Paging Doctor Math: Tug-Of-War Task

Following @mburnsmath on Twitter has paid off. This time the payment was an older task of hers, A Mathematical Tug-of-War. I did this task with my 7th graders, and while this may not have been the most difficult task I have ever presented, it may be the most accessible. When discussing this task during class with individual students and groups, I counted four distinctive approaches, with different variations of those four approaches present. I would categorize different ways as informal substitution, Algebra/combining like terms, unit rates, and assigning values (some of these overlap between the student work). I have examples of each posted at the end of the post.

Screen Shot 2017-01-16 at 7.31.20 AM.png

Can be found in 50 Problem Solving Lessons for Grades 1-6 Marilyn Burns Math Solutions Press 2003

Q2 What character(s) could you add to the losing side of round three to make the round a draw?

Q3 Dr. Edwards is teaming up with Ivan to form a tug-of-war dream team. Dr. Edwards is twice as strong as Ivan. You are forming your own team to tie Dr. Edwards and Ivan’s team. Give TWO possible team formations of Grandmas and/or Acrobats to TIE Dr. Edwards and Ivan’s team.

This is also a great example of a task that isn't necessarily real-world, but it is interesting for the students. Not everything has to be real-world all the time. The important thing is that the students are discussing the math involved. Maybe some will argue with me that this is real-world...I have seen a lot of wacky things on ESPN 2 late at night, but never the International Tug-Of-War Competition where animals and people are allowed to enter, although that would be interesting television. Same goes for this task...

A few of my students struggled to get started and were hung up on both sides needing to have an equal number of people in physical number and not in amount of strength. I gave the example of myself having a tug-of-war match with one of my student's kindergarten sisters. There would be one person on each side, but it wouldn't necessarily be equal. That worked well.

This task is also a good way to organically get away from a problem being on one side of the equals sign and one number being on the other side. The equal side doesn't necessarily mean question and answer like many students come to me thinking, but both sides being the same amount. When I previously taught 6th grade, problems like 3 + 5 - 2 = 1 + 1 + x would be difficult, and I think this task would help solidify what the equals sign really means.

I was disappointed that some of my students called me out on being as strong as two Ivan's, but in rethinking the reality of the situation, it probably depends on what four grandmas and what two acrobats I would be facing!