My students just did this… and I loved it. It was math class. It was math thinking. It was math questioning. It was math discussing. But it was holistic. There was social studies and art and math all getting talked about together. And best of all… there was no computation… and the kids loved it (mostly)…
and it looked like this…
… and I want to see them do it again.
A few weeks ago, I asked the students to figure out how many CD’s it would take to cover their four-desk pod. I didn’t tell them anything more than that.
How would you solve that problem?
I was very impressed with what I saw.
1. The questions: Do we need to cover the whole pod? Can they overlap? Can they hang off the edge? What if there are little bits of desk showing through? (Excellent questions because they all change “the answer”.)
2. The methods: All began by measuring their desks. Some chose to leave length and width separate, some chose to multiply into area. Some researched the dimensions of the CD and had to decide how they were going to use it.
3. The answers: There were several recurring ranges of answers, but in terms of the numbers, there were probably 15 different final answers and the students were okay with that considering the assumptions were different.
All of that reflects a TON of great math thinking and problem-solving, but the most convincing solution to many of the students was arguably the simplest. (Isn’t it always that way?)
Here is a photo of the solution:
Photo Credit: Heather Roadcap – Used with permission
The solution: Get a CD, trace it carefully, and count. Can you argue with that?
I have WordPress Blogger (and Ph.D. mathematics student) Jeremy Kun to thank for inspiring this post. His original post “Graph Coloring, or Proof by Crayon” not only lent me the title, but a ton of fantastic insight into the many, MANY different applications of this kind of mathematics. So, soon-to-be Dr. Kun, many thanks and I hope that you enjoy my take on this.
All right, the first part of this problem is a challenge. Print out (or transfer into paint or some other photo editing software) the map shown below. The challenge is to color the map in as few colors as possible making sure that no two states that touch each other are colored the same color.
Now, do the same thing with the Michigan county map shown below.
Now, do the same thing with the European map shown below.
Now, when you have done that, I want you to put into the comments the number of colors you had to use to meet the requirements of the problems for each map.
Part II will come when we get some data to work with.
I found this blog post, from the Makezine Blog using StumbleUpon (if you haven’t explored StumbleUpon, it’s great. Anyway…) This quote from George Hart is the opener of the article:
If you make a coffee table that express a mathematical idea and place it right in the middle of your living room, that certainly makes a statement to all who visit that math is central in your life.
Students may not be able to identify with math being central in anyone’s life, but the coffee table is still kind of a cool idea. A simple square coffee table (shown below) is built with cuts and hinges. (For my students who know not to trust the picture, the post states that it is a square, so that is a given.)
If the owner so chooses, the coffee table can be turned into a triangular shape (shown below).
So, the question becomes, what math can we do with this? What questions are there to ask? Of course, how could we answer those questions?
The first two questions that I have are based on the function of the coffee table. Which shape maximizes the number of people who can sit around it? Which shape maximizes the amount of stuff you can put on it?
How could we answer these questions? Are there other questions we can ask?
Post your ideas in the comments.