Which is your favourite answer? How do you know they are halves? They are of the same size and shape (identical)
Give paper strips But the equivalent fractions together Multiplying and dividing the numerator and denominator by the same number
Fundamental Concepts in Fractions
Teaching Fundamental Concepts in Fractions~ using Problem Solving Approach~ Peggy Foo Marshall Cavendish Institute
Focus of Singapore Math The central focus is on mathematical problem solving Reasoning, communication and connections
Exercise vs Problem Find the sum How many ways can I get 3? 275 + 418 = ___ −
Exercise vs Problem Exercise Problem Complex Simple, straightforward Novel Familiar Do not have routine Use routine procedures 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 SolvingProblem 1 Find different ways to represent halves and quarters?
Who is correct?Problem 2Allen thinks that ¼ of the rectangle is shaded. Sherlynthinks 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 correctProblem 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 FractionsFold a piece of paper into 4 equal partsShow 3 fourthsFold the same strip into 8 equal parts.How many eighths are equal to 3 fourths?How many twelfths are equal to 3 fourths?
Mixed NumbersShare 1 cake equally among 4 childrenShare 3 cakes equally among 4 childrenShare 5 cakes equally among 4 children