Power Up with 1 and -1: Mastering Exponents

Algebra 1 Grades High School 6:08 Video
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Lesson Description

Explore the fascinating world of exponents by focusing on the unique patterns that emerge when raising 1 and -1 to various powers. Learn how even and odd exponents affect the sign of the result.

Video Resource

Patterns in raising 1 and -1 to different powers | Pre-Algebra | Khan Academy

Khan Academy

Duration: 6:08
Watch on YouTube

Key Concepts

  • Exponents
  • Base Numbers
  • Even and Odd Powers
  • Sign Rules for Multiplication

Learning Objectives

  • Calculate the result of raising 1 to any power.
  • Determine the sign of the result when raising -1 to even and odd powers.
  • Apply the concept of even and odd powers to simplify exponential expressions involving -1.

Educator Instructions

  • Introduction (5 mins)
    Begin by briefly reviewing the definition of exponents. Pose the question: What happens when you raise 1 or -1 to different powers? This will pique students' curiosity and prepare them for the lesson.
  • Video Viewing and Note-Taking (10 mins)
    Play the Khan Academy video 'Patterns in raising 1 and -1 to different powers'. Instruct students to take notes on the key points, especially the explanations of why 1 to any power is 1, and the rules for -1 raised to even and odd powers.
  • Guided Practice (15 mins)
    Work through several examples together as a class. Start with simple examples like 1^5, (-1)^2, and (-1)^7. Gradually increase the complexity by including larger exponents like 1^100 and (-1)^25. Emphasize the reasoning behind each answer.
  • Independent Practice (15 mins)
    Assign practice problems for students to work on individually. These problems should include a mix of raising 1 and -1 to various powers. Circulate around the classroom to provide assistance and answer questions.
  • Wrap-up and Discussion (5 mins)
    Summarize the key concepts of the lesson. Answer any remaining questions and preview the next lesson on exponents.

Interactive Exercises

  • Exponent Sign Game
    Divide the class into two teams. Present an expression like (-1)^12. The first team to correctly identify whether the result is positive or negative (or zero in other cases) wins a point. This game reinforces the sign rules for exponents.
  • Online Practice on Khan Academy
    Have students work through the practice exercises on Khan Academy related to exponents and powers of 1 and -1. This provides personalized feedback and reinforces the concepts learned in the lesson.

Discussion Questions

  • Why is 1 raised to any power always equal to 1?
  • What is the difference between raising -1 to an even power versus an odd power?
  • Can you think of any real-world applications where understanding exponents with 1 and -1 might be useful?

Skills Developed

  • Understanding Exponents
  • Applying Mathematical Rules
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

What is 1 raised to the power of 25?

Correct Answer: 1

Question 2:

What is (-1) raised to the power of 10?

Correct Answer: 1

Question 3:

What is (-1) raised to the power of 15?

Correct Answer: -1

Question 4:

Which of the following expressions results in a positive value?

Correct Answer: (-1)^8

Question 5:

Which of the following expressions results in a negative value?

Correct Answer: (-1)^9

Question 6:

What happens when you raise 1 to any power?

Correct Answer: It always equals 1

Question 7:

What type of exponent will result in a negative number when the base is -1?

Correct Answer: Odd

Question 8:

Evaluate: 1^100 + (-1)^2

Correct Answer: 2

Question 9:

Evaluate: 1^50 - (-1)^3

Correct Answer: 2

Question 10:

Simplify: (-1)^10 * (-1)^3

Correct Answer: -1

Fill in the Blank Questions

Question 1:

1 raised to any power is always equal to ____.

Correct Answer: 1

Question 2:

(-1) raised to an even power is always ____.

Correct Answer: 1

Question 3:

(-1) raised to an odd power is always ____.

Correct Answer: -1

Question 4:

The exponent tells you how many times to multiply the ____ by itself.

Correct Answer: base

Question 5:

A negative number multiplied by a negative number results in a ____ number.

Correct Answer: positive

Question 6:

(-1)^20 + 1 = ____

Correct Answer: 2

Question 7:

If the exponent is zero, any number (except 0) to the power of zero is ____.

Correct Answer: 1

Question 8:

(-1)^0 - (-1)^1 = ____

Correct Answer: 2

Question 9:

When a number is raised to the first power, the answer is always ____.

Correct Answer: itself

Question 10:

(-1)^17 * (-1)^2 = ____

Correct Answer: 1

Educational Standards

A1.N.1:[Standard] Extend the understanding of exponents to include square roots and cube roots. A1.A.3:[Standard] Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

Teaching Materials

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