Math in Our World: Hamster Town

A stack of boxes of varying sizes.
An adorable hamster named Peanut.

Ling and Nguyet have a pet hamster named Peanut. They’ve been using cardboard boxes to build “Hamster Town” in their basement, designing and decorating houses, stores, schools, and more. They are collecting boxes so they can construct a few more buildings. They need:

  • Two or 3 boxes that have a volume of less than 1,000 cubic inches for houses.
  • A box that’s greater than 4,000 cubic inches for a library.

Here are the dimensions of the boxes they’ve collected so far:

BoxLength (in inches)Width (in inches)Height (in inches)
  1. What do you notice? What do you wonder?
  2. Show what is happening. Use pictures, models, or numbers.
  3. What mathematical questions can you ask about this situation? Answer all the questions you can!
  • Sketch and label the dimensions of the boxes.
  • Find the volume of one of the boxes.
  • Show your work to someone else, and explain your thinking. Did they understand?
  • Ask whether they have any other questions you can answer.

Do you have empty boxes around? Measure their dimensions and find their volumes. Are any of your boxes larger than Ling and Nguyet’s biggest box? What can you build by combining those boxes? What’s the volume of the combined structure?