Rational and Radical Exponents

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

This learning activity is intended to be used as an introductory lesson on rational exponents and solving exponential equations.  It can also be used as a bellringer for a day two lesson on rational exponents.

Phase

Before/Engage
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents. [Algebra I with Probability, 2]

UP:MA19.8A.2

Vocabulary

  • Radical
  • Rational exponent
  • Expression

Knowledge

Students know:
  • the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand. For example, 51/2=5 and 163/2=(161/2)3= (16)3=43=64.
  • The root index of the radical is the denominator of the rational exponent and the exponent of the radicand is the numerator of the rational exponent. For example, 4103= 103/4.

Skills

Students are able to:
  • Rewrite expressions from radical representations to rational exponents and vice versa.

Understanding

Students understand:
  • The meaning of rational exponents and how to convert between them and radical representations.
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.2

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

UP:MA19.A1.20

Vocabulary

  • Half
  • planes
  • System of linear inequalities.
  • Boundaries
  • Closed half-plane
  • Open half-plane

Knowledge

Students know:
  • When to include and exclude the boundary of linear inequalities.
  • Techniques to graph the boundaries of linear inequalities.
  • Methods to find solution regions of a linear inequality and systems of linear inequalities.

Skills

Students are able to:
  • Accurately graph a linear inequality and identify values that make the inequality true (solutions).
  • Find the intersection of multiple linear inequalities to solve a system.

Understanding

Students understand that:
  • Solutions to a linear inequality result in the graph of a half-plane.
  • Solutions to a system of linear inequalities are the intersection of the solutions of each inequality in the system.

Learning Objectives

The students will be able to use the properties of exponents to rewrite expressions involving radicals and rational exponents.

Activity Details

This activity will be used to introduce a lesson on radicals and rational exponents.  This would be a great day two bellringer to solidify the concepts that were previously taught.  The properties on the worksheet act as a reminder from the previous day's lesson and can be helpful as students complete the problems. 

1.) The teacher will need to display a copy of the worksheet on the board and pass out one copy for each of the students. 

2.) The teacher should verbally review each property on the worksheet aloud with the students. 

3.) Once the teacher has reviewed the different properties the teacher should have the students complete the sections.

4.) In the challenge section, the teacher should instruct the students to work together to complete the problems. 

 

Assessment Strategies

The worksheet will be used as the assessment to check for student understanding. 

Variation Tips

This worksheet could also be used as an after-activity.  It could be divided up with page one being a bellringer and page two being an exit ticket.

Background / Preparation

The teacher would need to make copies of the worksheet for each student.

Due to the length of the worksheet, the teacher could allow extra time for completion or allow students to work with a partner. 

Learning Activity (Before)

Rational and Radical Exponents

Learning Activity (During)

Rational Exponents and Solving Exponential Equations

Learning Activity (After)

Rational Exponents
Properties of Exponents Worksheet from Education.com
https://www.education.com/download/worksheet/175257/properties-of-exponents.pd

Approved Date

Owner (Author)

kristylacks
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