Unlocking Proportional Relationships: Finding the Constant of Proportionality

Algebra 1 Grades High School 2:34 Video
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Lesson Description

Learn how to identify the constant of proportionality from tables, determining if a relationship is proportional and finding the k value.

Video Resource

Constant of proportionality from tables | 7th grade | Khan Academy

Khan Academy

Duration: 2:34
Watch on YouTube

Key Concepts

  • Constant of Proportionality (k)
  • Proportional Relationships
  • Identifying Proportionality from Tables

Learning Objectives

  • Students will be able to identify if a table represents a proportional relationship.
  • Students will be able to calculate the constant of proportionality (k) from a table of values.
  • Students will be able to express a proportional relationship in the form y = kx.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a proportional relationship: two quantities are proportional if their ratio is constant. Introduce the term 'constant of proportionality' (k) and the equation y = kx.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Constant of proportionality from tables | 7th grade | Khan Academy'. Instruct students to take notes on the method for identifying the constant of proportionality.
  • Guided Practice (10 mins)
    Work through example problems similar to those in the video, demonstrating how to determine if a table represents a proportional relationship and how to calculate 'k'. Emphasize checking multiple (x, y) pairs to confirm proportionality.
  • Independent Practice (10 mins)
    Provide students with a set of tables. For each table, they should determine if it represents a proportional relationship. If it does, they should calculate and state the constant of proportionality.
  • Wrap-up & Discussion (3 mins)
    Summarize the key points: A proportional relationship exists when y/x is constant. That constant value is k, the constant of proportionality. Reiterate y = kx.

Interactive Exercises

  • Table Challenge
    Present a table with some values missing. Students must determine if it's possible to fill in the missing values so that the table represents a proportional relationship. If so, they must calculate the value of k and complete the table.

Discussion Questions

  • How can you tell if a relationship is proportional just by looking at a table?
  • What does the constant of proportionality represent in a real-world scenario?
  • Can a proportional relationship have a y-intercept other than zero? Why or why not?

Skills Developed

  • Analyzing data in tables
  • Identifying proportional relationships
  • Calculating the constant of proportionality
  • Applying the equation y=kx

Multiple Choice Questions

Question 1:

Which equation represents a proportional relationship?

Correct Answer: y = 5x

Question 2:

In a proportional relationship, if y = 12 when x = 3, what is the constant of proportionality?

Correct Answer: 4

Question 3:

Which table represents a proportional relationship?

Correct Answer: x: 1, 2, 3; y: 3, 6, 9

Question 4:

If y is proportional to x, and the constant of proportionality is 0.5, what is the value of y when x = 10?

Correct Answer: 5

Question 5:

In the equation y = kx, what does 'k' represent?

Correct Answer: The constant of proportionality

Question 6:

Which of the following must be true for a table to represent a proportional relationship?

Correct Answer: The ratio of y to x must be constant

Question 7:

A graph of a proportional relationship is a straight line that...

Correct Answer: Passes through the origin

Question 8:

If the constant of proportionality is 7, then...

Correct Answer: y = 7x

Question 9:

What is the constant of proportionality in the table: x:2, y:6; x:4, y:12; x:6, y:18

Correct Answer: 3

Question 10:

If y = kx and y increases when x increases, k is a ________ number.

Correct Answer: Positive

Fill in the Blank Questions

Question 1:

In a proportional relationship, the ratio of y to x is always a ________.

Correct Answer: constant

Question 2:

The equation for a proportional relationship is y = ________.

Correct Answer: kx

Question 3:

The constant of proportionality is also known as the ________.

Correct Answer: slope

Question 4:

If y is proportional to x, and when x = 5, y = 15, then k = ________.

Correct Answer: 3

Question 5:

In a proportional relationship, when x is zero, y is always ________.

Correct Answer: zero

Question 6:

A table represents a proportional relationship if the y/x values are always ________.

Correct Answer: equal

Question 7:

The constant 'k' in the equation y=kx helps find the change in _____.

Correct Answer: y

Question 8:

When the constant of proportionality is a fraction, the value of 'y' _________ as the value of 'x' increases.

Correct Answer: decreases

Question 9:

A relationship in which one quantity is a constant multiple of the other quantity is known as _________ relationship.

Correct Answer: proportional

Question 10:

The equation y = 4x represents a graph with constant of proportionality equal to _____

Correct Answer: 4

Educational Standards

A1.F.1:[Standard] Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems. A1.F.2:[Standard] Recognize and understand that families of functions are defined by their characteristics. A1.F.3:[Standard] Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems. A1.A.4:[Standard] Analyze real-world and mathematical problems involving linear equations.

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