Exponents and Exponential Functions

Lesson 4

Objective

Solve mathematical applications of exponential expressions.

Common Core Standards

Core Standards

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  • 8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.

Foundational Standards

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  • 6.EE.A.1

  • 7.EE.A.1

Criteria for Success

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  1. Use the properties of exponents in area and volume problems. 
  2. Simplify expressions using the properties of exponents.
  3. Change the base of exponential expressions to write equivalent expressions. 

Tips for Teachers

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This lesson reviews skills and concepts from 8.EE.1. Depending on the needs of your students, this lesson may be skipped or used in a different way. Students may need to spend time developing mastery with Criteria for Success #3, as this will be a useful tool when working with rational exponents in upcoming lessons. 

Anchor Problems

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Problem 1

The area of a triangle is represented by the expression $${12^4y}$$. The base of the triangle is represented by the expression $${3x^2}$$. Write an expression that represents the height, $$h$$.

Guiding Questions

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Problem 2

Find the value of $$n$$ that makes the equation true.

$$8^2\cdot4^n(2^2)^3=16^2\cdot(4^3)^5$$

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include geometric applications similar to Anchor Problem #1 and the Target Task
  • Include problems where students rewrite exponential expressions in the same base, similar to Anchor Problem #2
  • Include problems from the first few lessons of the unit as needed

Target Task

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Problem 1

A sphere has a radius that is given by the expression $${{1\over2}x^3}$$. What expression represents the volume of the sphere in terms of $${\pi}$$ and $$x$$

Problem 2

Determine the value of $$n$$ in the equation $$4\cdot16^n=4^{21}$$.