Equations vs. Functions: What's the Difference?

Algebra 1 Grades High School 4:18 Video
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Lesson Description

Explore the difference between equations and functions, understanding their definitions, representations, and relationships.

Video Resource

Difference between equations and functions | Functions and their graphs | Algebra II | Khan Academy

Khan Academy

Duration: 4:18
Watch on YouTube

Key Concepts

  • Equation: A statement of equality between two expressions.
  • Function: A relationship between variables where each input has only one output.
  • Representations of Functions: Functions can be represented by equations, graphs, tables, and verbal descriptions.

Learning Objectives

  • Students will be able to differentiate between equations and functions.
  • Students will be able to identify different representations of functions (equations, graphs, etc.).
  • Students will be able to determine if an equation can define a function.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they already know about equations and functions. Briefly discuss their initial thoughts and any prior knowledge they have on the topic. Introduce the video from Khan Academy as a resource to clarify the differences between equations and functions.
  • Video Viewing (10 mins)
    Play the Khan Academy video "Difference between equations and functions | Functions and their graphs | Algebra II | Khan Academy". Instruct students to take notes on key definitions and examples presented in the video.
  • Guided Discussion (15 mins)
    After watching the video, facilitate a class discussion based on the discussion questions. Encourage students to share their understanding and any remaining questions they have.
  • Interactive Exercise (15 mins)
    Have students complete the interactive exercise where they classify given examples as equations, functions, or both. This can be done individually or in small groups.
  • Wrap-up (5 mins)
    Summarize the key points of the lesson, emphasizing the difference between equations and functions, and the various ways functions can be represented. Assign the quizzes for assessment.

Interactive Exercises

  • Classifying Examples
    Provide students with a list of examples (e.g., x + y = 5, y = x^2, x = 3, input day of the week -> output meal). Have them classify each example as an equation, a function, or both. For each classification, students should provide a brief justification.

Discussion Questions

  • What is the key difference between an equation and a function according to the video?
  • Can you give an example of an equation that is not a function? Why is it not a function?
  • Can you give an example of a function? How do you know it is a function?
  • How can an equation be used to define a function?
  • What are some different ways to represent a function besides an equation?

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Conceptual Understanding

Multiple Choice Questions

Question 1:

Which of the following is the BEST description of an equation?

Correct Answer: A statement of equality between two expressions.

Question 2:

Which of the following is the BEST description of a function?

Correct Answer: A relationship where each input has only one output.

Question 3:

Which of the following is an example of an equation that is NOT typically a function?

Correct Answer: x = 5

Question 4:

Which of the following can represent a function?

Correct Answer: All of the above

Question 5:

In a function, what is the term for the set of all possible input values?

Correct Answer: Domain

Question 6:

In a function, what is the term for the set of all possible output values?

Correct Answer: Range

Question 7:

Which of the following is NOT a way to define a function?

Correct Answer: List of numbers

Question 8:

If a function is defined as "input a number and output that number plus 3", what is the output if the input is 5?

Correct Answer: 8

Question 9:

Which of the following equations represents a linear function?

Correct Answer: y = 3x + 2

Question 10:

What is a critical characteristic of a function?

Correct Answer: Each input has only one output

Fill in the Blank Questions

Question 1:

An ________ is a statement that two expressions are equal.

Correct Answer: equation

Question 2:

A ________ is a relationship between inputs and outputs, where each input has only one output.

Correct Answer: function

Question 3:

The set of all possible input values for a function is called the ________.

Correct Answer: domain

Question 4:

The set of all possible output values for a function is called the ________.

Correct Answer: range

Question 5:

Functions can be represented by equations, ________, tables, and verbal descriptions.

Correct Answer: graphs

Question 6:

The equation y = 5x - 2 can be used to ________ a function.

Correct Answer: define

Question 7:

In a function, each input is associated with only ________ output.

Correct Answer: one

Question 8:

An example of an equation that might not represent a function is x = ________.

Correct Answer: 3

Question 9:

If a function's input is the day of the week, and the output is a corresponding meal, this is a ________ description of the function.

Correct Answer: verbal

Question 10:

A function is a description of how quantities ________ together.

Correct Answer: vary

Educational Standards

A1.F.1.1:Distinguish between relations and functions. A1.F.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations. A1.A.3.1:Solve equations involving several variables for one variable in terms of the others.

Teaching Materials

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