Walking down the path to the surreal numbers part 2

I’ve got less time to write today because of a family trip, but the videos below show part 2 of our Family Math project about “checker stacks” and the surreal numbers.

The first part of the project is here:

Walking down the path to the surreal numbers

and we are following Jim Propp’s blog post about the surreal numbers which is here:

Jim Propp’s “The Life of Games”

The first thing we looked at today was “deep blue” stack. The surprise about this piece in the game of checker stacks is that its value appears to be positive infinity.

Next we quickly looked at the “deep red” piece and then looked at a blue + deep red stack whose value is pretty surprising. It was great to hear the ideas that the kids had about this stack.

Next we moved on to study the “deep purple” piece. This piece is pretty mysterious. I thought pretty hard about how to explain the value of this piece to the boys, but didn’t really come up with any good ideas. Instead we spent about 10 minutes exploring its value. That was a great conversation, but we never did quite get to the value of 2/3 that Propp gives in his blog. I’m ok with that outcome, though – I felt the conversation about the possible values was really great.

So, sorry for the quick write up of this 2nd project about the surreal numbers. I’m really happy to have seen Jim Propp’s blog and think there’s got to be a great way to use checker stacks for a neat math project for kids.

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The NY Times’s 8th grade math questions

Saw this tweet earlier today from Daina Taimina:

A direct link to the NYT article is here:

8th grade math questions in the NYT

I’m terrible at determining what sorts of questions will be difficult for kids, so I asked my older son (who is going into 6th grade) to talk through them. Here are his responses – the last two questions gave him a little difficulty.

(1) An algebra / arithmetic question – his solution is actually pretty clever

 

(2) A geometry / angle question – here he makes a little arithmetic mistake, but luckily the answer he finds after this mistake isn’t one of the choices.

 

(3) A question about similar triangles – this one also has a bit of arithmetic, but it all goes well.

 

(4) Some 3D geometry plus arithmetic with decimals. This one gives him trouble on two fronts. He uses an incorrect formula for the volume of the cone and has a bit of difficulty estimating the product (I don’t know if calculators were allowed on the exam or not, but we were just standing by the computer).

It was interesting to see the struggle estimating the product.

 

(5) More 3D geometry and arithmetic with decimals. Here he also had a little bit of trouble estimating the product he needed to compute. Luckily, though, the answers were far enough apart that even with that difficulty he was able to identify the likely answer.

I was surprised to see that this question – which seemed to me to be a little easier than the previous one – only had a 49% correct response rate compared to 70% on the question with the cone. Interestingly, right at this moment, those numbers are almost exactly reversed in the reader answers.