Properties of Exponents and Square Roots

Objective: Simplify algebraic expressions involving powers and square roots.


Materials:
- Flip video cameras (ideally, one for every 3 students)
- blank white paper
- scissors
- markers or colored pencils
- optional: tripod


Background: Students should have knowledge of the properties before making the videos. This lesson is meant to be a review of the properties, but could be adapted in multiple ways.


Activities:

- Show a Common Craft "In Plain English" video, such as "Borrowing Money in Plain English" or "Zombies in Plain English" (available from http://www.commoncraft.com/ or http://www.youtube.com/). Explain that students will be making a video in this same style to review the properties of exponents and square roots.

- Divide students into groups of three. Assign a property to each group. The properties I used are listed below. Note that this lesson would work for a review of any set of mathematical properties (such as the commutative, associative, and distributive properties).
- Product of Powers: b^m * b^n = b^(m+n)
- Power of a Power: (b^m)^n = b^(m*n)
- Power of a Product: (ab)^n = a^n b^n
- Negative Exponent: b^-n = 1/b^n
- Quotient of Powers: b^m/b^n = b^(m - n)
- Power of a Quotient: (a/b)^n = a^n/b^n
- Product of Square Roots: SQRT(a) * SQRT(b) = SQRT(ab)
- Quotient of Square Roots: SQRT(a) / SQRT(b) = SQRT (a/b)

- Explain that students will be making a Common Craft style video explaining their assigned property. They should keep the WWE acronym in mind as they prepare their video:
- What? - What is the property?
- Why? - Why is the property true? or Why would we use this property?
- Example - Give an example of how the property is used.

- Students should work in their groups to write a script and prepare papers and props for the videos. You can assign this part as homework if you are short on class time. Each group should practice the video multiple times before using the Flip camera, especially if groups will be sharing cameras.

- Each group member should choose one of the following roles:
- Narrator
- Paper/Prop Mover
- Camera Operator

- When students have thoroughly written a script, prepared and practiced their video (about one class period), they should use the Flip camera to record their video, Common Craft style. Videos should be about 30-60 seconds long. If groups are sharing cameras, you can require students to do only one take - mistakes are ok!

- After all groups have recorded, collect the videos and show them to the class as a means of reviewing the properties. I also post the videos to my class web site so students can review at home and show their families their hard work!


Evaluation/Assessment: Students can be evaluated on how well they collaborated on the project, how thoroughly they prepared before shooting the video, and the quality and accuracy of their explanations and examples.