Additive Property Concept Cartoon

This cartoon was developed to assess students’ ability to:

  • Reason about the weight of different sized pieces of the same material (rock)
  • Understand the additive property — that the weights of all the pieces of an object are equal to the weight of an object

This cartoon is typically used after Investigation 5.1, What happens to shells when we crush them?

Things to look for in student responses

Do students realize that the weight of all the broken pieces together equals the weight of the unbroken rock that needs to be moved up the hill?

  • Some students may agree with Leila that the weight will stay the same. For these students, look to see if they can also supply a deeper reason: for example, “because no more rock material has been added and none has been taken away.” or “the weight of the five parts equals the weight of the whole”, showing they can think of both the whole and the parts at the same time.
  • Others may agree with Fern failing to recognize that although there are more pieces, the amount of matter hasn't changed. These students may simply reason "more pieces is more" (a kind of undifferentiated more is more response.)
  • Still others, may agree with Tomas thinking erroneously that because each piece is lighter, the load will be less heavy, when, in fact, there is the same amount of matter to be moved as there was before. These children reveal that in focusing on the parts, they have lost track of the whole.