After seeing a plug for them on twitter I bought the PCMI books. They arrived yesterday:

The first book I picked up was *Moving Things Around* since the shape on the cover of the book is (incredibly) the same shape we studied in a recent project.

One more look at the Hypercube

I found a neat problem in the beginning of the book that by another amazing coincidence was similar to a (totally different!) problem we looked at recently:

Revisiting Writing 1/3 in binary

We started by talking about the books and the fun shape on the cover:

Now we moved on to the problem. It goes something like this:

Consider the number 0.002002002…. in base 3. What is this number? How about in base 4,5,7, and n?

We started in base 3 and the boys had two pretty different ways to solve the problem!

Next we moved on to base 4:

Now we moved to the remaining questions of base 5, 7 and N. Unfortunately I got a phone call I had to take in the middle of this video, so I had to walk away while the solution to the “N” part was happening.

We finished up with the challenge problem -> What is 0.002002002…. in base 2?

This is a pretty neat challenge problem 🙂

Definitely a fun start to playing around with the PCMI books. Can’t wait to try out a few more problems with the boys!

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