Creating inverses for non-invertible functions

This evening Katie and I were playing with functions again.  We were taking turns coming up with functions and having the other person guess the rule from a few example in-out pairs.  Katie was able to guess all of my functions (I didn’t have any mathematically difficult ones) and came up with a few good ones of her own.  For example:

  1. A →Z, B→Y, C→X
  2. katie→eitak, zoe→eoz
  3. 1→10, 2→9, 3→8

For the 3rd example, when I proposed that the rule was subtracting the number from 11, Katie said that this was not correct.  When I asked her what her rule was she said, “it’s the same as in the A →Z, B→Y, C→X case.”

Occasionally, Katie was coming up with not well-defined functions.  For example, one time her rule was: a word goes in and a rhyming word comes out.  While pointing out to her that some words have multiple rhymes, I had the thought of introducing her to not one-to-one functions and their lack of inverses.  I used the example of a person being mapped to their mother; if a mother with multiple children goes in, it is unclear which child should come out.  Katie’s reply: you can just have the older one come out!

About aofradkin

I enjoy thinking about presenting mathematical concepts to young children in exciting and engaging ways.
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6 Responses to Creating inverses for non-invertible functions

  1. I like Katie’s functions. They are not the ordinary ones. As for the rule for the second one, maybe, playing next time, you can try to discuss with her the fact that it is possible to create different rules for the same function (describe it in more than one way).


  2. These home exercises are amazing.
    Just another one для Кати:
    До -> до, ре -> си, ми -> ля. 🙂


  3. Christopher says:

    Wow. You touch on some lovely and deep mathematics in this brief conversation. Just wow. More to say; no time to say it right now. Thanks for writing this up!


  4. Pingback: Kid in the Machine | Musings of a Mathematical Mom

  5. Pingback: Functions in Kindergarten – A favorite | Musings of a Mathematical Mom

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