Rational Exponents and Solving Exponential Equations

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

8, 9, 10, 11, 12

Overview

This learning activity will be used during the lesson on rational exponents and solving exponential equations.  It is a video that consists of a lesson on rational exponents and exponential equations.

Phase

During/Explore/Explain
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 during a lesson on radicals and rational exponents.  This would be a day two activity to solidify the concepts that were previously taught.  The students would need to make sure that they were taking good notes during the video.  The teacher would take the notes for a grade and then return them to the students so that they would have them to study.  As the video is playing the teacher would need to stop the video during the problems so that the teacher can get feedback from the students to make sure that they are understanding the material.

  1. At approximately 2:58 the teacher should stop the video and go over the table making sure that the students understand how the speaker is getting her answers. Resume video once all questions are answered.
  2. At approximately 5:09 the teacher should stop the video and go over any questions that the students may have on the previous problems.  Resume video once all questions are answered.
  3. At approximately 6:12 the teacher should stop the video and go over any questions that the students may have on the previous problems.  Resume video once all questions are answered.
  4. At approximately 9:16 the teacher should stop the video and go over any questions that the students may have on the previous problems.  Resume video once all questions are answered.
  5. At approximately 13:14 the teacher should stop the video and go over any questions that the students may have on the previous problems. At this point there will be some video left, however, for this lesson, I would stop the video here and move on to the after activity.
  6. Once the video is over the class would then play the game, "Did you know?".  Each student would go around the room saying, "did you know..." and then following it with an observation from the video.  The goal of the game is to get to the last person without repeating something already said.
  7.  After the game, the teacher would hand out the exit ticket, Rational Exponents. The exit ticket would be graded.

Assessment Strategies

The student's notes would be examined to make sure the students had good material to study.

The teacher would assess the students during the video when she chose to stop the video and go over the problems.  The teacher would also need to encourage proper listening and interaction by walking around the room and monitoring student behavior.

The teacher would also assess students' knowledge of the game and the exit ticket. 

Variation Tips

The video could be used as a stand-alone lesson when the teacher has a substitute or wants to try a flipped classroom lesson.

Background / Preparation

The teacher would need to watch the video before class to determine where to stop the video and decide what questions to use and what problems to model.

Learning Activity (Before)

Rational and Radical Exponents

Learning Activity (During)

Rational Exponents and Solving Exponential Equations

Learning Activity (After)

Rational Exponents
Rational Exponents and Solving Exponential Equations Video
https://www.youtube.com/watch?v=E8OiTzPNlrM&t=854s

Approved Date

Owner (Author)

kristylacks
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