This is a unit on the "Properties of Exponents" that I created for my 9th Grade "Foundations of Math 1" class. (This class is designed for freshmen who are not quite ready for Math 1 and need remediation on 8th grade math objectives). The unit consists of 8 lessons, each containing a notes page and a practice page. I use the notes pages when presenting the new material to my class by using a document camera as I complete the problems and write in special notes to clarify the problems and emphasize the steps required to solve the problem. Following each notes page, there is a page of practice problems that students complete to practice the new skill being learned. As the learner progresses through this unit, the skills become more challenging and objectives are intertwined.
Lesson Titles are:
Lesson 1: Evaluating Powers - All exponents are positive at this point. The lesson focuses on positive and negative BASES and whether the the product will be a positive value or a negative value.
Lesson 2: Products of Powers - Students are guided through writing each power in expanded form and through this process, they discover that to multiply powers they should add the exponents.
Lesson 3: Power to a Power - Again students are guided through writing the factors in expanded form and subsequently discover that they should multiply exponents to raise a Power to a Power.
Lesson 4 - Quotients of Powers - This lesson follows the same pattern as lessons 2 and 3. Students discover that subtracting the exponents will produce the quotient of powers with the same base.
Lesson 5 - Zero and Negative Exponents - Students discover that all zero exponents result in a product of 1 and the negative exponents create a fraction. (Negative exponents are only in the numerator in this lesson)
Lesson 6 - Negative Exponents into Positive Exponents - Students are introduced to the concept that the negative exponent indicates INVERSE. They learn that a negative exponent in the numerator becomes positive when the power is moved to the denominator and that a negative exponent in the denominator becomes positive when the power is moved to the numerator.
Lesson 7 - Calculating with Negative Exponents - This lesson has students using the properties of exponents as they evaluate numerical problems using the Products of Powers, Quotient of Powers, and Power to a Power rules.
Lesson 8 - Applying Properties of Exponents - This lesson is an extension of Lesson 7 where students use the rules learned throughout the unit to evaluate algebraic terms.