## Tuesday, February 9, 2016

### Day 99: Slope & Factoring Error Analysis

Today's estimation was a 12 ounce bag of spice drop candies. Some students surprisingly thought they were the same size and used a proportion. Others said spice drops were bigger so they had to be less than yesterday's answer.

 I like how Natalie clearly explained how she got 3/4 of yesterday's estimate answer.

I passed back last Friday's assessment and reviewed the answers and common mistakes. I will be available Wednesday after school for any test corrections and/or retakes.

Students worked on unit rate and finding slopes from lines. They were exposed to the concept of lattice points to use to make their slope triangles. They've drawn growth triangles so I stressed to them that order matters in their fractions. They reviewed a problem that had 3 different sized slope triangles. The goal was to realize they were all similar and though different numbers they all simplified to the same slope ratio 5/4.

Then students examined 4 slopes that were improper fractions and reasoned which was the steepest and which one was the least steepest. They reasoned 5/7 is less than 1 so it was the steepest. 14/10 and 7/5 were both equivalent and both equally the steepest.

Yesterday in accelerated we ran out of time before students could share their answers for some of the classwork presented on the board. Luckily I took a picture of it, and wanted students to some error analysis with how a student factored 4x^2 +17x-15 below. I wanted the mistake to be anonymous and I wanted students to all see what was RIGHT about what they did and where the mistake needed to be fixed. They realized that one diagonal did not add up to the middle term (-12x and 5x added together did not equal positive 17x)

 Students reasoned that -12x and 5x did multiply to -60x squared but those two terms did not add to the middle term, 17x.
Students volunteered as I scribed what students were saying. I asked students how a diamond could help with the problem and they said that -15 times 4x squared was -60 x squared so that was the top product of the diamond and below should be 17x:

 I probed students how they got 20x and -3x. And how could someone use trial and error to test for numbers? One student actually said they thought of numbers that added to 17x while another, that I agreed more with, Zoe said she listed factors of 60, like what I wrote in the top right of the board.
 It came a little early but students factored 9x squared minus 4 mentally.
Some students encountered their first quadratic without a middle term. It took a big step to see that the bottom had to sum to zero, then they saw 6x and -6x were the addends and they multiplied to 36 x squared.

 Here Jeffrey rearranged the trinomial and used a generic rectangle and a diamond efficiently.
 I bought tiling turtles for my niece and Chris threw in a set of tiling pentagons. I made a spiral at home.