For some reason, students have a hard time with isolating one variable when there are two to work with.
This year, I could see that our experience with the iPad app, Dragonbox, helped some students with this task, but it was still overwhelming for some.
After our initial lesson, I could see that I needed to do some damage control before things got totally out of control.
In small groups, using a guided instruction approach for only those students needing extensive help (the others were busy making teaching videos of the concept), we revisited this lesson of cups, chocolate and counters.
3y + 2x = 6
3 y-cups stacked with two "positive" blue Easter eggs = 4 positive counters
Using this approach with two colored Easter eggs,
Students could see that I added two "negative" pink eggs to each side (demonstrating the Property of Equality)
With no more Easter eggs with the y-cups, we were able to divide our stack of 3 cups into three groups.
Now we just needed to divide the other side into three groups as well.
As students modeled the process with the cups, candy, and counters,
We also recorded it step by step on our homework paper.
When we got to a problem with a negative y, we had to do some thinking.
How were we going to represent a -y?
I simply flipped the cups upside down.
A perfect solution!
With the cups upside down, we weren't able to divide the objects on the other side and place them IN the cup without flipping the cups right side up (or in other words, multiplying each side by a -1).
-2y - 2x = 4
+ 2x
Need to flip the cups right side up.
-2y(-1) = 2y (2x + 4)(-1) = -2x - 4
Everything FLIPS!
It's a perfect demonstration of the power of -1!
No comments:
Post a Comment