A Puzzling Sort of Game

Which fraction activity would you rather work on?

Who Am I?
I am a fraction in reduced form.
My denominator is 3 more than my numerator.
My value is more than 0.5 and less than 0.7.
My numerator is prime.

Who am I?

The Dice Game
Roll two dice. Make a fraction with the smaller number over the larger. Then, your partner rolls the dice and makes a fraction the same way.

The person with the larger fraction gets a point.


I think a lot of people would go for the Dice Game over Who Am I?. Personally, I don’t like how the Dice Game depends completely on chance. I prefer games that give me a chance to figure out how to win. But that’s my view as an adult – I see a lot of kids get very excited by the roll of the dice! For all the teachers out there, which do you prefer?


What about your students?


I’m thinking about this question because of two students in my class last year. Neither was particularly motived most of the time, even though both were excellent mathematicians. But when I came up with some fun activity to do, I could usually grab the attention of at least one of them. Nope – scratch that. I could grab the attention of exactly one of them at a time.


One of them loved the dice game. He would come up with all sorts of creative (and correct) ways to explain to his partner why one of those fractions was larger, and did not want to stop playing.


The other kid had no interest in the Dice Game. But let him loose on a “Who Am I?” puzzle, and he was working frantically away at it. He came up to ask me if his answer was correct, and then he was willing to walk me through a detailed explanation of his reasoning.


It took me a long time to realize why I could not get both of them interested in the same activity, but it finally occurred to me. One of them loved games. The other loved puzzles. It was that simple.

What’s the difference — what kind of kid likes one or the other? I don’t have a
handle on that yet. I’m just glad I used some of each this year, so both of those two students had a chance to feel like they were in their element once in a while.

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