Friday, February 12, 2016

Day 100: Comparing, Interpreting +/- Slopes & Factoring Completely

Today's estimation was about jelly hearts. Some students thought they were the same size as the spice drops, but most students reasoned the jelly hearts were bigger, so they took up more space, therefore there should be less of them in the bag.

Making size comparisons, calculating percent error.
Here students used the visual clue of part of the bag being see through to estimate the whole bag.
Since today's lesson was the last day before a 5 day weekend (President's weekend), I decided each class would have a participation quiz. I like to do this with lessons that are somewhat review or introducing a concept that I think they will grasp more without my direction.

Students compared the slopes 5/2 and 2/5 to determine which was steeper. A lot of students described how one was greater than a whole and one was less, so since 5/2 was greater than a whole it was steeper.

Then they analyzed two lines of bank accounts. Students saw they both had a y intercept of 12, and they decreased and increased at the same rate. In one group I made the point of asking them, if the line is increasing, they are SAVING money? I showed them my wallet and I said am I saving money right now? They said yes, because you're not spending any. So, I said if the line is increasing are you saving money? They then realized they were gaining or making money in that situation.

Students found the slopes of each line and saw that when it was decreasing, it would make the slope negative. Part of the lines in the book have obscure lattice points that are deceiving so I didn't like those examples as much. But, it did bring up the concept of what the slope of a horizontal line is. They realized it was 0 because the y coordinates did not change and the x coordinates could be anything. So, zero over anything is zero.

Here students saw that lines with opposite slopes had the same angle. I noted students leaning and pointing at their group members book. I also advised a group to read 1 part of the problem at a time, not the whole thing. In the bottom right one student used the vocab from scatterplots: "As days increase, money decreases." Awesome!
I advised one team to make sure they were using a study team voice and ask their group the question before me. One group member was not writing as all the others did, I advised that person to ask them to repeat their reasoning if you didn't understand it the first time.
I like how a student said "remember the slope ratio, the top is y changing." One students line of questioning to their peer impressed me so much I told her she had a future career in teaching!
I like how one group gave the 5 and 2 in the slope 5/2 names: rise is 5, run is 2. One student said lettuce points instead of lattice points which we all agreed was kind of funny.
In accelerated students worked on factoring completely. Basically, they reasoned that if all 3 terms had a common factor, then there would be multiply ways to factor it. They realized they can factor out the common factor, and then factor what was in parentheses. Some students asked when they were going to use this in real life and I told them that it would be helpful when graphing these quadratic equations. I expanded by saying when you throw something it travels through the area in a parabolic arc so we would be studying that.

I like how group 3 reminded each other what the top and bottom parts of the diamond represented. While some students, about 6 in the class learned factoring at Kumon, some students heard their method but still liked using generic rectangles and diamonds because it keeps their work organized. Naturally I agreed and thought that you could find any mistakes easier.

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