Properties of Exponents (Day 1 of 2)

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SWBAT simplify Algebraic expressions using properties of exponents

Big Idea

Students will use Cheerios to visualize 4 important properties of exponents (Product Rule, Quotient Rule, Power to a Power, and Power to a Quotient)


10 minutes

Today's class is the first lesson in the Polynomials Unit.  Students will formally review the properties of exponents, which was initially taught in middle school, during the next two classes.  I feel that it is important to spend the time in the beginning of this unit with this topic, as it lays the groundwork for the subsequent concepts we will study.

Students will complete the Do Now in 5 minutes. We will then review the answers as a whole group.

Next, a student will read the objective, "SWBAT simplify Algebraic expressions using properties of exponents". 

Before moving forward, I will ask a few students to define "exponent" in their own words.

Cheerios Lab

10 minutes

**Instructor Note: Each student will need two small dixie cups of cereal. I used regular cheerios to represent "x" and chocolate cheerios to represent "y" ***

A fun way to introduce the properties of exponents is through this short exploration that I completed with the class as a whole group. I will model the properties of exponents using Cheerios:

  • Multiplication: When Cheerios are placed side-by-side it is the same as multiplying them together. After you use the Cheerios to construct a question, you can simply count how many Cheerios are present to get your final answer. 
  • Division: A pair of Cheerios will cancel each other out if they are on top of each other.
  • Power to a Power: We will use the Cheerios to create a certain number of groups (denoted by the outside exponent) of what the number of Cheerios inside the parentheses (exponent that is inside the parenthesis)

This activity is a good introduction to the properties of exponents, as it allows students to visualize what is going on, and make a lasting connection to the properties work.

Guided Notes + Group Practice

30 minutes

Students will follow along using this Presentation and Guided Notes. Students will use the same guided notes today and tomorrow.

For each property, I will  begin by providing the class with four solved problems to write in the "Example" column in their guided notes. We will then work together as a class to derive a few sentences that explain the property for the "Rule" column. I will then ask a few student volunteers to come up to the front to use Cheerios to prove that our explanation is correct. Students will then draw a visual example in the "Why This Works" column. 

Slide Four: Product of Power Property, Quotient of Power Property

Slide Six: Power to a Power, Power to a Quotient

Independent Practice

20 minutes

Students will practice simplifying expressions with the properties of exponents using this Handout from the Kuta Software website.

The directions on the handout tell students that their answers should only contain positive exponents. I will tell them to disregard this part of the instructions, and that their answers can contain positive and negative exponents.

Students will begin working with negative exponents during our next class.


10 minutes

I will ask a few students to summarize what we learned in class today, and to describe the purpose of the Cheerios exploration in their own words. Students will then complete an Exit Card.