Recently Christopher Danielson published an interesting shapes book online – “Which one doesn’t belong?”
As of January 26th, the 3rd version of it can be found via this tweet:
I decided to spend some time today having the kids talk through 5 of the 11 pages. It was an interesting and enjoyable exercise where I purposely played virtually no role at all. If an explanation contained an incorrect statement (about a right angle, say) I did not correct it. The goal was simply to hear their explanations.
I had my older son pick 5 numbers from 1 to 11 at random, and then I went through those slides in the book with each kid individually. Those 10 conversations are presented below. For each slide, the first video is my younger son and the second is my older son.
I think the videos speak for themselves, so I won’t add much comment except to say that both kids found talking about slide 8 to be the most difficult.
Overall my impression is that this was a good exercise to go through with both kids. Both of them stayed engaged for all five of the exercises and found several of the explanations of what didn’t belong to be pretty challenging. For my younger son (who is in 3rd grade), I think one important challenge was translating the mathematical ideas of similarity / difference he saw into words. For my older son (5th grade) the challenge was to provide explanations that didn’t rely on computation.
I would happily recommend spending time talking through the pages of this book to anyone working with elementary school kids. It would probably be interesting for older kids, too, though that’s a little outside of my experience just now.
Here are the conversations for slide 1 (plus the introduction to the exercise with each kid):
slide 3:
slide 7:
slide 8:
and finally slide 11:
Mike's Math Page 
Please tell us that going to 11 (end of discussion of slide 8 with your younger son) was a Spinal Tap reference!
Ha ha – it want but I laughed pretty hard when he said it
Another thing to do with the shapes book is to make your own pages. So far, I have 3 that have failed to appeal to Chris:
Numbers
Polar
Fractals?
Wait, Joshua! Those didn’t fail to appeal to me at all! I loved them and said so. Sorry if you felt left out of the fun—wasn’t my intention. I noticed them on wodb.ca, and am thankful to Mary Bourassa for creating a space to share everyone’s original creations.
I was just being impatient. I wrote this comment before you had time to respond.
In any case, congrats on the publishing contract and I hope the book gets into many, many, hands, both little and big.