Another fantastic day!
We began with the name game, with a total of 210 names said. We then shared our solutions to the Caterpillar problem, listing 4 different formulas and ideas for more.
We then moved into the “Gross Problem” to complicate our instincts on how place value interacts with subtraction. Solutions presented included subtracting mixed numbers and how that also draws upon similar ideas when borrowing.
Just before lunch we discussed using conceptual understanding to build procedural fluency.
After lunch we discussed the “iceberg” model, and how any topic is supported by many earlier ideas.
We then moved into multiplicative algorithms, in particular how the Partial Products (or area method) is tucked into both the standard algorithm and the lattice method.
Read Principles to Actions, the section titled “Support Productive Struggle in Learning Mathematics” (p. 48-52). In your notebook, write a response to this prompt:
Review the “Beliefs about teaching and learning mathematics” chart (p. 11, Obstacles). What beliefs are evident in Ms. Flahive’s and Ms. Ramirez’s classrooms (see fig. 21 on page 51)? What impact do those beliefs have on students’ opportunities to grapple with the mathematical ideas and relationships in the problem?
Watch the following videos which relate to productive struggle
Science of Thinking: https://www.youtube.com/watch?v=UBVV8pch1dM
Don’t Get Stuck: https://www.youtube.com/watch?v=VrSUe_m19FY