Four cubes for four ways to get from Town A to Town B

A 3-stick for each of the four cubes or ways to get from Town B to Town C

Fundamental Principle of Counting: If there are M ways to do one thing and N ways to do another, there are MxN ways to do both.

Four ways to get from Town A to Town B and three ways to get from Town B to Town C. How many ways to get from A to B and then to C?

Using snap cubes for ways, 4 cubes would show the number of ways to get from Town A to Town B, and a 3-stick for each of the four cubes would show the number of ways to get from Town A to Town B and then to Town C. Joining the 3-sticks to show how many ways would be combining “neatly” (by 3s).

Division as Separating “Neatly” (into 2s, 3s, 4s…)

Grouping or repeated subtraction:

Twenty marbles to be put in bags, five to a bag. How many bags?

Using snap cubes for marbles, a 20-stick would be separated “neatly” into 5-sticks. The answer would be the number of 5-sticks.

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