In order to discuss the homework from last night (the Library Fines problem and the temperature problems), we used the homework review strategy of “Using a Chart to Choose Items for Discussion.”

Then we continued yesterday’s discussion on addition and subtraction of signed numbers, and we began our consideration of multiplication. What IS multiplication, anyway? Turns out: it is repeated addition, but it’s a lot of other things too!

We were able to enjoy some beautiful weather during our lunch break. Upon return, we discussed conceptual understanding and procedural fluency and how these two dimensions of mathematical proficiency can complement one another.

We applied ideas from the “iceberg” article to construct our own gallery of posters. These posters let us illustrate the conceptual understandings that lend “floating capacity” to the “icebergs” of mathematical procedures. The posters look great and contain many important ideas. See pictures below.

Finally we extended our discussion of multiplication to consider how the distributive property lays out the relationship between addition and multiplication. We also saw how factoring common terms, such as (6+15)=3*(2+5), is only the distributive rule in reverse.

Homework for tomorrow (Thursday):

Math HW:
Problem 9 on page 4.7 (area of a staircase).  (The area is not 32).  If problem 9 was easy for you, do 10.

Problem 7 on page 4.23 (multiplying by 9 trick).

Pedagogy HW:

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?