# findingEMU

## 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.

(Paraphrased)
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.