Monday, September 21, 2015

Day 15: New seats, color coding algebra tile perimeters, finishing identifying functions

It being the 15th day of school, I divided 180 by 15 and got 12. I think that is my goal to have 12 group changes through out the year. That way everyone has a chance to work with everyone else.

Estimation 180 was number of staples in a box. Students argued Day 15 staples in a box should have been 5040, (24 strips)(210 per strip), wondered why 5000?? Great % error discussion.

We got a reply from the man behind Estimation 180 himself.. Mr. Stadel:

We started discussing the unit tile after students read 2-2 about the side length being 1 and it's area being 1 square unit. I asked them why this was true and we discussed length times width for area and how 1 times 1 is 1 square unit. Tomorrow lesson's was supposed to be perimeter but Ms. Demailly and I both discussed perimeter at the same time.

When I asked them to measure the side length of the teal skinny rectangle they said 3 and a quarter and definitely not 4 or 5. I basically said it's non-commensurate and no amount of whole units can make a teal side length, so we don't know it's length. What do we call that in math? A variable. The most popular one? x. (choral response)

Once the unit tile, x, x squared, and y were on the board, I introduced color coding side lengths of 1. Then of x, and finally y. Then I had students figure out the last 2 tiles perimeters and areas we hadn't covered (xy and y squared) and color code them.

I projected a picture of tiles and you can see the awesome progression one group went from a description, to an algebraic expression, to a simplified expression below:

We will finish up this lesson tomorrow, self-correct homework after estimation, and then pass back assessment #2 from Friday and enter the scores on the Skills sheet I talked about on Friday. It's a shortened schedule because we have the fundraising assembly as a 6th period double period, 7th and 8th graders going first.

In accelerated I gave students time to finish the Function lesson. I asked questions about each of the first 3 tables and why they were functions or not. One group who thought they were done thought that it wasn't a function if 2 different inputs had the same output. Gabriel pointed out that on the soda machine there were 2 different buttons or inputs for Blast, but they both had the same output, and the machine was still functioning consistently. 

I asked what students thought about the graphs. The last question is great because it asks, are all lines functions? One student said x = 0 is not a function because it has points all along the y-axis. This lead right into the discussion of the vertical line test. We took some shortened version of the notes CC 8 kids did last year in a blog post on here entitled "We out here trying to function."

Below I asked if x= y squared is a function. They said no because when x=1, y is 1 and -1. So, the input, 1, has two different outputs, 1 and -1 at the same time. Therefore, it's not a function.

I asked if y=x squared is a function. Is it okay for the input -2 and 2, to both have ouputs of 4? In this case, yes. It passed the vertical line test, twice in this case.

Students got started on the next section that discusses domain. We did not discuss range, yet.

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