Today Andrea began with an informative talk about productive struggle and had us individually think about how we feel when we are productively struggling and when we are struggling unproductively. We then went over the solution of the library problem and came up with different ways to approach it.
We did a gallery walk with the homework of coming up with a word problem involving subtraction.
Marina began our discussion of multiplication and we discussed how to view it as repeated addition and as an array. We had a good discussion about the order of the numbers in the array and which means what. It was determined that 2 x 3 means add 3 twice or 3 + 3 while 3 x 2 means add 2 three times or 2 + 2 + 2. I realized that I was using the phrase “order does not matter” incorrectly – I should be saying that “the opposite order leads to the same answer”.
Before lunch we began finding the area of geometric shapes by only using the area formula for a rectangle.
After lunch we began discussing the distributive property and how it relates to factoring. Many found that using boxes made the process of multiplication easier to see.
So 5(x + y) could be viewed as an area model and factoring could as well.
We also discussed the justifications for all the algorithms we use for multiplication.
We ended by using the Iceberg article to create icebergs for the procedures or skills that you determined in last night’s homework that you consider essential for your grade level to learn. We did a gallery walk to make comments on the different icebergs and will pick up with that again tomorrow morning.
HW for tonight:
Math 4.9 and 4.12 – finish, pg 4.23 any piece of it.
Pedagogy – read P to A pages 48-52 and respond to the 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?