Two problems from a Christopher Danielson paper

A discussion on Twitter about yesterday’s project:

A really neat conjecture shared by Tracy Johnston Zager

led to this paper from Christopher Danielson getting posted in a thread (the direct link to the paper is in the bottom tweet):

I’m terrible at evaluating the difficulty that kids will have with various math problems, but the two problems at the beginning of the paper looked interesting so I thought I’d give them a try.

The first problem is about determining the largest rectangle (out of 5 choices) with a fixed perimeter, and the second problem asks you to find the perimeter of a region with an unusual shape. Here are each kid’s response to the questions. This was nice exercise – the kids had some pretty interesting thoughts:

Question 1

Older son:

Younger son:

Question 2

Older son:

Younger son:

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Comments

One Comment so far. Leave a comment below.
  1. ben,

    A bit of a tangent but in considering the numerical equivalent of the rectangle issue Arthur Benjamin started talking about recording a table of the various products for a fixed sum. It makes a good notice and wondering exercise to see the total pattern i.e. the presence of the squares. For example: Try a product of 20 and there are spin offs to why the maximum is 10 * 10 and for him to a neat trick for finds the product using the (x – n)(x + n) property.

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