Saturday, January 28, 2017

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.

Q1
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!






(The 100% reference loses its meaning after the first round, and we discussed that after this was submitted)

Other Task Posts Examples (more available in previous entries)...

Pokemon Go

Man Versus Squirrel

Shrinking Dollar

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Tuesday, January 10, 2017

Toothpick Task 2017

I had an icy two-hour delay this morning, and when you operate off the a combination of getting to school by 6 every morning and living 40 minutes away from school, I never find out about the delay until after I arrive. I enjoy these mornings because I get to catch up on some work. I had a few students come in 3 hours before school started to work, I submitted a manuscript review for Mathematics Teaching in the Middle School, and worked on questions for an upcoming MTMS Twitter chat (which you should join the 3rd Wednesday of each month at 9ET/8CT with using #MTMSchat).

To the task...

Additional Information 

Q1~How many complete rows of toothpicks can you make with the amount given?
Q2~Will there be any extra? How many?
Q3~How many more would you need to complete the next full row?
Q4~How many toothpicks would the container need to create 20 rows?
Q5~If someone wanted to know how many toothpicks would be in the 75th row and you didn’t want to build that big of a pyramid, what could you do to find that answer fast? How do you know that will work?

The first part of this toothpick task (by @ddmeyer http://bit.ly/2jzv0sZ) begins innocently enough, with students trying to find out how many full rows could be made with the given amount of toothpicks. The interesting part to this is how students choose to solve this first problem. Almost all of the students (I did this with 7th grade, but could work for 5-8 or more). will start by dividing 250 by 3, not fully thinking what the result will mean. Once it is understood what this answer of 83ish means (asking a quick question about what does the 3 mean normally brings light to this problem), students branched off into three different ways to solve: a full blown picture, a chart, or a combination. Within these three options, most students either went with the tooth pick totals, or the total number of triangles. While many of these options will be similar, the different number of ways to solve this problem speaks to the accessibility of this task.

Question 5 is a great question as well because you can get into some generalizing. Some students automatically search for patterns, but some don't think of that as an option. Making it more explicit helps students understand that finding patterns is an option that can always be looked for. Patterns may not always be prevalent, but at least now students know that option exists.

This task will help us move into some tasks with some equation/expression writing built in such as Central Park, In-N-Out Burger, and Detention Buy-Out.

Enjoy the student work below! I especially like the one towards the middle where the students exclusively used triangles instead of individual toothpicks like many of the students used.

Note: As I was typing this, we are now cancelled :-(





 




Other Task Posts Examples (more available in previous entries)...

Pokemon Go

Man Versus Squirrel

Shrinking Dollar

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