I bought our Christmas tree today. The teenager who sold it to me at the VFW assured me it was a good one and would last the season, “no problem.” I’ll take his word for it as I’m not quite done with my Arborist degree. The kids love the day I bring home the Christmas tree, for obvious reasons. After I set it up in the stand I took out two brand new boxes of tree lights (since I stepped on last year’s lights, rendering them usable, but dangerous).
The kids were super excited! New Tree! New Lights! My daughter Ellie saw the lights and asked, “is two boxes going to be enough?”
Why does she do this to herself? Shouldn’t she know better by now? I’m sure you can imagine her excitement when she looked at me and saw that “I’m going to end up blogging about your question” look on my face.
So I directed her to the box, which outlined the capacity of the string of lights thusly:
We had two boxes, and she’s 12 and pretty good with arithmetic, so she quickly arrived at the fact that we had “approximately 123 ft” of lights. At this time I did what any self respecting father of 4 who also has a deep passion for mathematical questions but also has a penchant for self preservation would do.
I put the lights on the tree. Is there adequate lighting?
Here’s the ornament I made in Kindergarten
And this “ornament” is me at 21. I keep my old college ID around for emergencies.
And this is how I think most people see me these days.
You see, you can’t do the math problem BEFORE decorating the tree and live to see another day. You’ve got to give in to the beast that is “the holiday season” and put your questions on hold until after the practical matters have been completed.
Now remember, Ellie asked if I’d have enough lights for the tree. I rephrased it as ” Will these two boxes give the tree adequate lighting?” Adding the word “adequate” puts a degree of ambiguity into the question that allows other students to discuss what “adequate lighting” really means to them, based on their own Christmas tree experiences and preferences.
To turn up the math dial a bit (as Dan Meyer would say) here’s some information.
The tree is 90 inches tall, floor to top tip. But the green lit portion of the tree begins 2 feet off the ground, so the green portion is only 66 inches tall. In a stroke of mathematical genius (luck) the tree is also 66 inches wide at its base. Since no one ever puts the lights on the very very outside of the tree surface, we’ll hypothesize that the tree is a cone (which it is not…but whatever).
Now the fun really began. I wanted to start in on the math. I wanted to follow the path of the lights. I wanted to draw a cone, start measuring surface area and distances and spirals. I wanted to get super Mathal (it’s a word). My daughter, on the other hand, drew from her own experience and coupled it with a desire to end this conversation and said “I saw a cool thing at the store. Check it out.” At which time she took out my computer and found this:
Looks like the good people at Kmart have already done the math for me. According to them, this 6 foot tall tree (6 inches taller than my green one) needs only 250 lights to create this spiral. Each box of our lights had 300, albeit in leaf-like pairs. At that, Ellie said, “I guess it makes sense that the two boxes were enough. Bye” And she walked out of the room.
If you’ve read Instant Relevance, you know that I love moments like these. Sometimes I lose the value of the moment by trying to make it about my love for mathematics, when really, it was just a great conversation about possibilities. Take the time to engage in the great conversations with your students, and when you can, take the next step to make a strong lesson plan out of it. But remember, you don’t always have to do both to #MakeItReal.
To my friend Alice Keeler: you may need some more lights.
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