Exploring Exponents

Today grade 9s had a chance to build exponent models. We looked at representing x squared and x cubed using toothpicks and plasticine.

We noticed that anything with an exponent 2 is a square, and anything with an exponent 3 is a cube. We also noticed that the base of the exponent is representing the side length of the cube or square we make.

Since we were ready for a bigger challenge, I made up a spicy concept circle to try.

This one needed a bit more explaining. We looked at how x squared is a square, but also how it’s (x) times (x), how the length is x and width is x. This helped us look at (x)(y) as a rectangle with length x and width y. We introduced skewers as the y values.

We needed to talk about what an (x^2)(y) and an (x)(y^2) would be. We understood that they’d be 3 dimensional, but it took a while to realize that they’d be square based prisms, one with a toothpick square, and one with a skewer square.

We looked also at building (x+y)^2 which is something that challenges students in grade 10.

inside the (x+y)^2 we see an x^2 and a y^2 and also 2 rectangles that are both (xy). We can equate (x+y)^2=x^2+y^2+2xy.

Hopefully as we move forward with exponents and exponent laws we will have a sense of like terms, and simplifying, but also what happens if we multiply (x)(x)(x), and how we get x cubed. We’ll move from the concrete to the visual and abstract as the week progresses.