Friday Fave for February 17

Unusually early springlike weather in large parts of the country has the Friday Fave looking ahead to swimming pool season, and nothing goes with swimming pools quite as well as algebra.

The Pool Border Problem is a classic for a reason. There are many ways to count the tiles on the border of a square pool. Different counting methods generate different algebraic expressions, and we can check the equivalence of these expressions by verifying that each will correctly count the number of tiles bordering an n by n pool.

This new Desmos version adds iterative feedback. If you think the expression 3n+8 describes the number of tiles bordering an n by n pool, we’ll let you see whether that works for all values of n.

The expressions students write impact what happens on the screen, and the activity turns a wide range of student input into meaningful feedback. The expressions collect in the dashboard for the teacher to use for creating classroom conversations.

Dive on in, the water’s fine, and the pool’s border is perfectly tiled!