## Friday, December 18, 2015

### Day 73: Equal Values Method, Graphing Systems & Intro to Residuals

Today's estimation was estimating the height of the 2012 Rockefeller tree. In the picture it's sideways which made it harder for students to visualize it being upright. Most students overestimated and were surprised at the height. I liked when students said the man in the picture is 6 feet, so it's probably 10 men tall. That's sound reasoning.

Class started with me asking students, what were the 3 ways we solved the chubby bunny problem? Give me 1 method. They said one was making 2 tables. I probed students to tell me how the table showed us the answer (7 years, 26 pounds in both tables). Then they told me the second way was graphing and they said the answer showed up when the points lined up at the point of intersection. I asked them what that coordinate was, and they said (7,26). They had trouble recalling the third way because 1 or 2 classes didn't get to that point in the closure of the lesson.

So, at least a few students knew how to combine the two equations into one. The bunny was y=3x+5, and the cat was y=1x+19. I liked how Jonas interpreted it as just take away the y = parts and put them next to each other. Yes, with an equals sign. I think when they hear substitution of the expression that y equals into the other equation, they get a bit confused.

After they told me how to solve x+19=3x+5, I asked how can we find out how much they both weighed at 7 years? They said check your solution. When you check it, you get 26=26, verifying that the equations are equal when they both have x equal to 7.

They then worked on writing a system of equations for two high schools growing and shrinking. At least 2 groups omitted the negative sign for one schools growth, and during closure we discussed and analyzed that mistake. It was a great opportunity to learn from.

Then they graphed the growth of two trees, a ficus, and an oak tree that grew from an acorn, y=2x+0. They also confirmed their answer using the equal values method. The assessment on Friday students will not have to interpret the 2 equations, I'll give them those and they'll have to graph both, find the point of intersection, and confirm it algebraically using the Equal Values method.

In accelerated students revised a MARS task called Scatter Diagrams. I wanted them to be more specific in most of their answers. Then we used the scatterplot from the Candle Lighting Task and then analyzed negative and positive residuals and what they meant. They also worked on a problem involving sugar and the weight of sugar. They analyzed the slope and y-intercept, and then figured out if negative or positive residuals would be better. Students reasoned a negative residual would be better because it has less sugar than what they predicted.

Remember:

RESIDUAL = ACTUAL - PREDICTED