I finally got a chance to try out the Slope Intercept clothesline math activity, introduced by Chris Shore and recapped via video introduction by Andrew Stadel. I took his advice and showed 0 in the middle with the other 4 benchmark numbers turned around. Students reasoned that to the left we should have -1 then -2, and on the right just 1 and 2. I showed students this image before this.
Some background information: I introduced this activity on a Friday in my Math 7/8 support class, but the 7th graders were in the back working on weekend homework and the 8th graders were done with their assignment due friday so I distributed the purple variable or you could technically call them parameters of each linear equation pictured on the following picture:
These students had previously worked on the mixed up algebraic expressions from Mr. Stadel's page where 2 colors of paper worked well. In this activity, in hindsight, it didn't work as well and I know for next time I would do the following: Make the benchmark numbers purple (-2,-1,0,1,2) and make m3 and b3 blue paper because it's a blue line. Make m2 and b2 on white paper because it would show up as black text and red paper (one student saw it as an orange line, which I said doesn't really matter because we know you're not talking about the black or blue line) for the m1 and b1 cards.
After seeing that above image, I started by asking what students noticed. Some said they saw parallel lines...(?) and another said all the lines are eventually going to intersect (I honestly did not notice that at first). This brought my attention to an idea. There are blank expression cards and I could easily write x on one and y on each and ask if we have an idea what these might be if Tommy thinks these lines will eventually intersect? (You can make the argument that x is 2 and y is 1 if you can convince others that the lines will intersect at (2,1)... but I suppose students could write and solve a system to see what it would be with the agreed upon values..?
I passed out m1 and b1 to one table, m2 and b2 to another, and m3 and b3 to a third. I wonder if I should only make an x and y clothesline card if they ask for it, or if I have 8 table groups just give each table one clothesline card to bring up in turns after taking notes on a personal whiteboard of where they see it placed in comparison with the other ones. That's what I will do for the next time.
Students knew that b was the starting point or y intercept of the graph and they knew m would be the growth. Aidan reasoned that since the black line doesn't increase or decrease it's growth must be zero, so he put m2 under 0. By the way, all of these are subscript numbers and the students immediately noticed that also.
Emma reasoned that the blue line was increasing so it must have a positive slope so she put m3 under 2. We didn't discuss why 2 may be a better choice than 1 (future conversation). She also reasoned that the y-intercept was on the negative side of the y axis so it must be -2, so she put b3 under -2.
Students struggled with differentiating or figuring out the b values for the 1st and 2nd lines. They especially struggled with the growth of the first line.
The good news is I will revisit this activity with these same students and the rest of the class in the mainstream class and they should have some valuable contributions to make.
Also, for the next time I pasted the graphic of the graph on a google doc 4 pages in a row, and then printed it and changed it to 4 copies per page so I can photocopy and chop the graphs for students to paste into their notebooks and take notes of the activity.
Students also had the option of attaching a second parameter to a first using a clothespin.
To extend this lesson I could introduce the screen shot of a desmos graph and ask if they are still correct. I restricted the domain so students could draw on a hard copy or prove they intersection using substitution. Open it up to notice and wonder.
@mr_stadel @MathProjects @Desmos after using whole number benchmarks show this. Is our clothesline still correct?— Martin Joyce (@martinsean) December 19, 2016