Tuesday, October 20, 2015

Day 34: Completing Tables to Graph a Rule & Factoring Using AlgebraTiles

The estimation was a package of diapers. I asked students if the sticker in the middle helped them at all. Some students said the sticker was about 5 diapers wide, and the package was about 7 stickers wide, so 35 diapers. Some said up to the sticker is 10 diapers, so double that and the total is 10 diapers. Both were sound reasoning. I think some were surprised how thick they were.

In lesson 3.1.4 I gave each table group 2 sticky dots and 2 x-values. I structured it better after first period. I wrote the rule y=-5x+12 and modeled it for x=0, and how you showed your work with substitution. They then got an output value which created an ordered (x,y) pair. They then wrote that coordinate on the sticky dot and graphed it on the board. I asked what patterns they noticed with the graph and the points. As the graph was going left to right, as x increased by 1, y decreased by 5. I asked where they could see that in the rule. They said it's after y= and before the x. Also, I asked what point was easy to see. They said the one on the y-axis. They said it was (0,12). Same question. They said it's the plus 12 part of the rule.

Then I had students copy the table that had x values from -4 to 4 and they had to figure out the y values for the rule y=2x+1. This reinforced that I need to reteach integers to the class, seeing how students struggles with negative values. I also encouraged them to calculate 2 and try to see a pattern. They then setup their own x and y axes, graphed the points, and connected the points to form a line. They also practiced on a parabola, and we discussed how to properly say it. Also, what a vertex is, and what the vertex of y=x^2 is. I related a lot of this lesson back to the first week when they did the Algebra Walk on Day 5.

In accelerated, we got to a lesson I was really excited about. They were given a jumbled mixture of algebra tiles in a picture and were told to build a rectangle. Then to label the side lengths and set it equal to the area of the sum of the algebra tile's individual's areas. All the students that do enrichment math work at Kumon finally understood what factoring meant with algebra tiles. I encouraged students that already knew procedures to use the tiles to challenge and push themselves. I took a bunch of pictures of configurations students made and also some of the creative arrangements along with some jokes of is this one okay? (the really long 1 unit wide rectangle). One student joked that people that work at Kumon have to eat too. I got a good laugh out of that one.

Oh, and this student was a bit off task, but brought up an interesting point. He claims he now knows what y equals in algebra tiles (purple is y squared). He says it must be 5 and 1/2 because 2 y's are 11 unit tiles long. He's trying to prove that the tiles are non-commensurate, and I'll remind him that they are. Y is unknown!

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