Day 1 – Four 4’s Leading to a School-wide Competition

Welp, here it goes. Gonna try to do the 180 blog this year.


Today, in my Problem Solving 2 class (it’s an Exeter-aligned integrated math course for mostly sophomores) we started with the Four 4’s problem. It’s very easy to state – make all of the numbers 1 through 20 with exactly four 4’s and any operations you can think of (ex: 1 = (4+4)/(4+4)). I would say about 80% of them got pretty into it.

I really wanted to do this though so that we could think about “problem solving” and what makes good problem solvers. Here were their reflections based on this activity:

  • You need to be patience and tenacious
  • You don’t need to work in order – do what you can do, solve easier problems and they help you solve the harder ones
  • Sometimes you just have to try stuff even if you don’t know exactly where you are going
  • You can use some answers to get others and some patterns to find other answers
  • Sometimes you need to take a break and come back later

They got all but 11, 13 and 19.

I had them write solutions on these strips of paper because my secret goal is to put this up in the math hallway (with empty strips for all the numbers up through 100) and start a school wide competition. So basically, when you get an answer, you take down the strip, write the solution and put it back with your name. We’ll see how it works. I could see it tanking, but it might be cool!


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