This task is from Tools for NC Teachers. Students look at various ways to tile a patio using a given number of square tiles. This is remixable. 

Task preview

A landscaping company visits the school to talk about the possible ways to tile a patio and picnic area near the playground.  The school can afford between 24 and 30 square tiles.

Part 1:

For each of the proposed number of tiles (24-30), determine all of the possible dimensions of rectangles you could make.

Part 2:

The space for the patio is configured so that there cannot be any more than 10 tiles in a row. For the proposed number of tiles (24-30), determine which numbers would work as the total number of tiles.

Part 3:

Which number of tiles provides the most flexibility in terms of the possible ways that the tiles could be arranged?  Explain your reasoning.