Today was a second garden hose next to yesterday's. A lot of students were successful, it wasn't a trick estimation.
Today was sports dress up day. I wore a Stephen Curry jersey and this student wore a Barry Bonds ASU jersey. I had to take a picture.

Barry Bonds throwback 
Students reasoned about the data table of Nate's claim that cars with lower odometer readings cost more. Today students setup a graph and made a scatterplot. They estimated where a car with 23000 miles would go. Then they drew a line of best fit. I advised students that you should try to have equal amounts of points above and below the line. Then they used the line of best fit to predict how much a car with 80,000 miles would cost.

Katie's graph was scaled and labeled properly. 
In accelerated students learned a new method to write a system of equations given two points on a line. Basically, you substitute the x and y coordinates into y=mx+b. Then students realize they can subtract them and eliminate b to solve for m. Then they plug m into one of the equations to solve for b, then they can write their equation.
Then they are given the coordinates (6, 256) and (2,16). Some students tried subtracting 16 from 256 and couldn't get the answer. I asked students how the b variables cancelled before. They said because they were subtracted. I said will these eliminate if they're subtracted? A lot of students had an a ha moment and saw that they had to be divided.
This eliminates a because a divided by a is 1. Then they subtract the exponents because it's dividing. Then they take the 4th root of both sides to solve for b and plug it back in to solve for a. Students need practice verbalizing the language of saying taking the 4th root of both sides.

Writing a linear equation from 2 points on the left. Writing an exponential equation on the right. 
After class ended, Aaron came up to me and showed me this method. Quite interesting. Basically multiplying one equation by 16 on both sides. Then he set the two equations equal to each other because they both equaled 256. Then he divided both sides by b squared. Then the a's were able to cancel, and he solved for b. It takes a few more steps, but it quite creative and makes more sense now that I summarized it there. Go Aaron!
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