Exponents Demystified: Zero and First Powers

Algebra 1 Grades High School 5:07 Video
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Lesson Description

Explore the intriguing world of exponents, focusing on the properties of zero and first powers. Understand why any non-zero number raised to the power of zero equals one and how the first power relates to the original number.

Video Resource

Raising a number to the 0 and 1st power | Pre-Algebra | Khan Academy

Khan Academy

Duration: 5:07
Watch on YouTube

Key Concepts

  • Exponents as repeated multiplication
  • Zero power property (a^0 = 1, where a ≠ 0)
  • First power property (a^1 = a)

Learning Objectives

  • Students will be able to explain the concept of exponents as repeated multiplication.
  • Students will be able to state and apply the zero power property.
  • Students will be able to state and apply the first power property.
  • Students will be able to calculate expressions involving zero and first powers.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of exponents as repeated multiplication. Briefly discuss examples like 2^3 and 5^2. Introduce the idea that we're going to explore what happens when the exponent is 0 or 1.
  • Video Viewing (10 mins)
    Play the Khan Academy video "Raising a number to the 0 and 1st power". Instruct students to take notes on the video's explanation of why a number to the zero power is one and a number to the first power is itself.
  • Discussion and Explanation (10 mins)
    Lead a class discussion based on the video. Reinforce the key concepts using different examples. Emphasize the 'multiplying by 1' analogy presented in the video. Address any misconceptions or questions that arise.
  • Practice Problems (10 mins)
    Provide students with practice problems involving numbers raised to the zero and first powers. Include both positive and negative numbers. Also, use variables in the practice problems, e.g., x^0, y^1.
  • Wrap-up (5 mins)
    Summarize the key concepts of the lesson: any non-zero number to the zero power is 1, and any number to the first power is itself. Preview upcoming lessons related to exponents.

Interactive Exercises

  • Exponent Card Sort
    Create cards with expressions like 5^0, (-3)^0, 7^1, and (-2)^1. Students sort the cards into groups based on their value (1 or the base number).
  • Whiteboard Race
    Divide the class into teams. Present exponent problems (e.g., 10^0, (-4)^1, x^0, y^1) on the board. The first team to correctly solve the problem wins a point.

Discussion Questions

  • Why does it make sense that any non-zero number raised to the zero power equals one?
  • How does the concept of repeated multiplication help us understand exponents?
  • Can you think of a real-world scenario where the zero power property might be useful?
  • Why is a negative number to the zero power positive one, and not negative one?

Skills Developed

  • Applying mathematical properties
  • Problem-solving
  • Abstract reasoning

Multiple Choice Questions

Question 1:

What is the value of 9^0?

Correct Answer: 1

Question 2:

What is the value of (-5)^0?

Correct Answer: 1

Question 3:

What is the value of 12^1?

Correct Answer: 12

Question 4:

What is the value of (-8)^1?

Correct Answer: -8

Question 5:

Which of the following is always equal to 1 (assuming x is not 0)?

Correct Answer: x^0

Question 6:

Which of the following is always equal to the base (x)?

Correct Answer: x^1

Question 7:

Simplify: (4x)^0

Correct Answer: 1

Question 8:

Simplify: (7y)^1

Correct Answer: 7y

Question 9:

What is the value of (1/2)^0?

Correct Answer: 1

Question 10:

What is the value of (-3/4)^1?

Correct Answer: -3/4

Fill in the Blank Questions

Question 1:

Any non-zero number raised to the power of zero is equal to ____.

Correct Answer: 1

Question 2:

Any number raised to the first power is equal to ____.

Correct Answer: itself

Question 3:

5^0 = ____

Correct Answer: 1

Question 4:

10^1 = ____

Correct Answer: 10

Question 5:

(-2)^0 = ____

Correct Answer: 1

Question 6:

(-6)^1 = ____

Correct Answer: -6

Question 7:

x^0 = ____ (assuming x is not 0)

Correct Answer: 1

Question 8:

y^1 = ____

Correct Answer: y

Question 9:

(1/4)^0 = ____

Correct Answer: 1

Question 10:

(-5/8)^1 = ____

Correct Answer: -5/8

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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