The Halfway Game

Pick any two proper fractions and find the one halfway between them. Try 1/4 and 1/2: their sum is 3/4, and halving gives 3/8 — the exact midpoint. Plot all three on a sketched number line and check the spacing. This drill sharpens your sense of where fractions live relative to each other.

Now play estimation roulette. Shown 7/12, is it closer to 1/2 or to 2/3? Compute: 7/12 minus 6/12 = 1/12, and 8/12 minus 7/12 = 1/12 — equidistant. Many fractions sit closer to 1/2 than intuition suggests, because 1/2 is the center of gravity of the proper-fraction range.

Repeat for ten minutes across three days. You start seeing fractions as points on a line, not puzzles on a page.