Unlocking Proportionality: Finding the Constant 'r'

Algebra 1 Grades High School 1:45 Video
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Lesson Description

Explore the concept of proportionality and learn how to determine the constant of proportionality (r) from tables of values. This lesson reinforces algebraic thinking and problem-solving skills.

Video Resource

Proportionality constant from table

Khan Academy

Duration: 1:45
Watch on YouTube

Key Concepts

  • Proportionality
  • Constant of Proportionality (r)
  • Linear Relationships
  • Tables of Values
  • Equation y = rx

Learning Objectives

  • Students will be able to define proportionality and the constant of proportionality.
  • Students will be able to identify the constant of proportionality (r) from a table of values.
  • Students will be able to apply the formula y = rx to solve for y, given x and r.
  • Students will be able to verify proportionality by checking if the ratio between y and x is constant.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of proportionality and the general form of the equation representing a proportional relationship (y = rx). Briefly discuss how 'r' relates x and y. Mention that the Khan Academy video will help visualize the topic.
  • Video Viewing (5 mins)
    Play the Khan Academy video 'Proportionality constant from table'. Instruct students to pay close attention to how the instructor identifies the constant of proportionality. Students should take notes during the video.
  • Guided Practice (10 mins)
    Work through the example from the video on the board, emphasizing the steps involved in finding the constant of proportionality. Reinforce the idea of testing the 'r' value with different x values from the table to see if they produce the correct y values.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing tables of values representing proportional relationships. Ask them to determine the constant of proportionality (r) for each table. Circulate to provide assistance as needed.
  • Review and Wrap-up (5 mins)
    Review the answers to the independent practice problems. Address any remaining questions or misconceptions. Summarize the key concepts of proportionality and the constant of proportionality.

Interactive Exercises

  • Table Completion
    Provide students with a table where some values of x and y are missing. Give them the constant of proportionality and ask them to fill in the missing values.
  • Proportionality Checker
    Provide students with several tables, some representing proportional relationships and some not. Ask them to identify which tables represent proportional relationships and explain their reasoning.

Discussion Questions

  • What does it mean for two quantities to be proportional?
  • How can you determine if a relationship is proportional from a table of values?
  • Why is the constant of proportionality important?
  • Can you think of real-world examples of proportional relationships?

Skills Developed

  • Problem-solving
  • Analytical Thinking
  • Pattern Recognition
  • Algebraic Reasoning

Multiple Choice Questions

Question 1:

If y = rx, what is 'r' called?

Correct Answer: Constant of Proportionality

Question 2:

In a proportional relationship, if x = 2 and y = 6, what is the constant of proportionality?

Correct Answer: 3

Question 3:

Which equation represents a proportional relationship?

Correct Answer: y = 2x

Question 4:

If r = 5 and x = 3, what is y?

Correct Answer: 15

Question 5:

In a table showing a proportional relationship, if x doubles, what happens to y?

Correct Answer: y doubles

Question 6:

If x=4 and y=8, and x=6 and y=12, what is r?

Correct Answer: 2

Question 7:

In the equation y = rx, x is the ____ variable.

Correct Answer: Independent

Question 8:

If y=10 and r=2, what is x?

Correct Answer: 5

Question 9:

Which of the following tables shows a proportional relationship?

Correct Answer: x:1, y:2; x:2, y:4; x:3, y:6

Question 10:

What should remain the same between all x and y values in order to be proportional?

Correct Answer: y/x

Fill in the Blank Questions

Question 1:

In the equation y = rx, 'r' represents the _______ of proportionality.

Correct Answer: constant

Question 2:

If y is proportional to x, then as x increases, y _______.

Correct Answer: increases

Question 3:

The formula for a proportional relationship is y = _______.

Correct Answer: rx

Question 4:

If x = 7 and r = 3, then y = _______.

Correct Answer: 21

Question 5:

In a table, you can find 'r' by dividing any y value by its corresponding _______ value.

Correct Answer: x

Question 6:

If y is proportional to x, that means y/x is always a _________.

Correct Answer: constant

Question 7:

When graphed, a proportional relationship forms a _______ line through the origin.

Correct Answer: straight

Question 8:

The x and y values will always have the same _____ in a proportional equation.

Correct Answer: ratio

Question 9:

If y = 10 and x = 5, then r = _____.

Correct Answer: 2

Question 10:

For the points (4, 8) and (8, 16) to be proportional, they both need to have a value of ____ for r.

Correct Answer: 2

Educational Standards

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. A1.F.3:Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems.

Teaching Materials

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