While they were working on it, a variation sprang to mind: instead of starting with two integers, you can start with any two (positive) fractions. This version of the game is most interesting if we insist that only reduced fractions are allowed to be written down.

We played that variation a couple times, but my students weren’t as excited about it. *I* thought it had potential, though.

]]>It’s great to hear back and to hear of the interest your students have with this little game.

The more Math I learn, the more I write on this blog, the more I pay attention to what readers want, the more I realize that the very basics are what’s needed. And I don’t mean the basics as they’re taught in school. I’m talking about the most fundamental concepts that need to be explored to be internalized and appreciated.

I attended Stanford, majoring in Math. I didn’t enjoy my mathematical experience there. I much more enjoyed the play and exploration I was doing in High School and Junior High School.

When I attended the prestigious Ross program in the late 70’s the head of the program, Professor Arnold Ross, a renowned professor and brilliant man always reminded us to think deeply of simple things. That advice has stuck and I’m always looking for fun little explorations that spark curiosity. With curiosity students will learn themselves what they need to be successful.

You and your students might enjoy my most recent post about 8 simple paper and pencil Math games. They can each be explored to great depth and enjoyment.

Thanks again, Andree, for checking back in with us.

]]>The only information I gave them were the rules of the game, a demonstration of the game with one student, and that they should make as many observations as possible about the numbers used to see if they can determine who will win in every game. I also introduced the idea of “1st player / 2nd player” so that we had some common vocabulary to discuss strategy. Here are the student observations:

If both numbers chosen are even, the 2nd player wins.

If both numbers are odd, the 1st player wins.

If one number is odd and one is even, then the 1st player wins. (The students have not confirmed this but they feel strongly that it is true.)

Some student teams quickly learned the value of getting a difference of 1. Other teams used their time to find numbers that did not have many differences at all ( for example: 10 and 15; 3 and 6). Their observations are screaming out for a discussion of why these statements are true.

I really like the Cut The Knot site and appreciate the link to Euclid’s Game. A confession: would you believe that never ran across Euclid’s Algorithm until I was teaching, and then only through independent reading and never in a class? So this is pretty new to me. I am still groping about in the dark on the relationship with this game and Euclid’s Algorithm and the GCD. I need to spend extended time with pencil and paper as I go through the information. I can see that this exploration, when I am prepared, can be used with the older kids at school.

I am preparing a post with links to this post. Thank you for this post. It is far richer than it seems at first read.

]]>Do report back and let us all know how the games goes with the fifth graders.

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