Monday, October 19, 2015

Day 33: The Big C's & Equation Mat w/ Alg Tiles

Today's estimation was how long is the new paper towel roll? They already know how many sheets a new paper towel roll has, so I will ask all the classes what do we already know about a new paper towel roll?

Today will be a recap if what they learned on Friday when I was out with the Big C's pattern from lesson 3.1.3. I want to show students these awesome posters that I plan to have my TA make for my class to help operate a graphing calculator:

Also, students will be inputting their x,y tables into the graphing calculator, and then graphing their rule and noticing what happens. Here are the instructions from my blog post from last year:

  1. First off, press STAT, then press Edit...
  2. Here you will see a screen with 3 columns labeled L1, L2, and L3.
  3. L1 represents your x values, and L2 represents your y values. Enter in a list of points, in this case it was (1,9) (2, 15) (3, 21)
  4. When you press GRAPH in the top right, you'll get 3 points.
  5. For some students, no points showed up. I troubleshooted this problem and found out that you need to press "2nd" "STAT PLOT" (where the Y= button is) and make sure that your Plot 1 is on so that the L1 and L2 values show up.

(end of anticipation lesson plan, start of reflection on lessons)

So, estimation went alright. I liked that some students estimated the length would be 10 inches, so 10 *80 is 800 inches, then divide that by 12 to see how many feet long it was. I also asked students to see how Mr. Stadel calculated that the paper towel was 93.3 feet long. This took some careful noticing.

I discussed with two of my classes in particular the sub report from Friday. I wasn't happy with 2nd and 3rd period's performance. I talked about how a student can be one of 5 people when a substitute is teaching:

  1. A positive leader
  2. A negative leader
  3. A positive follower
  4. A negative follower
  5. A bystander
I discussed how it is easy to be a negative leader or negative follower, but much harder to be a positive leader and positive follower. A bystander at least does their work, but does not regulate on other students. A positive leader and sometimes a positive follower are the only people that direct their peers to make better choices, and are clearly the most difficult roles to play.

I took the chance to discuss this with students outside, before giving them their new teams. I had students discuss for 5 to 10 minutes Figures 0 and 4 for the Big C's, the table, the rule, and the graph. Some students thought the rule was y=x+6, and some thought it was y=6x+3. They also had difficulty describing what Figure 100 looks like, but some were able to input 100 for x and find that Figure 100 had 603 tiles. I tried to get students to label sides, and notice any patterns related the figure numbers. The beauty of finding Figure 100, is it is a nice transition to finding "Figure X," which leads to the rule. As I guided students through that while asking questions, they were amazed that it ended up with the rule, and also gave a chance to review combining like terms. I asked where does 6 show up in our pattern? It's the growth. Where does 3 show up in our pattern? It's the number of tiles in Figure 0.

Unfortunately I only had 4 graphing calculators that had working batteries so I had to demonstrate the table and rule using Desmos on the projector. Then they reviewed their answers to the last problem that analyzed ideas about how many tiles were in certain figure numbers.

In accelerated, it was a 2 day lesson in 1 day. The perimeter of algebra tiles was a review, but students were definitely confused about some of the legal moves and solving equations with tiles in the negative region. I'm not too worried about this because students showed their proficiency of solving equations on assessments prior. I will make sure they are tested again on equations that have the distributive property like 2(x+3) and -(x-3).

Students were able to show their ideas of finding the perimeter of tiles, and student volunteers showed and explained how they found the perimeter of two complex algebra tile figures.

Tomorrow will be brand new, and show an intuitive way of factoring quadratics using algebra tiles.

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