A Robert Talbert inspired conversation about Fibonacci numbers

Saw this interesting tweet from Robert Talbert yesterday:

The whole lesson is really interesting read. I decided to try out one small piece of it with the boys today – which Fibonacci numbers are even. The idea was to hear how they would approach “proving” that every third number in the list was even.

Here’s what my older son had to say – one interesting thing in this discussion was his thoughts about the proportion of the even and odd Fibonacci numbers. The confusing idea here is that both sets are infinite. I put off the details of that discussion for another day:

And here’s my younger son – he picks up on the two odds, one even pattern and has a pretty good explanation of why the pattern continues:

So, a fun little exercise. It is always interesting to me to hear the language that kids use to describe advanced mathematical ideas.

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