A middle-school math teacher, Ms. Alcala, shared the activity, “My Favorite No” on the Teacher Channel. I highly recommend watching the video. The idea is to collect work from students and then share, anonymously, one incorrect solution that you really like. You might like it because it’s a different approach or because of how much was correct about it or because it’s a common mistake. The idea is to share some work that’s not perfect in a very positive, non-judgmental way, and engage students in thoughtfully critiquing the work. Students get to work on the mathematical practice, “Construct Viable Arguments and Critique the Reasoning of Others” while also sharing and strengthening their content knowledge.

This week, reading student submissions to “Teeter Trio” I was struck by this awesome, but ultimately incorrect, submission:

Seesaw Balance POTW
A seesaw can balance with more than two people on it. The product of each person’s weight and distance from the fulcrum contributes to the balancing. If the sum of those products on one side equals the sum of the products on the other side, balance is achieved.
-As far as I know balance can be achieved when both sides are equal when the products are added in other words, wd=wd, when w is weight and d is distance from the fulcrum.
Shareef and his two little sisters, Marshay and Janeka, are playing on a seesaw. Shareef weighs 30 pounds more than Marshay and 35 pounds more than Janeka, so Shareef sits on one side to balance the two girls on the other.
-If Shareef is trying to balance the other two girls on the other side than we need to know everyone’s weights to fill in the equation of wd=wd.
Shareef=s
Marshay=m
Janeka=j
-Since Shareef is 30 pounds more than Marshay and 35 pounds more than Janeka than we have two different equations for her.
s=30+m
s=35+j
-Since we know this information we can find Marshay’s weight by putting these two equations together like so.
35+j=30+m     Subtract 30 on both sides
5+j=m
-For Marshay’s weight we get m=5+j and Janeka’s weight can’t be found so it will just be represented by the letter j.
Shareef is sitting 6 feet from the fulcrum and Janeka is sitting 4 feet from the fulcrum. If the seesaw is balanced, find a function that expresses Marshay’s distance from the fulcrum in terms of her weight.
-Now that we know Janeka’s distance and Shareef’s distance from the fulcrum but we need to know Marshay’s distance from the fulcrum. Her distance will be represented by the letter d. now that we have all the pieces of information than we can fill in the equation of wd=wd. (The right side will be Shareef and the left will be Marshay and Janeka)
wd=wd
6(35+j)=d(5+j)+4j       subtract 4j on both sides
6(35+j)-4j=d(5+j)        divide (5+j) on both sides
6(35+j)-4j/5+j=d         distribute the 6 and combine like terms
210+2j/5+j=d              Simplify
2(105+j)/j+5=d
Marshay’s distance from the fulcrum is 2(105+j)/j+5=d.

To help you think about what might be incorrect, it’s important to know that in the follow-up you will be given Marshay’s weight and asked to help calculate how far from the fulcrum she should sit.

My questions to you are:

1) What do you find awesome about this submission?

2) How would you fix it without redoing the problem? Is there a way to tweak this answer to make it better match what was asked?

Some Teeter Trio links in case you are interested: