KEY constructs in ThinkingMath@onSponge are intended to aid the pupil to gain a critical conceptual understanding (conceptual learning) of the problem before deciding on the right method (procedural knowledge) to use to get the solution, as mentioned in the Introduction to ThinkingMath.
Here we deal with the Repeated Identity key construct. This is introduced in P3, used across P3 to P5, and revised at P6.
The clues indicating this key construct are "as much as" or "as many as". These may be used with different individuals or objects, and refer to multiplication. Some of these different individuals or objects will be repeated, hence the name Repeated Identity. Though it may appear as if they are represented by different numbers, they are actually the same.
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For further practice and more examples, see the following book units:
Conquer Problem Sums P3: Units 4.1, 5.5, 6.3.
This example provides a guide on tackling problem sums on Averages using the Repeated Identity key construct.
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For further practice, see the following book unit:
Conquer Problem Sums P5 : Unit 4.4
In this method, use Lowest Common Multiple (LCM) to make the amounts the same for the repeated individual. This method is faster than drawing models.
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For further practice and more examples, see the following book units:
Conquer Problem Sums P4: Unit 2.13.
Conquer Problem Sums P5: Units 2.5, 2,6, 2.7, 3.2, 3.3, 3.5, 9.7, 9.8, 9.9, 9.11.
Conquer Problem Sums P6: Unit 6.1.
Under Type 1, the number given in the problem for the repeated individual/object is a direct representation of the model, either in total or part. In the example, the repeated individual is Xavier.
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For further practice and more examples, click on the following:
More samples from Conquer Problem Sums series
More samples from Conquer Problem Sums series
Under this type, the number given in the problem for the repeated individual/object will not be a direct representation of the model. Thus the initial model drawn will require further additions of number blocks, similar to model drawing for the ‘More Than/Less Than' key construct.
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For further practice, see the following book unit:
Conquer Problem Sums P4: Unit 1.16.
Under Type 3, the number given in the problem will indicate a difference between the individuals who are not repeated. Find the values for the individuals who are not repeated first and then find the repeated individual.
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For further practice and more examples, click on the following:
More samples from Conquer Problem Sums series
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
Part-Whole Relationship
Equal Fractions, Internal Transfer, Guess & Check
Number x Value, External Change, Gaps & Differences
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