Number of Cases worksheets for Grade 6 (Elementary School)

The aim is a way of counting every possible case without missing any and without counting any twice. The difference between combinations, which are ways to choose, and permutations, which are ways to arrange, is confirmed with tables and tree diagrams, and the work extends to choosing with repetition, Counting Routes, and the Multiplication Principle.

Counting the choice of A and B separately from the choice of B and A doubles the answer for a combination, and this is the most frequent error. Answering 12 for choosing 2 people out of 4 is the pattern. With permutations the reverse happens, the order is ignored and the answer halves, and with routes the longer way round goes uncounted.

Converting between units is what comes next, in The Structure of Measurement Units; before that begins, this unit confirms every possible combination by counting each one without missing it or counting it twice. The tool changes here from finding a value with an expression, as in Proportion and Inverse Proportion, to the plainer method of counting things out one by one.