Thursday, October 1, 2015

Day 23: Notes on "legal moves" & writing equations given slope and a point

Today's estimation was how many pads of paper in a package. It created a good opportunity to discuss how to write a repeating decimal as a fraction. Some students said a teacher had told them you're not allowed to write a repeating decimal in a percent. I've never heard of that before. Is that true? Some knew that 16.6 repeating is the same as 16 2/3.

In CC8, we took notes by having an interactive lecture. I asked students what was the first "legal" move to simplify algebra tiles. They told me making zero pairs. So, they gave me an example, and I asked for a second example. The first example is 2 differently shaded tiles, same region. The 2nd way is 2 same shaded tiles, but different regions, that cancel each other out. That leads to talking about flipping tiles from the negative region to the positive region. That explains why a positive in the positive region cancels out with a positive in the negative region. Finally, we talked about balanced sets. There was some overgeneralization of this rule in 2nd period, so I clarified in that class and all the others that an x tile on each expression mat can be removed as a balanced set if the tiles have the same shading and are in the same region on each mat.

Then I had volunteers guide me through simplifying problems A through C. They directed me using the language on the board. We gave 3 second claps to students. Then I instructed them to finish up d through F. After circulating, I had new volunteers direct me how to simplify it. Then we did our weekly community building where all the students stand up and I say if you love basketball stay standing, if you have 2 siblings, stay standing, etc until we get down to 1 person.

Finally, in all classes except 5th period, we discussed the last problem which simplifies to 2x and -6 on the right side. Some students assumed that since the x tiles were positive that they must be larger than -6. Some students reasoned that if x was -10, then the right side would be greater. I then asked what would make them equal. Students said x would have to be -3. That is a preview of when we will be solving equations using the equation mat.

In accelerated, we went over a baby chick problem where you are given the chick's weight after 9 days and it's constant rate of growth per day. We talked about how to use a table. Students were impatient and wanted to jump to the algebraic way. None had solved it with a graph. We discussed that way briefly.

What frustrated me was that some students who already knew how to write an equation given slope and a point were disrespectful and not empathetic to students who did not know yet. I had students explain to me how to do it, but their explanations were not clear enough for students who did not know the method. We took brief notes on it, and I emphasized that when you are systematic, show your steps and work, it's easy to see your thinking process and any mistakes.

The notes consisted of:

1. Substitute the slope, m, into y=mx+b.
2. Substitute the coordinates of the point (x,y), for y and x in the equation.
3. Solve for b. (Asked where that showed up in using a table to solve)
4. Substitute m and b back into the equation.

I will have to once again have a talk with my accelerated students. About 8-10 students learned the method in Kumon, on their own, or in another country. They are not being empathetic to students whose parents do not send them to this extra support or have the self-motivation to learn material beyond the scope of Algebra I or before we have covered it. Also, one student was talking about point slope form which was easier. I hated saying it, but I said that we hadn't gotten to that in the book yet, which is why I hadn't talked about it yet.

Tomorrow students will be assessed on skill 6, graphing an equation in y=mx+b form, which should be review. For CC 8 students will be assessed on their ability to simplify expression comparison mats and write an inequality.

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