# Diagrams, week 5

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: $\frac{1}{2}+\frac{1}{6}$ Others will partition each of the wholes and distribute one of these pieces to each sharer (bottom), yielding $\frac{4}{6}$ . Or sometimes $\frac{4}{24}$. 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 $\frac{4}{6}$ or $\frac{4}{24}$ of.