fundamental concepts in fractions
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Teaching Fundamental Concepts in Fractions
~ using Problem Solving Approach~
Peggy FooMarshall Cavendish Institute
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Focus of Singapore Math
The central focus is on mathematical problem solving
Reasoning, communication and connections
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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
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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
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Teaching through Problem Solving
Problem 1
Find different ways to represent halves and quarters?
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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?
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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
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Example
4 parts are in equal size when the shapes are different.
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Who is correct
Problem 3:
From the previous task, Allen concludes that ½ is bigger than ¼. Sherlyn thinks Allen is wrong again.
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Learning Points
Allen is wrong.
½ may not be bigger than ¼.
It depends on the quantity of the whole used.
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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?
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Mixed Numbers
Share 1 cake equally among 4 children
Share 3 cakes equally among 4 children
Share 5 cakes equally among 4 children