Geometric forms representing mathematical thinking

Distinguishing intervals from marks on a number line

Counting marks differs from counting the equal intervals between them. Find the number of intervals and the value of each before calculating distance.

A SHORT EXERCISE

Try it yourself first.

Divide the interval from zero to one into four equal parts. Find the third mark after zero and its distance from one.

View the solution or example answer

Each interval is 1/4. The third mark is 3/4, and its distance from one is 1/4. The starting zero mark is not the first interval.

Your next step.

Mark the unit interval first and keep spaces equal. Extend the example from zero to two: with four equal intervals, each is now 1/2.

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