Unlocking Proportional Relationships: Sanitizing Solutions and Beyond!

Algebra 1 Grades High School 4:03 Video
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Lesson Description

Explore proportional relationships using a real-world example of sanitizing solutions. Learn to identify and apply the constant of proportionality to solve problems.

Video Resource

Proportional relationships example

Khan Academy

Duration: 4:03
Watch on YouTube

Key Concepts

  • Proportional Relationship
  • Constant of Proportionality
  • Linear Equations
  • Ratios and Rates

Learning Objectives

  • Identify proportional relationships in real-world scenarios.
  • Calculate the constant of proportionality.
  • Apply the constant of proportionality to find equivalent ratios and solve problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by introducing the concept of proportional relationships. Ask students for examples they encounter in daily life (e.g., recipes, scaling maps). Briefly explain that this lesson will use a Khan Academy video to explore this concept further.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Proportional relationships example'. Instruct students to take notes on the key steps the instructor uses to solve the problem.
  • Guided Practice (15 mins)
    Work through the example problem from the video together as a class. Emphasize the steps involved in finding the constant of proportionality and using it to check if different combinations are proportional. Create a table similar to the video. Encourage students to ask questions and participate actively.
  • Independent Practice (15 mins)
    Provide students with similar problems to solve independently. For example: * If Sarah uses 2 cups of flour for every 1 cup of sugar in a recipe, which of the following combinations are proportional: (4 cups flour, 2 cups sugar), (6 cups flour, 4 cups sugar), (5 cups flour, 2.5 cups sugar), (3 cups flour, 1.5 cups sugar) ? Circulate to provide assistance and answer questions. Review the answers as a class.
  • Wrap Up (3 mins)
    Summarize the key concepts covered in the lesson. Reiterate the importance of understanding proportional relationships and the constant of proportionality. Preview the quiz and fill in the blank activities.

Interactive Exercises

  • Ratio Match
    Provide students with a set of cards with different ratios. Ask them to match the cards that represent proportional relationships.
  • Proportion Wheel
    Using a digital or physical wheel, provide one value in a proportion (e.g., bleach amount) and have students calculate the corresponding value (e.g., water amount) based on the constant of proportionality.

Discussion Questions

  • What are some other real-world examples of proportional relationships?
  • How can you determine if a relationship is proportional from a table of values?
  • How does the constant of proportionality relate to the slope of a line?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Mathematical reasoning

Multiple Choice Questions

Question 1:

What is the constant of proportionality in a proportional relationship?

Correct Answer: The ratio between two quantities that remains constant.

Question 2:

If y is proportional to x and y = 6 when x = 2, what is the constant of proportionality?

Correct Answer: 3

Question 3:

Which of the following equations represents a proportional relationship?

Correct Answer: y = 5x

Question 4:

If the ratio of apples to oranges is 3:4, and there are 12 apples, how many oranges are there?

Correct Answer: 16

Question 5:

In a proportional relationship, if one quantity doubles, what happens to the other quantity?

Correct Answer: It doubles.

Question 6:

What is another term for constant of proportionality?

Correct Answer: Slope

Question 7:

If y = kx represents a proportional relationship, what does 'k' represent?

Correct Answer: The constant of proportionality

Question 8:

Which table shows a proportional relationship between x and y?

Correct Answer: x | 1 | 2 | 3 y | 3 | 6 | 9

Question 9:

A map has a scale of 1 inch = 50 miles. If two cities are 3 inches apart on the map, what is the actual distance between them?

Correct Answer: 150 miles

Question 10:

Which of the following is NOT a proportional relationship?

Correct Answer: Area of a square and the length of one of its sides.

Fill in the Blank Questions

Question 1:

In a proportional relationship, the ratio between two quantities is always a _________.

Correct Answer: constant

Question 2:

The equation y = kx represents a proportional relationship, where k is the __________.

Correct Answer: constant of proportionality

Question 3:

If y is directly proportional to x, and x doubles, then y __________.

Correct Answer: doubles

Question 4:

If the constant of proportionality is 4, then y = __________ x.

Correct Answer: 4

Question 5:

A graph of a proportional relationship is a straight line that passes through the ___________.

Correct Answer: origin

Question 6:

The bleach to water ration in the video is an example of a ___________ relationship.

Correct Answer: proportional

Question 7:

If 2 pens cost $3, then 6 pens will cost $__________.

Correct Answer: 9

Question 8:

The constant of proportionality can also be called the ___________ of the line.

Correct Answer: slope

Question 9:

In a recipe, if you need to triple the ingredients, that is an example of a __________ relationship.

Correct Answer: proportional

Question 10:

In direct variation or proportional relationships, as one variable increases the other ___________

Correct Answer: increases

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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