Building Enduring Mathematical Understanding, one lesson at a time.

Archive for the month “July, 2012”

Lesson: Tricky Tables

Earlier this summer I applied for a job (it was a part-time position to go with my current part-time position, so now I will be teaching full-time . . .but that’s a whole different story) and was asked to “present” a ten minute “mini-lesson” as a part of the interview. Well, in reality, I am not so sure how much can be accomplished in just ten minutes (and I believe it ended up going significantly longer than that) but I pulled out part of a series of activities that I have used with my eighth-graders for the past two years.

The main focus was working first individually, then in pairs/threes on completing the tables below:


It seems like a fairly simple task, finding a constant increase or constant decrease pattern and filling it in, but nonetheless, there were a few challenges. There were both “math and non-math” people on the interview team, and it was interesting to see how they approached the problems.

-What strategies would YOU use to solve the problems?
-How do you think middle schoolers would approach the task?
-What misconceptions might crop up?

-What questions would you ask to guide discussion?
-What would be some “next steps?”

-What Enduring Mathematical Understanding can be developed by completing these tasks?

Here is a link to the next part in the series.


Flashback Friday: Half and Double

When my son was about six years old we would “play math” when we were in the car, or getting dinner ready, or just “playing.” I remember asking him what 7 x 8 was, and hearing a reply that went something like this: “Well, 7 x 8 is the same as 14 x 4, and 14 x 4 is the same as 28 x 2, so. . . 56!” It was not quite what I expected, but then I recalled a brief conversation we had had some time earlier involving the number 12.

Son: “3 x 4 is 12, and so is 6 x 2.”
Me: “Yes. . .?”
Son: “Does that always work?”
Me: “What?”
Son: “That if you double 3 you get 6, and half of 4 is 2.”
Me: “Well, what do you think?”

I could see the gears turning as he thought about it in his mind – picturing the four groups of three changing into the two groups of six. I don’t recall the resolution of the discussion, but apparently it was enough to satisfy him so that it became a strategy that he began to use on a regular basis. I am certain that I did not encourage it as a “method,” just an interesting occurrence.

A few weeks after the “7 x 8” question, I asked it again, expecting that he might remember “56” from his previous “derivation.” Here’s what I got: “Well, 7 x 8 is the same as 14 x 4, and 14 x 4 is the same as 28 x 2, so. . . 56!” He showed exactly the same enthusiasm for “solving the puzzle” that he had a few weeks earlier, not recollecting that he had, in fact, solved it before.

Contrast that with the child who has memorized 7 x 8 = 56, and would be able to repeat it back in the blink of an eye. Who has more Enduring Mathematical Understanding?

Hello world!

After years of lurking around the online math community, I have finally decided to take the plunge. This blog, findingEMU, stands for finding Enduring Mathematical Understanding, a continual goal that I have for myself and my students as I provide opportunities for them to build their own understanding, in and out of the classroom.

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