Fundamental Concepts in Fractions

Teaching Fundamental Concepts in Fractions

~ using Problem Solving Approach~

Peggy FooMarshall Cavendish Institute

Focus of Singapore Math

The central focus is on mathematical problem solving

Reasoning, communication and connections

Exercise vs Problem Find the sum

275 + 418 = ___

How many ways can I get 3?

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Exercise vs Problem

Exercise

Simple, straightforward

Familiar

Use routine procedures

Problem Complex

Novel

Do not have routine procedures

Problem Solving Approach

Does not always have to come after teaching of basic concepts and skills

Can take place at the beginning of a topic to teach basic concepts

Teaching through problem solving

Teaching through Problem Solving

Problem 1

Find different ways to represent halves and quarters?

Who is correct?

Problem 2

Allen thinks that ¼ of the rectangle is shaded. Sherlyn thinks that Allen is wrong because the triangles are different?

Learning Points

Allen is correct.

Each equal part can be identical (same size and shape)

Each equal part can also be of the same size but different shape

Example

4 parts are in equal size when the shapes are different.

Who is correct

Problem 3:

From the previous task, Allen concludes that ½ is bigger than ¼. Sherlyn thinks Allen is wrong again.

Learning Points

Allen is wrong.

½ may not be bigger than ¼.

It depends on the quantity of the whole used.

Equivalent Fractions

Fold a piece of paper into 4 equal parts

Show 3 fourths

Fold the same strip into 8 equal parts.

How many eighths are equal to 3 fourths?

How many twelfths are equal to 3 fourths?

Mixed Numbers

Share 1 cake equally among 4 children

Share 3 cakes equally among 4 children

Share 5 cakes equally among 4 children