After going through the post I scrapped what I’d planned to do with the boys tonight and asked each of them to go through Kaplinsky’s three questions.

I’m doing a geometry course with my older son this year, so I expected that these questions would be accessible to him. My younger son hasn’t done geometry formally, but has been involved in lots of geometric discussions through stuff we do for the blog and also MOEMS problems and I hoped he had enough familiarity with rectangles to be able to make sense of the questions. I think his answers to questions #2 and #3 are extremely interesting.

The three questions are:

(1) What is the perimeter of a rectangle that measured 8 units by 4 units?

(2) List the dimensions of a rectangle with perimeter 24 units.

(3) Of all the rectangles with perimeter 24, which has the most area?

The ideas behind these questions are in the Kaplinsky’s blog post linked above, each kid’s answers are below. Older son first:

Question 1:

Question 2:

Question 3:

Next up – younger son:

Question 1:

Question 2:

Question 3:

It was interesting to me that both kids assumed that the rectangles would have integer sides, thus reducing the 3rd question to a problem about a finite number of rectangles. It was also interesting to me to see my younger son dive into the classic question – is a square a rectangle?

I don’t know enough to be able to figure out what level of fluency the boys show in their approach to the three questions, but I can say it was an interesting hear them talk through the problems. Fun little project after a 3 hour drive back from Boston. Thanks to Tracy Johnston Zager for sharing the post and to Robert Kaplinsky for the interesting read.

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