CHIJ Our Lady of Good Counsel

MahasarakhamRajabhat University Transforming The Mathematics Classroom Dr Yeap Ban Har Principal Marshall Cavendish Institute Singapore Director for Curriculum & Professional Development Pathlight School Singapore 12 – 13 August 2010 Princess Elizabeth Primary School CHIJ Our Lady of Good Counsel Day 1 Catholic High School (Primary) Keys Grade School, Manila

Beliefs Interest Appreciation Confidence Perseverance Monitoring of one’s own thinking Self-regulation of learning Attitudes Metacognition Numerical calculation Algebraic manipulation Spatial visualization Data analysis Measurement Use of mathematical tools Estimation Mathematical Problem Solving Reasoning, communication & connections Thinking skills & heuristics Application & modelling Skills Processes Concepts Numerical Algebraic Geometrical Statistical Probabilistic Analytical Mathematics Curriculum Framework

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.

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

Jerome Bruner 210 Pictorial Representation Symbolic Representation

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? Chocolates Sweets Jim 12 Ken 12 12 12 12 18

Bar Model Methodin Singapore Textbooks

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

Lessons to Practise Skills

Practising Multiplication My number is 2! The product is 12. National Institute of Education

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 Subtraction Activity 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

Problem Solving Scarsdale School District, New York, USA Arrange cards numbered 1 to 10 so that the trick shown by the instructor can be done.

Teachers solved the problems in different ways. Scarsdale School District, New York, USA

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?

Conceptual Understanding

Conceptual Understanding of Division of Whole Number by a Fraction

Conceptual Understanding of Multiplication of Fractions

Day 1

MahasarakhamRajabhat University Transforming The Mathematics Classroom Dr Yeap Ban Har Principal Marshall Cavendish Institute Singapore Director for Curriculum & Professional Development Pathlight School Singapore 12 – 13 August 2010 Princess Elizabeth Primary School CHIJ Our Lady of Good Counsel Day 2 Catholic High School (Primary) Keys Grade School, Manila

effective mathematics teaching learning theories BinaBangsa School, Indonesia

Bruner

Bruner Division The concrete  pictorial  abstract approach is used to help the majority of learners to develop strong foundation in mathematics. National Institute of Education, Singapore

Division Princess Elizabeth Primary School, Singapore

CHIJ Our Lady of Good Counsel

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