Clip 2/9: lesson part 1b
In this clip, Mia Buljan works with her students on a number talk, using a mental math approach to multiplying a two-digit number and a one-digit number. She encourages her students to identify regularity among the various approaches identified, and guides them toward identifying the commutative property.
MIA BULJAN: I had collected the answers “69,” “70,” “56,” and “65” for the answers to the problem I presented (5 x14). Angel is the second student I called on, and his answer was 56. His strategy was to use what John Van de Walle describes as a “whole number strategy” of doubling 14 twice. He uses the visualization that Marlene shared to recognize and fix his error of only adding 4 of the 14s instead of the 5 fourteens that are in the problem.
I remembered that Angel had given me the total of 56 from when I was collecting their answers at the beginning of the number talk. I also knew Angel as a very flexible thinker, and I felt sure he could work out his thinking in real time.
In this case, I’m using the Sociomathematical Norm of errors being sites for learning. Not only does Angel get to share some powerful computation strategies as he works through his error, we also get to surface, as a class, the enduring idea that arguments can be very convincing (such as Marlene’s visualization of equal groups) and that we can use known facts to get started toward an answer, rather than counting everything by ones the minute we get stuck.
When Angel explains how he combined 28 and 28 I take the opportunity to frame two big concepts that we had been working on as a class all year. First, I still had a handful of students at this point who counted everything by one. You can see the answer 69 that was collected was my big clue that students are still doing this. It’s so easy to get off by one or two with this cumbersome strategy as the quantities grow. So I really drive it home here that Angel is using all of the strategies for combining 28 and 28 that we have been developing and working on for the whole school year.
The second mathematical idea that Angel articulates that I ask the rest of the class to reflect on (or engage with his thinking on) is how he added 48 + 8. My students had full command of the “make-a-ten strategy” for single-digit addition. In other words, with 8 + 8, they know that they can break one 8 into 2 and 6 and add 2 to the other 8 to make 10 + 6. However, connecting this make-a-ten strategy to applying it to two-digit numbers is a big transition in thinking. In other words, that 48 is two away from a ten (50) the same way that 8 is two away from ten. I pose the question, “Why does he decompose 8 into 2 and 6? Why not 3 and 5 or 4 and 4?” because I want them to articulate that 48 is 50 with 2 missing and Angel needed the 2 from the 8 to make it 50. It’s almost the exact same questions we used to make sense of the make-a-ten strategy with smaller quantities, and I want them to connect the two ideas in their thinking.
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