Comparing Rates: Which is Faster?

Algebra 1 Grades High School 3:19 Video
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Lesson Description

This lesson explores how to represent and compare rates using linear equations and tables. Students will learn to determine which rate is greater by analyzing equations and calculating rates from given data.

Video Resource

Representing and comparing rates | Linear equations and functions | 8th grade | Khan Academy

Khan Academy

Duration: 3:19
Watch on YouTube

Key Concepts

  • Rate as a ratio
  • Comparing rates
  • Representing rates with equations
  • Proportionality

Learning Objectives

  • Calculate rates from given data (e.g., miles per hour, revolutions per minute).
  • Represent rates as linear equations (y = kx, where k is the rate).
  • Compare rates expressed in different forms (equations, tables, verbal descriptions).
  • Determine which rate is greater in a given scenario.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of rate as a ratio that compares two quantities with different units (e.g., miles per hour, dollars per item). Discuss real-world examples of rates and their importance.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Representing and comparing rates | Linear equations and functions | 8th grade | Khan Academy'. Instruct students to take notes on the examples provided in the video.
  • Guided Practice (15 mins)
    Work through similar examples as in the video, focusing on converting information into rate equations and then comparing. For instance, give data points in a table and ask students to calculate the rate and compare it to a given equation.
  • Independent Practice (15 mins)
    Provide a worksheet with various problems involving comparing rates in different formats. Include problems with real-world contexts. Encourage students to work independently and offer assistance as needed.
  • Wrap-up (5 mins)
    Summarize the key concepts and address any remaining questions. Preview the next lesson, which builds upon this concept.

Interactive Exercises

  • Rate Match Game
    Create a matching game where students match rates expressed in different forms (equations, tables, verbal descriptions) to their numerical value.
  • Rate Race
    Divide the class into teams and provide each team with a set of rate problems to solve. The first team to correctly solve all the problems wins.

Discussion Questions

  • How can you tell which rate is faster if one is in equation form and the other is in a table?
  • What real-world situations involve comparing rates?
  • Why is it important to understand rates and how to compare them?

Skills Developed

  • Calculating rates
  • Comparing rates
  • Converting between representations
  • Problem-solving
  • Analytical Skills

Multiple Choice Questions

Question 1:

Which of the following equations represents the fastest speed, where 'y' is distance in miles and 'x' is time in hours?

Correct Answer: y = 65x

Question 2:

A car travels 240 miles in 4 hours. What is its average speed in miles per hour?

Correct Answer: 60 mph

Question 3:

Which of the following represents a slower rate than 80 miles per hour?

Correct Answer: y = 75x

Question 4:

Company A produces 150 items in 3 hours. Company B produces 220 items in 4 hours. Which company produces items at a faster rate?

Correct Answer: Company B

Question 5:

If a train travels at a rate of 75 miles per hour, how far will it travel in 6 hours?

Correct Answer: 450 miles

Question 6:

Which equation shows the slowest rate? 'y' represents distance and 'x' represents time.

Correct Answer: y=25x

Question 7:

A machine makes 500 products in 5 hours. What is the rate of production per hour?

Correct Answer: 100 products/hour

Question 8:

Which car has a greater rate of speed? Car A travels 300 miles in 5 hours, and Car B travels 250 miles in 4 hours.

Correct Answer: Car B

Question 9:

A plane can fly 1200 miles in 3 hours. What is the average speed of the plane per hour?

Correct Answer: 600 miles per hour

Question 10:

If y=90x represents the rate of a train, what does the 90 represent?

Correct Answer: speed

Fill in the Blank Questions

Question 1:

The rate is calculated by dividing __________ by time.

Correct Answer: distance

Question 2:

In the equation y = kx, the variable 'k' represents the __________.

Correct Answer: rate

Question 3:

If a car travels 300 miles in 5 hours, its speed is __________ miles per hour.

Correct Answer: 60

Question 4:

A higher number of revolutions per minute (RPM) indicates a __________ rate of rotation.

Correct Answer: faster

Question 5:

To compare two rates, they must be expressed in the same __________.

Correct Answer: units

Question 6:

If y = 75x represents the rate of an object moving, then y is __________.

Correct Answer: distance

Question 7:

The rate of revolutions per minute is an example of a __________.

Correct Answer: ratio

Question 8:

The higher the miles per hour, the __________ the vehicle is moving.

Correct Answer: faster

Question 9:

A rate of speed is an example of a __________ relationship between distance and time.

Correct Answer: proportional

Question 10:

__________ allows us to understand the relationship between how things change in comparison to each other.

Correct Answer: rates

Educational Standards

A1.F.3.1:Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations. A1.A.4.1:Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret slope and the x- and y-intercepts of a line. A1.F.1.1:Distinguish between relations and functions.

Teaching Materials

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