Exponents and Scientific Notation

Lesson 3

Math

Unit 1

8th Grade

Lesson 3 of 15

Objective


Investigate patterns of exponents with positive/negative bases and even/odd bases.

Common Core Standards


Core Standards

  • 8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.

Foundational Standards

  • 6.EE.A.1
  • 7.NS.A.2

Criteria for Success


  1. Understand that an odd number raised to any non-negative power is always odd.
  2. Understand that an even number raised to any positive power is always even.
  3. Understand that a negative number raised to any odd power is always negative, and raised to an even power is always positive.
  4. Understand that a positive number raised to any power is always positive.
  5. Look for and make use of structure that exists with exponentials in order to make general conclusions (MP.7).
  6. Look for and make sense of repeated reasoning with exponentials in order to make general conclusions (MP.8).

Tips for Teachers


  • Though this lesson is centered on exponents, this is also an opportunity to have students investigate other patterns and structures in the number system with the objective of having students justify their reasoning, convince others, and defend their conclusions (MP.3).
  • This is the last of three review lessons approaching 8.EE.1 intended to cover concepts and skills involving exponents. This lesson can be extended or condensed as appropriate for your students.
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Anchor Problems

25-30 minutes


Problem 1

Consider the statement: A negative number raised to any whole number power will be negative.

Is this statement always, sometimes, or never true? Justify your response.

Guiding Questions

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Student Response

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Problem 2

Consider the statement: An odd number raised to an odd power will be odd.

Is this statement always, sometimes, or never true? Justify your response.

Guiding Questions

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Student Response

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Problem 3

What is the last digit of $${7^{2023}}$$? Explain.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Seven to the What?!?Note, the exponent has been changed to reflect the current year

Seven to the What?!?, accessed on Aug. 3, 2017, 3:53 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Which statements below are true? Select all that apply. Choose one answer you said was true and justify your response. 

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Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include always, sometimes, never problems similar to Anchor Problems 1 & 2 involving exponent and other number sense reasoning; ensure students provide adequate justifications.
  • Include problems with patterns of powers of 10.
  • Include any other review with exponent concepts and skills.
  • Challenge: Determine if there are values for $$a$$ and $$b$$ that would make this inequality true: $$(-a)^b\leq-(a)^b$$

Next

Investigate exponent patterns to write equivalent expressions.

Lesson 4
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Review of Exponents

Topic B: Properties of Exponents

Topic C: Scientific Notation

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