This task helps students understand how area and volume are affected when shapes are scaled up in size. For example, if you double the dimensions of a square, how is the area affected? What if you triple the dimensions? Excerpt of the task:

Imagine a rectangle with an area of 20 sq. cm.

What could its length and width be? List at least five different combinations.

If you enlarge each of your rectangles by a scale factor of 2, what would their new dimensions be? What would their areas be? What do you notice? What happens when you enlarge rectangles with different areas by a scale factor of 2? We looked at this problem in a math teacher’s circle meeting. The board work is below. You can read the notes here: http://nyccami.org/growing-rectangles