Comparing Rates: Fish Tanks and Beyond!

Mathematics Grades 7th Grade 3:12 Video
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Lesson Description

Learn how to compute and compare rates using real-world examples, like determining the best fish tank volume per fish!

Video Resource

Practice computing and comparing rates | Ratios, rates, and percentages | 6th grade | Khan Academy

Khan Academy

Duration: 3:12
Watch on YouTube

Key Concepts

  • Rate as a ratio
  • Comparing rates using division
  • Unit rate
  • Converting Improper Fractions to Mixed Numbers

Learning Objectives

  • Students will be able to compute rates given different quantities.
  • Students will be able to compare rates and order them from least to greatest.
  • Students will be able to interpret rates in a real-world context.

Educator Instructions

  • Introduction (5 mins)
    Begin by discussing real-life examples of rates, such as speed (miles per hour) or price per item. Ask students where they encounter rates in their daily lives. Briefly review the concept of ratios.
  • Video Viewing and Guided Practice (15 mins)
    Play the Khan Academy video "Practice computing and comparing rates | Ratios, rates, and percentages | 6th grade | Khan Academy." Pause the video at key points to explain the steps involved in calculating and comparing rates. Work through the fish tank problem together as a class. Encourage students to ask questions.
  • Independent Practice (15 mins)
    Provide students with similar problems involving comparing rates. Examples: Comparing the fuel efficiency of two cars (miles per gallon), determining the better buy between two differently sized products (price per ounce). Have students work independently or in small groups to solve these problems.
  • Class Discussion and Review (10 mins)
    Bring the class back together to discuss the solutions to the independent practice problems. Review the steps involved in calculating and comparing rates. Address any remaining questions or misconceptions.

Interactive Exercises

  • Rate Calculation Challenge
    Divide the class into teams. Present each team with a real-world scenario involving rates. The first team to correctly calculate and compare the rates wins a point. Continue with different scenarios until one team reaches a predetermined number of points.
  • Online Rate Comparison Tool
    Use an online tool (e.g., a rate calculator or a spreadsheet) to explore the impact of changing different variables on the overall rate. For example, investigate how changing the distance traveled affects the miles per gallon.

Discussion Questions

  • What are some other examples of rates that we use in everyday life?
  • Why is it important to have the same units when comparing rates?
  • How can converting to a unit rate help when comparing different rates?

Skills Developed

  • Calculating rates
  • Comparing and ordering rational numbers
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

What is a rate?

Correct Answer: A ratio that compares two quantities with different units.

Question 2:

Which of the following is an example of a rate?

Correct Answer: 5 miles per hour

Question 3:

To compare rates, what must you ensure?

Correct Answer: The units are the same or can be converted.

Question 4:

A store sells 3 shirts for $27. What is the rate per shirt?

Correct Answer: $9

Question 5:

Car A travels 200 miles on 10 gallons of gas. Car B travels 300 miles on 12 gallons of gas. Which car has better fuel efficiency?

Correct Answer: Car B

Question 6:

What is a unit rate?

Correct Answer: A rate where the denominator is one

Question 7:

Which tank has the *least* volume per fish if Tank A has 5 fish in 40 liters, Tank B has 12 fish in 100 liters, and Tank C has 23 fish in 180 liters?

Correct Answer: Tank C

Question 8:

What is the first step in computing the rates of various scenarios?

Correct Answer: Listing the given values

Question 9:

Which of the following is an improper fraction?

Correct Answer: 8/5

Question 10:

To convert a mixed number back to an improper fraction what must you do first?

Correct Answer: Multiply the whole number by the denominator, then add the numerator

Fill in the Blank Questions

Question 1:

A ______ is a ratio that compares two quantities with different units.

Correct Answer: rate

Question 2:

A rate where the denominator is one is called a _______ rate.

Correct Answer: unit

Question 3:

To find the unit rate, you ______ the numerator by the denominator.

Correct Answer: divide

Question 4:

If one store sells 5 apples for $3 and another sells 8 apples for $4, the store with the lower price _______ apple has the better deal.

Correct Answer: per

Question 5:

If you drive 150 miles in 3 hours, your average speed is _____ miles per hour.

Correct Answer: 50

Question 6:

To order the volume per fish from least to greatest, you must first _______ each rate.

Correct Answer: compute

Question 7:

Tank A has 5 fish in 40 liters. Therefore there are ____ liters per fish.

Correct Answer: 8

Question 8:

The remainder when using long division can be written as a ______.

Correct Answer: fraction

Question 9:

When comparing rates you must use the same ____.

Correct Answer: units

Question 10:

To convert an improper fraction to a mixed number you must use _____ ______.

Correct Answer: long division

Educational Standards

7.N.1:Read, write, represent, and compare rational numbers, expressed as integers, fractions, and decimals. Explain and apply the concept of absolute value. 7.A.2:Identify and justify proportional relationships using mathematical models and situations; solve problems involving proportional relationships and interpret results in the original context. 7.N.2:Calculate with rational numbers, with and without positive integer exponents, to model and solve mathematical problems.

Teaching Materials

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