When Ms. Lopez asked her class to use their tiles and make rectangular arrays for the counting numbers 1 to 12, Robert made only one rectangle for 4 (1 by 4) and one for 9 (1 by 9). He did not form a 2-by-2 square and a 3-by-3 square for these numbers because he said they were not rectangles. What would you say to Robert?
I would explain to Robert that squares are actually a special type of rectangle. A rectangle is defined as a shape with four sides, with opposite sides being equal in length and all angles being right angles. A square meets these criteria, as it has four equal sides and right angles.
Therefore, a 2-by-2 square and a 3-by-3 square are indeed rectangles. In fact, they are special cases of rectangles called square rectangles, where all sides are equal in length.
Encourage Robert to think of squares as a subset of rectangles. All squares are rectangles, but not all rectangles are squares.