Friday, February 19, 2016

Day 104: Equation from 2 points, Scatterplot & X-intercepts

Todays estimation was how many pages in a Rolling Stone magazine. It was more than most students expected. Yesterday's estimation was Harper Lee's To Kill A Mockingbird. Coincidentally and sadly, she passed away today. One student actually already knew it. A little eerie.

I loved the homework problem I reviewed with students today. It was so relevant to the assessment and what we've been working on: slope. Students were instructed to graph (-6,3) and (-3,-1). I graphed it and asked students how to find the slope. They said first draw your slope triangle. To find the height, they said subtract 3 and -1. I reviewed 3-(-1) with a plus and minus drawing. Students said that gets you the vertical change because it's the y coordinates. Then to get the base of the triangle, -6 -(-3) which gets you -3. They told me these 2 facts combined to make the slope 4/-3. I asked them if -4/3 was the same? They thought about it and agreed.

From here, they saw on their graph that the y-intercept was (0,-5). I asked them why this makes it easy to write an equation. They said that in y=mx+b, m is the slope, so put -4/3 in, and b is the y-intercept, so put in -5. So, the equation is y=-4/3x+(-5).

I wanted to preview a method from Algebra 1 that they'd probably see next year. I asked them how they could use algebra to find the y-intercept, especially since I just sketched my graph and I couldn't count any tick marks. I wrote the equation y=mx+b and substituted -4/3 for m. I said how can I use this? y=-4/3x+b? In each class I got 1 or 2 hands to raise. That wasn't enough for me. So, I went over to the coordinates and selected one. I asked them what the first digit represented. They said x. And the second? They yelled out Y!!! So.. I underlined that with my hand, and walked back over to the equation and underlined the whole equation.

To my delight, at least 6 more hands raised up and they said to substitute the coordinates for x and y into the equation. I asked them how to multiply fractions, then they chorally told me the steps to solve for b. They liked seeing this and were amazed that algebra got them the answer.

One curious student asked, could we have used the other coordinate? I told her to try it out. If it's also on the line, shouldn't it work?

Writing an equation from two coordinates. Solving for B.
Students had a limited amount of time for the classwork. They revisited the Newton's revenge problem. Students realized that starting at the origin made all the data clump together making it hard to draw a line of best fit. Some students rescaled their graphs so they could make a line of best fit easier.

This student made a big graph, then realized he wanted to rescale it.
This graph at the bottom was properly scaled and shows how easier it was to draw the line of best fit.
A few students wrote an equation of the line of best fit and used it to test if the roller coaster was safe for Yao Ming to ride on.

In accelerated we went over graphing y=x^2-8x+7. I asked what we could get right away with the choice of vertex, x-intercepts, and y-intercepts. They said it was (0,7) because if you plug in 0 for x y would be 7. I asked them what we could do with this quadratic. They said factor it. I asked them how this could help us. Some said to plug in 0 for y. Therefore, the x intercepts are (7,0) and (1,0). They said the vertex is halfway, so 7-1 is 6, half of 6 is 3, so 1+3 is 4, so the x coordinate of the vertex is 4. I asked how to get y, and they said plug 4 into either equation. I plugged it into the factored one which I always think is the easier way. That got us -9. Therefore, all the requirements were there to graph it completely.

Students worked on the zero property, but there were a lot of disruptions with students coming back from the music field trip, so we will finish up this lesson on Monday and then take a pre test on a formative assessment lesson on quadratics.

Homework problem review.
I was impressed with how this student solved this quadratic without factoring the common factors out first. I'll review this a bit on Monday, to make the students life easier.

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