Square Numbers

How to play & why it works

A pure drill on the squares: 7², 13², 20² — answer as fast as you can. The range runs past the usual times-table ceiling of 12 up to 20², where the genuinely useful (and rarely drilled) facts live.

Squares are the power facts of arithmetic. They anchor estimation of any product (14 × 16 sits right next to 15²), they are the raw material of square-root sense, and algebra leans on them constantly — difference of squares alone makes dozens of mental calculations trivial.

Learn the teens as a block: 13² = 169, 14² = 196, 15² = 225 have no pattern to lean on, so pure recall is the only route — which is what makes this drill worth running. 16² through 19² can be reconstructed from (a±b)² tricks until recall catches up.

The free MathIt app pairs squares with the difference-of-squares trick (17 × 23 as 20² − 3²) and squares-ending-in-5, inside a full mental-math curriculum.

Squares past 12 are the gap nobody drills. Times tables stop at 12 × 12, but 13² through 20² show up constantly in area problems, Pythagorean triples and quadratic work — and most students recompute them every time because nobody ever asked them to memorise the set.

They also carry the square roots for free. A student who knows 17² = 289 recognises √289 on sight, which turns a large class of algebra questions from a calculation into a recall. The list is only twenty items long, which is a very cheap thing to own.