The Border Problem

I love this example! It shows how important it is to allow students to find (and explain) their own ways of answering mathematical questions instead of always showing them how to do them.

What Did You Do In Math Today?

I have a new favourite problem!!  It looks like this:

Without counting one by one, determine how many shaded squares are in this 10×10 grid.


This is not a new problem.  I think it’s appeared in many books and possibly even textbooks throughout the years.  My first exposure to it was actually in Jo Boaler and Cathy Humphreys’ book “Connecting Mathematical Ideas”.  I loved watching the video of middle school students explaining the way they saw the problem and then eventually generalizing the methods for an nxn square, but I always wondered what it would look like in a high school class.  Luckily one of my good friends allowed me to come in and try this problem with her class.  It was awesome!  Like exactly what I was hoping it would be!  Maybe even a bit better!  Here’s how it went:

1.  We put the graphic above up for a…

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