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5. Additive structures: introduction to aggregation and partitioning
Introduction
Progress to the use of abstract notation (+, − and =) as a way of representing the part–part–whole structure.
Teaching points
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Teaching point 1: combining two or more parts to make a whole is called aggregation; the addition symbol, +, can be used to represent aggregation.
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Teaching point 2: The equals symbol, =, can be used to show equivalence between the whole and the sum of the parts.
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Teaching point 3: Each addend represents a part, and these are combined to form the whole/sum; we can find the value of the whole by adding the parts. We can represent problems with missing parts using an addition equation with a missing addend.
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Teaching point 4: Breaking a whole down into two or more parts is called partitioning; the subtraction symbol, −, can be used to represent partitioning.