So I’m driving down a country road margined with make-shift lots selling Christmas trees every quarter mile and I’m struck by a thought. The thought is motivated by the all too common experience of dressing a newly purchased tree with a string of lights and realizing that the string of lights runs out before the branches do, leaving either an obvious bare rung of base branches or me having to start all over wrapping the lights. My guess is that we’ve all done this – miscalculated the length of stringed lights with the amount of branches to cover.
What a great query for a secondary math class! I think to myself. If I were still in the classroom I would pose this holiday problem to my kids. It would go like this:Suppose you had a Christmas tree that was 7′ tall and 5′ wide at the bottom row of branches. If you had two equal strings of lights with which to adorn the tree, how far down from the top should the first string of lights go so that you had enough left with the second string to cover the rest of the tree?
This is not a simple problem. It involves surface area of a cone, the Pythagorean Theorem, similar triangles, proportions, and solving a simple quadratic. That’s what makes it such a nice problem to ponder with kids. Not only is it seasonal but, like all real-world problems solvable with math, there are many different mathematical concepts and skills embedded in it. I should point out that I would not actually do this kind of math when dressing a tree, but it is a curiosity that can be solved quite accurately using math. [For those brave enough to try it, the answer appears below.]
I suppose what drives me to write this blog entry has also to do with my concern that, in this day of state curricula and district pacing guides, math teachers just don’t get to ponder real-life math problems or use relevant, timely quandaries to teach this subject. I suspect many math teachers would not even notice a real-life application unless it was a textbook word problem or specifically suggested by the district pacing guide. In our desperate attempt to unify instructional materials (to make them “teacher proof”), we have removed original thinking from our teachers’ lesson designs. What also gets removed is the spark that can ignite a teachable moment or a higher-order educational experience for our students.
If you’re a secondary math teacher, I encourage you to try this problem with your kids. I’d love to hear how it goes. dven.