Now that you have explored ideas about volume and space filling, you are now to investigate the fifth-grade geometry lesson sequence to see how these lessons supported the development of the students' mathematical understandings.

You should watch all three lessons before beginning any of the challenges 4 A–H:

• Day 1:
  Visualizing two-dimensional drawings of three-dimensional shapes
• Day 2:
  Determining the number of cubes required to fill a box
• Day 3:
  Informal explorations of the impact of dimension on volume of a box

---

Note for the instructor:
There are various ways to approach the 4 A–H challenges. In developing this program, we have found it useful to divide the class into groups, with each group studying one challenge in depth. Thus, the Challenge 4 challenges are organized in this way.