Unlocking Proportional Relationships: A Deep Dive

Algebra 1 Grades High School 5:12 Video
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Lesson Description

Explore proportional relationships, constant of proportionality, and how to distinguish them from non-proportional relationships. Learn to identify, analyze, and apply these concepts in real-world scenarios.

Video Resource

Introduction to proportional relationships | 7th grade | Khan Academy

Khan Academy

Duration: 5:12
Watch on YouTube

Key Concepts

  • Proportional Relationships
  • Constant of Proportionality
  • Equivalent Ratios

Learning Objectives

  • Define and identify proportional relationships between two variables.
  • Calculate and interpret the constant of proportionality.
  • Differentiate between proportional and non-proportional relationships through examples and analysis.

Educator Instructions

  • Introduction (5 mins)
    Begin by introducing the concept of proportional relationships. Briefly explain that the video will cover identifying and understanding these relationships.
  • Video Viewing (10 mins)
    Play the Khan Academy video "Introduction to proportional relationships". Instruct students to take notes on key definitions and examples.
  • Guided Practice (15 mins)
    Work through examples similar to those in the video. Focus on identifying the ratio between variables and determining if the ratio remains constant. Include both proportional and non-proportional scenarios.
  • Independent Practice (15 mins)
    Provide students with practice problems to solve individually. Include a variety of scenarios, some presented in tables and others as word problems.
  • Wrap-up and Discussion (5 mins)
    Review key concepts and answer any remaining questions. Briefly discuss the importance of proportional relationships in real-world applications.

Interactive Exercises

  • Ratio Matching
    Present students with a set of ratios. Ask them to identify which ratios are equivalent, demonstrating their understanding of proportional relationships.
  • Real-World Scenarios
    Present various real-world scenarios (e.g., scaling a recipe, calculating unit price). Students determine if the scenarios represent proportional relationships and calculate the constant of proportionality if applicable.

Discussion Questions

  • How can you determine if a relationship between two variables is proportional?
  • What does the constant of proportionality represent in a real-world context?

Skills Developed

  • Problem-solving
  • Analytical thinking

Multiple Choice Questions

Question 1:

Which of the following relationships is proportional?

Correct Answer: y = 3x

Question 2:

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

Correct Answer: y doubles

Question 3:

What is the constant of proportionality in the equation y = 5x?

Correct Answer: 5

Question 4:

Which of the following tables represents a proportional relationship?

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

Question 5:

If the ratio of cats to dogs is 2:3, and there are 6 cats, how many dogs are there?

Correct Answer: 9

Question 6:

Which equation represents a proportional relationship?

Correct Answer: y = 4x

Question 7:

What is the constant of proportionality in the table where x = 2, y = 8 and x = 4, y = 16?

Correct Answer: 4

Question 8:

If y = kx, and y = 10 when x = 2, what is the value of k?

Correct Answer: 5

Question 9:

Which relationship is NOT proportional?

Correct Answer: Area of a square and the length of its side

Question 10:

If 5 apples cost $2.50, what is the cost of 12 apples, assuming a proportional relationship?

Correct Answer: $6.00

Fill in the Blank Questions

Question 1:

In a proportional relationship, the ratio between two variables remains ________.

Correct Answer: constant

Question 2:

The constant of _________ is the constant value that relates two variables in a proportional relationship.

Correct Answer: proportionality

Question 3:

If y is directly proportional to x, then y = kx, where k is the _________ of proportionality.

Correct Answer: constant

Question 4:

A relationship is not proportional if the ratio between the variables is _________.

Correct Answer: not constant

Question 5:

Equivalent _______ are essential for determining proportional relationships.

Correct Answer: ratios

Question 6:

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

Correct Answer: constant

Question 7:

If y = 6x, then y is said to be _________ proportional to x.

Correct Answer: directly

Question 8:

If one variable changes, and the other variable changes by a constant factor, the relationship is _________.

Correct Answer: proportional

Question 9:

The graph of a proportional relationship is a straight line that passes through the _________.

Correct Answer: origin

Question 10:

If the cost of 3 items is $9, then the cost of 7 items is $21, assuming a _________ relationship.

Correct Answer: proportional

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.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

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