Same & Different: Partitions & Wholes

Look at the two pictures. What do you notice?

A shows a rectangle with 8 equal parts. It has 4 triangles on the top and 4 on the bottom. The 4 connected parts in the center are shaded, and form a rhombus. B shows a rectangle with 4 equal parts. It has 2 rectangles on the top and 2 rectangles on the bottom. The top right part and the bottom left part are shaded.
  1. How are pictures A and B mathematically the same, and how are they different?
    • A and B are the same because …
    • A and B are different because …
  2. Make a third rectangle. Explain how your picture is the same as pictures A and B, and how it is different.