I've been working on radicals with my Algebra I class. They've been having a very difficult time with the idea that something squared is a number times itself. So if I ask them what the square root of 25 is, they give me a totally blank look.
Out of desperation, I drew a square on the board, labeled the area inside 16 square units and labeled each side as 4. I told them the number under the square root is the area found inside a square. We know the area is length times width or side times side. The square root sign is asking for the length of any side. Because its a square, the sides are all the same length and you only have to write down one side.
This is the first time I've taught it this way but it made it easier for students to visualize and find the square root of a number. For cubed roots, I drew a 3 dimensional cube with a volume of 8 and showed how the height, width, and length were each 2 inches. I only needed the 2 written once because each length was the same.
It actually worked quite well. My students often drew a small square on the side of the page, filled in the area, and found the side length much faster than teaching it the traditional way. So when I moved to simplifying I talked about perfect squares (relating them to area again) and a square that is not perfect.
I have a story I use to help students remember which value is taken out. There are two sisters who share a house. One sister is perfect. Her hair is always done perfectly, her make up is perfect, even her clothing is just perfect. The other sister is comfortable, doesn't worry about looking perfect all the time. The perfect sister goes out to the front porch to flirt with the boys while the not so perfect sister stays inside to read a book or play a game.
If a student asks me if they got the problem right, I simply ask "Did the perfect sister leave the house?". They can easily figure out if they did it right.
Now the question I have for everyone. "Do you think its fine to teach square roots this way?" Thanks in advance for your input.