We're Going on a Square Hunt: Simplifying Radicals

The class spent a week exploring the Pythagorean Theorem.  After creating a need with the students to handle square roots, on Friay we went over how to simplify them.  This topic has always been a bit dry and never quite landed with the students.  I have always talked about trying to find perfect squares and use those to break down the number.

The previous night was parent-teacher conferences.  I had some free time and the other math teacher and I started talking about the very topic of simplifying radicals.  He said he just went over it with one of his HS classes.  He used a factor tree approach and was very successful.  So this ignited a crazy idea for the lesson....

So as the class entered today I played this video of Michael Rosen acting out the book We're Going on a Bear Hunt.  The kids looked at me and screen like I was crazy.  They stared in a silent weirdness at the board for the first minute.  Then a crazier thing happened...they started singing along.  They all remember this book.  They started laughing and getting really into it.  It was really fun.

After the video, I showed them a couple slides.  I used images from the book but changed the words.

We're going on a square hunt.  

We're gonna catch a big one.

What a beautiful day.

Were not scared.

Oh no, a radical. 

A big, scary radical.

We can't square root it.

We can't go around it.

We have to go through it.

My mini-version of the story ended with a picture and the square root of 28.
We then broke down 28 by using a factor tree.  We ended up with Sqrt(2x2x7).

I then talked about how we are now starting the "square hunt."  We went looking for a length and a width that would make a square.  We found the 2x2 to make a square.  However, the 7 had no pair to make a square so we left it in the cave.  Then we rewrote it as....2 Sqrt(7).

We went through another example or too like this.  The students really caught on to the method. I am hoping that at some point some students find the shortcut during the method.  Even if they don't, this method easily gets exapnded to variables, cube roots, and higher.

Anyway it was a really fun day and the students learned something.  All in all a great day!