Diagonal is not straight

Zoe and I often play games where one of us makes a figure with some objects (stones, chips, snap-cubes, etc.) and the other one has to make an identical figure.  Today, for this purpose, we were using an old Russian game with pegs (really a generalization of tic-tac-toe where you have to make 5 in a row, but that didn’t matter to us).   At some point, Zoe made the following figure:


(Her final figure actually had the yellow pegs all the way across.)

She then said,”Mommy, now you copy my long straight line.”

What interested me most was not the figure that she made but that she was so explicit about what it was that she made so that there would be no mistake about it.  This led me to an idea.  I made the following picture:


Then I asked Zoe whether this was a straight line.  As I had suspected, the answer was no (accompanied by a “why are you asking me a silly question” look).  And then I asked Zoe what the figure was.  Her answer: it’s like a bishop moves, it’s a diagonal!

At this point it was time for her to go take her bath and so we had to stop.  But now I wish that I had taken it a little bit further.  What if I had rotated the board a bit, so that the line looked horizontal from her perspective, and asked the same question?  Would the answer have changed?  I guess there is always tomorrow!

About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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4 Responses to Diagonal is not straight

  1. But it’s like a bishop moves!!!!! I just can’t think of a response to that logic!


  2. tarelka7 says:

    Wow! What a smart little girl!
    I really like your idea, I’m now curious to try it with my daughter.
    Also I wanted to ask you the name of that game. We tried playing a similar concept game on the paper, but I think it’ll be more fun to play it with pegs.
    Thank for sharing your awesome ideas.


  3. David says:

    I thought it was a Japanese game, not Russian. 🙂


  4. David says:

    Also, this reminds me of when my daddy would walk me to school. I got to walk straight, and he would have to zigzag. But then there was a section of the sidewalk where the lines between squares were diagonal, so then he would get to go straight, and I had to zigzag!


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