# Blog Recap: 2019 Day 3

This morning we:

1. Discussed the “sum of odds” problem (1 + 3 + 5 + …….+ 99)
2. Built on that to work on the “Insatiable Caterpillar” problem
3. Then we worked on the Piggy Bank Problems
4. 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 The 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.