Working through a series of rational number workshops for 3—5 grade teachers. My colleague, the incomparable Anne Bartel, drew these diagrams to help illustrate an important difference in two ways children might solve a problem in which 4 things are shared among six people.
To wit: Many kids will share out halves first, and then deal with what’s left over (top), generating a sum for an answer: Others will partition each of the wholes and distribute one of these pieces to each sharer (bottom), yielding . Or sometimes . We should be on the lookout for these different solutions and use them to generate mathematical conversation (esp. the importance of saying what we have or of.