THREE key constructs are presented here, with the key emphasis on gaining an understanding of the problem first before moving on to decide what procedure to apply to get the solution. This dual approach (gain conceptual understanding first, followed by the steps to get the solution) is the hallmark of ThinkingMath@onSponge's Conquer Problem Sums series as mentioned in the Introduction to ThinkingMath.
The three key constructs in this article: Equal Fractions, Internal Transfer, and Guess & Check.
Equal Fractions key construct is applied for problems in the books for P4, P5 and P6.
No drawing of models is needed; instead make both numerators the same using the principle of common multiple. In the example below, the Model Method (Method 1) is used as a comparison. Notice that the new fractions of the Units Method (Method 2) are equal to the number of the relevant parts in the model.
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Internal Transfer key construct is associated with the "Equal Stage (Type 3)" key construct. It is applied for problems in the books for P3 and P4 and revised in P6.
Internal transfer happens when one individual gives to the other. The transfer takes place strictly between these two individuals. This means when one individual gives away a certain amount, the other individual will gain by the same amount. The strategy involves drawing the model at the stage where both have an equal amount.
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Guess & Check key construct is applied for problems in the books for P3 and P4 and revised in P6. It is important to note that intelligent guessing is a key skill that develops over time with greater experience in mathematical problem solving. This means, you become better at guessing with practice!
Solving a problem under this key construct requires using your previously learned knowledge to make an intelligent guess of a step that can solve the problem, and then mentally checking to see if your thinking is logical and valid, before proceeding with the next step. To begin, always start with an equal amount on both sides.
More samples from Conquer Problem Sums series
Click below for other articles in our series on key constructs:
Introduction to ThinkingMath / Key constructs in Conquer Problem Sums
More Than/Less Than (Comparison, Division)
More Than/Less Than (Types 1 - 3)
Equal Stage
Repeated Identity
Part-Whole Relationship
Number x Value, External Change, Gaps & Differences
