Unlocking Proportionality: Finding the Constant in Equations

Algebra 1 Grades High School 2:23 Video
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Lesson Description

Learn how to identify the constant of proportionality in linear equations. This lesson explores manipulating equations to the y = kx form and applying this knowledge to solve related problems.

Video Resource

Constant of proportionality from equation

Khan Academy

Duration: 2:23
Watch on YouTube

Key Concepts

  • Constant of Proportionality (k)
  • Linear Equations
  • Solving for a Variable

Learning Objectives

  • Students will be able to define the constant of proportionality.
  • Students will be able to manipulate linear equations to identify the constant of proportionality.
  • Students will be able to determine which equation has a specific constant of proportionality.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of proportional relationships and the general form y = kx, where 'k' is the constant of proportionality. Briefly discuss how this concept relates to real-world scenarios (e.g., distance traveled at a constant speed).
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Constant of proportionality from equation'. Instruct students to take notes on the examples provided in the video.
  • Guided Practice (10 mins)
    Work through similar examples as the video, demonstrating the steps to isolate 'y' and identify 'k'. Start with simple equations and gradually increase the complexity. For instance: 1. 2y = 6x 2. 5y = 15x 3. 3y = 9x
  • Independent Practice (10 mins)
    Provide students with practice problems to solve independently. Include problems where they need to solve for 'y' and problems where they identify the equation with a specific constant of proportionality.
  • Review and Wrap-up (3 mins)
    Review the key concepts and address any remaining questions. Briefly preview how this knowledge will be used in future lessons.

Interactive Exercises

  • Equation Transformation Game
    Divide students into groups and provide each group with a linear equation. The goal is to transform the equation to isolate 'y' in a race against other groups.
  • Constant of Proportionality Scavenger Hunt
    Create a list of equations and hide them around the classroom. Students find the equations, solve for 'y', and identify the constant of proportionality. The first student to correctly identify all the constants wins.

Discussion Questions

  • What does the constant of proportionality represent in a real-world scenario?
  • How does manipulating the equation help us find the constant of proportionality?
  • Can the constant of proportionality be negative? What would that mean?

Skills Developed

  • Algebraic Manipulation
  • Problem Solving
  • Analytical Thinking

Multiple Choice Questions

Question 1:

What is the constant of proportionality (k) in the equation y = kx?

Correct Answer: The value you multiply x by to get y

Question 2:

What is the constant of proportionality in the equation 2y = 10x?

Correct Answer: 5

Question 3:

Which equation has a constant of proportionality of 3?

Correct Answer: y = 3x

Question 4:

If y = 4x, what is the value of y when x = 2?

Correct Answer: 8

Question 5:

In the equation 5y = 15x, what operation is needed to isolate y?

Correct Answer: Divide by 5

Question 6:

Which of these equations does NOT represent a proportional relationship?

Correct Answer: y = x + 1

Question 7:

What is the constant of proportionality in the equation y = 0.5x?

Correct Answer: 0.5

Question 8:

If the constant of proportionality is 7, and x = 3, what is y?

Correct Answer: 21

Question 9:

The equation y = kx represents:

Correct Answer: A proportional relationship

Question 10:

In the equation 6y = 24x, what is the constant of proportionality?

Correct Answer: 4

Fill in the Blank Questions

Question 1:

The constant of proportionality is the value that you ________ x by to get y.

Correct Answer: multiply

Question 2:

In the equation y = kx, 'k' represents the _________ of proportionality.

Correct Answer: constant

Question 3:

To find the constant of proportionality in the equation 3y = 12x, divide both sides by ________.

Correct Answer: 3

Question 4:

If y = 6x, the constant of proportionality is ________.

Correct Answer: 6

Question 5:

An equation in the form y = kx represents a ________ relationship.

Correct Answer: proportional

Question 6:

If the constant of proportionality is 4, the equation is y = ________ x.

Correct Answer: 4

Question 7:

If y = 2x and x = 5, then y = ________.

Correct Answer: 10

Question 8:

The equation y = kx goes through the _________.

Correct Answer: origin

Question 9:

To isolate y in an equation, you perform ________ operations.

Correct Answer: inverse

Question 10:

If 4y = 16x, then y = _________x.

Correct Answer: 4

Educational Standards

A1.A.3.1:Solve equations involving several variables for one variable in terms of the others. A1.A.4:Analyze real-world and mathematical problems involving linear equations. A1.F.1:Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems.

Teaching Materials

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