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Rational Exponents Lesson Plan

Instructor: John Hamilton

John has tutored algebra and SAT Prep and has a B.A. degree with a major in psychology and a minor in mathematics from Christopher Newport University.

Utilize this helpful lesson plan to educate your students about the intricacies of rational exponents. They will watch a video, take a brief rational exponents quiz, and take part in an activity which will reinforce newly learned math concepts.

Learning Objectives

After this lesson, your in-class or homeschool students will be able to:

  • Identify the components of rational exponents and radical expressions
  • Juxtapose the terms ''rational number'' and ''rational exponent''
  • Show two different ways to write a rational exponent

Length

1 - 1.5 Hours

Materials

  • Copy of the transcript of the video lesson, which is titled Rational Exponents, along with the related lesson quiz, one per student.
  • Erasers
  • Index cards
  • Markers
  • Stopwatch or timer
  • Two printable worksheets, one containing 25 rational exponents, and the other containing 25 radical expressions. You will need to prepare these ahead of time and have enough copies so that each pair of students has one of each worksheet.
  • Whiteboard

Key Vocabulary

  • Index
  • Radical expression
  • Radical symbol
  • Radicand
  • Rational exponent
  • Rational number
  • Root number

Curriculum Standards

  • CCSS.Math.Content.6.NS.C.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

  • CCSS.Math.Content.6.NS.C.7

Understand ordering and absolute value of rational numbers.

Instructions

  • Let your students know they will be studying rational exponents.
  • Ask them if anyone has studied them previously, or can even give an example of a rational exponent.
  • Start the Rational Exponents video and pause for the first time at 0:31. Ask your students:
    • How would you define a rational number?
    • How would you define a rational expression?
    • Can you give three examples, using three different letters, of rational expressions?
  • Now restart the video and pause for the second time at 1:17. Ask them:
    • How would you write a radical symbol?
    • What is an index?
    • What is a radicand?
    • How would you rewrite a rational exponent, using two different methods?
  • Next restart the video and pause for a third time at 2:14. This time ask:
    • Can you convert a rational exponent to a radical expression?
    • Can you convert a radical expression back to a rational exponent?
    • Do you see how a rational exponent and a radical expression can mean the same thing?
    • What is an alternate name for the numerator in a radical expression?
    • What is an alternate name for the denominator in a radical expression?
  • Restart the video and pause for the final time at 2:59. Ask the students:
    • How does the presence of parentheses change the way we read rational exponents?
    • If the radical expression has no number in the index, which number do we assume is there?
  • Restart the video and have your students view the lesson summary.
  • Finally, go back and review the video in its entirety, and ask your students if they have any relevant comments or questions about rational exponents.
  • Have the students take this lesson quiz, so as to determine if they comprehend their newly acquired information on rational exponents.

Discussion Questions

  • Which do you think is more difficult, converting from rational exponents to radical expressions, or converting from radical expressions back to rational exponents?
  • How do you think famous mathematicians like Archimedes and Euclid were able to manage to ''invent'' rational exponents and radical expressions hundreds of years ago?
  • Who are some real-life scientists who might use rational exponents and radical expressions? (Examples might include NASA workers and particle accelerator employees.)

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