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 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.