6 = 18

• Tell me 18.

Lessons forProblem Solving

Problem Solving

Arrange cards numbered 1 to 10 so that the trick shown by the instructor can be done.

Problem Solving

Scarsdale School District, New York, USA

Teachers solved the problems in different ways.

Scarsdale School District, New York, USA

The above is the solution. What if the cards used are numbered 1 to 9? 1 to 8? 1 to 7? 1 to 6? 1 to 5? 1 to 4?

Scarsdale School District, New York, USA

Conceptual Understanding

Conceptual Understanding of Division of Whole Number by a Fraction

Conceptual Understanding of Multiplication of Fractions

Day 1