How can we measure the weights of our cubes?

This is the heart of students’ investigation of weight, and it might get “messy” as they struggle to achieve comparability using the nonstandard measures.

The students face a quandary: They must weigh each cube, but their measures are mixed. Should they sort them out into three piles — paper clips, washers, and bears? Should they use the same measure for all three cubes, or should they use paper clips for one, washers for another, and bears for a third? Or should they create some sort of mixed unit, perhaps “1 small pile of stuff” or “10 mixed items”?

Offer no opinion on these matters. Rather, acknowledge the difficulty and ask, “What do you think?” and “Why?”

Check to see that students understand how to use the balance in this new way, that they handle the instrument carefully, and that they adjust the balance as needed. Also, make sure they record their weight measurements in their notebooks.

Have each group record their weights for the three cubes in the class table, making sure they identify the units.