Classroom Resource

Equivalent Expressions Using Exponents

Subject Area

Mathematics

Grade(s)

7, 8, 9, 10, 11, 12

Overview

Students will apply their critical thinking skills to learn about multiplication and division of exponents. This interactive exercise focuses on positive and negative exponents and combining exponents in an effort to help students recognize patterns and determine a rule.

This resource is part of the Math at the Core: Middle School collection.

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.14

Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions. [Grade 8, 3]

Unpacked Content

UP:MA19.7A.14

Vocabulary

  • Integer Exponent

Knowledge

Students know:
  • That whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced.

Skills

Students are able to:
  • Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents.

Understanding

Students understand that:
  • Just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
  • The exponent can be translated (visually. i.e. listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense.
Mathematics (2019) Grade(s): 8

MA19.8.3

Develop and apply properties of integer exponents to generate equivalent numerical and algebraic expressions.

Unpacked Content

UP:MA19.8.3

Vocabulary

  • Integer Exponent

Knowledge

Students know:
  • that whole number exponents indicate repeated multiplication of the base number and that these exponents indicate the actual number of factors being produced.

Skills

Students are able to:
  • Develop integer exponent operations in order to generate equivalent expressions through addition, multiplication, division and raising a power by another power with expressions containing integer exponents.

Understanding

Students understand that:
  • just as whole number exponents represent repeated multiplication, negative integer exponents represent repeated division by the base number.
  • The exponent can be translated (visually, listing out the factors) to represent the exact number of factors being repeated so that the use of integer exponent operations ("rules") can be proven/make sense.
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]

Unpacked Content

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.A1.1

Explain how the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for an additional notation for radicals using rational exponents.

Unpacked Content

UP:MA19.A1.1

Vocabulary

  • Exponent
  • Root
  • Rational Exponent
  • Radical -nth root
  • Rational exponent

Knowledge

Students know:
  • Techniques for applying the properties of exponents.

Skills

Students are able to:
  • Correctly perform the manipulations of rational exponents by analyzing and applying the properties of integer exponents.
  • Use mathematical reasoning and prior knowledge of integer exponents rules to develop rational exponent notation for radicals.

Understanding

Students understand that:
  • The properties of exponents apply to rational exponents as well as integer exponents.
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.

Unpacked Content

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.
Link to Resource
https://aptv.pbslearningmedia.org/resource/mgbh-math-ee-8exp/equivalent-express…

CR Resource Type

Interactive/Game

Resource Provider

PBS
Accessibility
License

License Type

Custom

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Comments or Notes

This resource is free for students and teachers to use. 

Approved Date

habradley
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