**This morning we:**

- Discussed the “sum of odds” problem (1 + 3 + 5 + …….+ 99)
- Built on that to work on the “Insatiable Caterpillar” problem
- Then we worked on the Piggy Bank Problems
- Then we played (and nailed!) the name game

**After lunch we:**

Discussed how developing conceptual understanding can support procedural fluency. We generated the list below:

- ”Concrete to abstract” : concrete action supports conceptual understanding, and this provides access to be able to model themselves
- Hands-on activities –> mental representations –> supports abilities to do procedures
- If only procedural skills: kids either remember or they don’t, and then don’t have resources
- “transfers” to other problems, other representations. THIS IS MATHEMATICAL THINKING
- Our job is to create problem-solvers. We have so many tools, kids need to know how and when and why to use them.
- Provides meaning (beyond ”just for the test”)

Watched video of Rachel’s renaming of a mixed number into an “improper fraction”

Then we developed iceberg posters representing concepts that build “floating capacity” for a variety of procedures.

We ended the day by naming the properties of multiplication. This related to today’s mathematical themes: *There are many multiplication algorithms, each with their own advantages,* and T*he methods of decomposing and recomposing are especially key to making sense of multiplication algorithms.*

**Tonight’s homework:**

Read *Principles to Actions* section on productive struggle (pp 48-52).

Read the article we distributed called *Supporting productive struggle with communication moves.*

Spend 20 minutes on the “Handshake problem” on the Evening Reflection page of Day 3.