This morning, we began by reviewing the “100 Days of Christmas” and the Handshake problems. We connected each of them to the triangular number problem from the previous day.

Then we dove into more math – formally introducing the idea of multiplication. We discussed the power of the area model for thinking about multiplication of fractions. We related the stacks of pennies from the Piggy Bank problem to the one-to-many correspondence model.

We examined various properties of multiplication: the commutative property and the associative property and justified them using the models of multiplication.

[then, Nursen led a pedagogy discussion]

After lunch, we returned to the properties of multiplication. We dug into the distributive property, and how this can be justified using the area model, and how it supports the algebra skills that students will need in later math courses. Finally, we examined the multiplicative property of one, the multiplicative property of zero, and the multiplicative property of -1.

[then, Nursen led a pedagogy discussion. Participants were grouped by grade bands, and made “icebergs” for a procedure or skill that students develop in their grade band.]

Homework:

Math Homework:

Complete Block 3, p. 12, and the new page on “Adjective-Noun theme for multiplication.”

Pedagogy Homework:

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?
Find a task/activity from your curricular material(s) that supports productive struggle.