Rational Exponents

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

In this learning activity, students will practice using the properties of exponents to rewrite expressions involving radicals and rational exponents. linear expressions using the properties of operations.  This learning activity should be used after a lesson on rational exponents and solving exponential equations. It can be used as extra practice or as an assessment. 

Phase

After/Explain/Elaborate
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

  1. The teacher will display the worksheet whole-group and allow students enough time to complete problems 1 through 8 on the worksheet.
  2. After the students have had ample time to work on problems 1 through 8 on the worksheet, the teacher will review the answers.
  3. Once the students have proven they understand how to use the properties of exponents to rewrite expressions involving radicals and rational exponents, the teacher will tell the students to complete problems 9 through 22 individually for an assessment grade. The teacher will remind students to simplify. The teacher will also remind students that their answer should contain only positive exponents with no fractional exponents in the denominator.
  4. At the end of class, the teacher will bring the students back to a whole-group discussion to determine any problems they faced while completing the worksheet. 

Assessment Strategies

The students' worksheets would be graded to assess students' understanding of using the properties of exponents to rewrite expressions involving radicals and rational exponents.

Variation Tips

The worksheet could be started in class and finished for homework.

The teacher could also work on the even-numbered problems with the students in class and have them do the odd-numbered problems for homework.

Background / Preparation

The teacher will need to secure a way to display the worksheet whole group.

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

Learning Activity (Before)

Rational and Radical Exponents

Learning Activity (During)

Rational Exponents and Solving Exponential Equations

Learning Activity (After)

Rational Exponents
Simplifying Rational Exponents from Kuta Software
https://cdn.kutasoftware.com/Worksheets/Alg2/Simplifying%20Rational%20Exponents…

Approved Date

Owner (Author)

kristylacks
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