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.