Today's estimation was how many staples in a box of mini staples. There was some good reasoning. Most students underestimated. The ones that were close predicted that each row would have double what you can see because the staples are packed inside of each other to maximize space.

We reviewed how to represent -3x + 4 and showed 4 different ways. Students told me what to do on the virtual tiles on the board. After the first volunteer I had students vote: thumbs up you agree, thumbs sideways you're not sure, thumbs down you disagree. This was great formative assessment feedback for me. I could see who was still confused and made me realize I made a good choice to continue clearing up misconceptions. I called on students to give reasoning for their vote. The best conversation was for the expression -(y-2).

Some students reasoned that -(y-2) is the same is -1(y-2), so use the distributive property. They also reasoned that you could put y-2 in the negative region. I wanted to stress both of these understandings. Basically, if you have a subtraction sign outside the parentheses, you can put the expression inside as it but in the negative region.

This particular expression is where I see the most useful aspect of algebra tiles. Often students will only distribute the negative sign to the first term in parentheses. When both terms are in the negative region, it makes sense to flip them both up to the positive region, therefore taking the opposite of each term.

Students continued with parts c and d of the problem and some got to interpreting the algebra tile models and writing expressions. Then students took a mastery assessment on skills 3, 4, and 5. It seems that students have trouble when a percent error is over 100%. I think it's a lack of understanding of the relationship between decimals, whole numbers, and percents. Skill 4 was worded poorly, so as an 8th grade team we decided to take two different answers, based on the students reasoning for their answer. Finally, skill 5 was combining like terms and overall students seemed pretty successful with that.

In accelerated, students revisited y=mx+b. There was one expression that peaked many students interested that had inputs of 1, 2, and 3, with outputs of 3, 9, and 27, respectively. I didn't want to give them the answer and students reasoned it must be an exponential function like the infection problem from chapter 1. As a class I asked them to notice how we can get the numbers 3, 9, and 27. Harrison came up with y=3^x and Nicholas showed me a method I believe he learned in Kumon that helps you write an exponential expression when you know 2 coordinates, one being the y-intercept. That was a learning experience for me.

Students took skill 5 for the first time, graphing a quadratic and fully describing it using all the vocabulary from when we worked with Polygraph: Parabolas.

I noticed students are confused with what minimum and maximum are. A few remembered that it has to do with the vertex. Also, a few incorrectly wrote the coordinates for their x-intercepts. The ones who wrote just the x-intercept number and not the coordinates avoided this mistake, but I will be stressing you need to write the coordinates, to reinforce that the x-intercept is when the Y coordinate is zero.

A few students stayed after school to show me their homework, corrections on prior assessments, and retake skill 2, solving linear equations and interpreting their solutions. One student was unclear that if you get let's say x + 2 = x + 1 that it's undefined. I discussed that undefined is a concept for slope and for finding the domain of functions. When an equation is not solveable, we call it "no solution" not undefined.

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