Paging Doctor Math: 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...

Informational Video

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 :-(