Friday, April 13, 2018

That Feeling You Get When You Solve a Hard Math Problem

Have you had a kindness? Pass it on.  ~Henry Burton

That Feeling You Get When You Solve a Hard Math Problem

The numbers click in place like a combination lock. You have
cracked the code, you
have mastered the challenge! The problem had
you cornered, but it was decimals that gave you a
way out. A mathematical kindness
was bestowed by the universe: a “Pass
Go Collect $100” card, and it
gives you the joy and energy to carry on.

©Mary Lee Hahn, 2018

A couple of my students had a great day in math this past week. (One was the future astronomer from Day Two's poem.) We were working on irregular volume and they got to the challenge problem -- making an irregular figure with a total target volume of 325 cubic units...with the additional self-imposed challenge of not using a 1 in their answer. So, for example, they didn't allow themselves this solution: 10x(3x10) + 5x(5x1). They were stumped at the end of math class, but later, at the end of the day, they grabbed their papers out of the pile and kept working while we waited for the buses to be called. The student who gave me this quote asked, "Can we use decimals?" I answered, "Why not?!" and he promptly found a solution: 10x(3x10) + .25x(10x10).


  1. I celebrate all math moments that end in success. I tell students I do Macy's math--percent off. Maybe that will be a poem one day! The simile in the first line is wonderful.

  2. Although we generally celebrate literacy in schools, I don't think we celebrate the aha moments in math nearly as much as we ought to. I know this feeling of when,
    "The numbers click in place like a combination lock"

  3. Love that first line!

    And cool that a decimal helped solve that problem. Would have liked to know how the idea to use decimals came up in the first place...? Where did that insight come from? Cool.

    1. A week or so prior to this in our opener/number talk, I gave the class an input/output puzzle that had 1.1-->16 and 3.5-->40 as the first two clues. This guy kept posing possible solutions that didn't work with the decimal and he finally asked the hive mind, "How do you get rid of the decimal?" Huge breakthrough for him, and my heart soared at the number of hands that went up, remembering our work with powers of 10. (answer: (n*10)+5 )

      THAT'S where his insight came from...and SO fun that I can draw this line of logic!!

      I think I love teaching Math almost as much as LA. Thinking is so much more visible.

  4. What a great story! I agree that it is REALLY cool that you know where that story started and how the thinking was transferred to the new, different situation. I can't help but think that this student transferred not just a strategy from math (which is cool enough) but also a sense of how someone figures out what is relevant and what is not; an entire BIG IDEA that playing around and trying stuff out is something you do when you encounter a problem; and that they have a stronger identify of being capable of doing that kind of work!

    I don't teach math anymore (Sad.Sad.Sad.) but I've found that teaching science gives me a similar kind of WoW. The other day a kid, out of the blue, asked: Why do balloons lose air when they get cold?
    I: You mean...get smaller?
    She: Yes.
    I: You already know the answer to your question: Think about what happens to particles in a gas when you heat them...
    She: Um...OOOOOOOH! Now I get it! They expand when you heat them and they get closer when you cool them down. The balloon doesn't lose any air at all!! I wonder if the balloon would get bigger again if you heated it up?
    I: Let's try it.


    1. Yup. THOSE moments are what it's all about!!

  5. I know that feeling at times. Especially when it's math

  6. What a victory! Well done that kid, who kept poking at the lock until the combination revealed itself. And well done to the teacher who teaches them to use their minds and not give up and go for the easiest answer.