Dive into Square Pools !

In my activity, you have been given the job of tiling square swimming pools. Each pool has a water surface measured in blue square centimeter cubes (call them the ‘pool tiles’). Surrounding each square pool is a deck border made of the other colored cm cubes (call them the ‘deck tiles’). The first pool has only one pool tile, and the second pool needs enough pool tiles to make the water surface into a square made from cm cubes. You need to figure out how many pool tiles and how many deck tiles are needed to build any size square pool. Look for a relationship between each pool’s number to the number of pool tiles and deck tiles it has, as you first build the smallest square pool and then move on to build increasingly larger square pools.

In the middle grades, algebraic thinking moves from informal explorations to formal algebraic considerations; from the concrete to the abstract. The goal of this activity is for students to discover interconnectedness between visual patterns, methods of organizing information (e.g., through the use of T-tables, functions, and graphs), algebraic and geometric symbolism and formulas for problem solving.