Math biographies for my kids

My older son came home from day 2 of 7th grade today. As we chatted about his day at school he told me that they wrote “math biographies” in math class today. I didn’t press him on what he talked about in his bio, instead I thought it would be fun to use the same idea for a short set of math videos tonight.

Here’s what my older son had to say about his “math biography”

Favorite topics he’s learned about so far: higher dimensions and 3d printing

Topic he’s excited to learn:  trigonometry (which he thinks is advanced geometry)

Fun sort of one-off project we’ve done:  Creating the 120-cell

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An unsolved problem he thinks is neat:  The Collatz Conjecture

Topic in math that he’s seen / learned but doesn’t believe:  1 + 2 + 3 + 4 + .  . . . = -1/12

Here’s the whole conversation:


Next up I asked my younger son (mostly) the same questions. Here’s what he had to say:

Favorite topics he’s learned about so far: fractals and binary numbers

Topic he’s excited to learn:  Calculus and logs, though he doesn’t know what those topics actually are 🙂  The topic that he knows a little bit about but wants to learn more of is imaginary numbers.

An unsolved problem that he thinks is interesting:  the Collatz conjecture.  I’m surprised that both boys mentioned this since we probably haven’t talked about it in over a year.  It is a fun problem for sure, though.

Something that you’ve learned but don’t necessarily believe:  The Koch snowflake has an infinite perimeter and a finite area – yes!!

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I really like asking kids about their math biographies – it makes for a really fun conversation!

John Golden’s visual pattern problem

We seem to always start our year off with a Fawn Nguyen-like problem. Today it happened by accident when I saw this visual pattern problem from John Golden:

We tried out the problem for a little after dinner math challenge tonight. Here’s what the boys thought initially – I was happy to see that they noticed that they could look at the pattern going backwards as well as forwards:


At the end of the last movie the boys wanted to make the base for the next tower. We did that with the camera off and then started looking at the pattern again.

I was a little surprised that they wanted to make this next piece rather than just talk about it, but making it did seem to help them see what the pattern was. In fact, their initial guess at the pattern was totally different from what I saw 🙂


So, although we didn’t get all the way to the formula for the nth step, we did find a way to determine (in theory) the number of blocks on any of the steps. I remember playing around with these difference tables in high school and being absolutely amazed – it is fun to be able to play around with them with the boys now.