Princeton Review

 Lesson Plan: Introduction to Ratios 

Lesson Objectives

  • Define and identify ratios
  • Express ratios in different forms (a:b, a to b, a/b)
  • Understand the relationship between quantities in a ratio

FL BEST Standards

  • MA.6.NSO.3.1: Given a mathematical or real-world context, represent ratios as equivalent fractions, percentages or decimals.
  • MA.6.NSO.3.2: Given a mathematical or real-world context, determine a ratio that describes the relationship between two quantities.
  • MA.6.NSO.3.3: Extend previous understanding of multiplication and division to compute products and quotients of positive fractions by positive fractions, including mixed numbers, with procedural fluency.

Prerequisite Skills

  • Basic fraction knowledge
  • Understanding of division
  • Plotting points on a coordinate plane

Key Vocabulary

  • Ratio
  • Part-to-part
  • Part-to-whole
  • Comparison
  • Equivalent ratios

Warm-up Activity (5 minutes)

Display a group of 3 red balls and 2 yellow balls on the board or using a digital presentation. Use this companion slide show:

https://www.media4math.com/library/slideshow/simple-ratios

Ask students to:

  1. Calculate the fraction of red balls (3/5)
  2. Calculate the fraction of yellow balls (2/5)
  3. Discuss how they can compare the number of red balls to yellow balls

Guide the discussion towards the idea of comparing quantities directly (3 to 2) rather than using fractions. This will help introduce the concept of ratios as a different way to express relationships between quantities.

Teach (25 minutes)

Definitions

  • Ratio: A comparison between two quantities.
  • Part-to-part: A ratio that compares different parts of a whole to each other.
  • Part-to-whole: A ratio that compares one part of a whole to the entire whole.
  • Comparison: The act of evaluating two or more quantities to determine their relationship.
  • Equivalent ratios: Ratios that express the same relationship between quantities, even though the numbers may be different.

This slide show of definitions also provides examples of the terms:

https://www.media4math.com/library/slideshow/basic-ratio-definitions

Overview of Ratios

Use this slide show to go over the basic concepts around ratios:

https://www.media4math.com/library/slideshow/overview-ratios

Application of Ratios: Zoo Animals

Continue with an application of ratios by looking at this example of ratios of zoo animals from the San Diego Zoo, which is also summarized in this slide show:

https://www.media4math.com/library/slideshow/application-ratios-zoo-animals

Let's say the San Diego Zoo has:

  • 8 elephants
  • 24 monkeys
  • 12 zebras

Demonstrate different ways to express ratios using these animals:

  1. Elephants to monkeys:
    • 8:24 (simplified to 1:3)
    • 8 to 24
    • 8/24 (simplified to 1/3)
  2. Zebras to elephants:
    • 12:8 (simplified to 3:2)
    • 12 to 8
    • 12/8 (simplified to 3/2)
  3. Monkeys to zebras:
    • 24:12 (simplified to 2:1)
    • 24 to 12
    • 24/12 (simplified to 2/1)

Explain the difference between part-to-part ratios (like elephants to monkeys) and part-to-whole ratios (like monkeys to total animals).

Application of Equivalent Ratios: Vehicle Ratios

Now, introduce equivalent ratios using a different context: a parking lot with cars, motorcycles, and SUVs. You can use this slideshow or use the information below:

https://www.media4math.com/library/slideshow/applications-equivalent-ratios-vehicle-ratios 

Let's say a parking lot has:

  • 40 cars
  • 10 motorcycles
  • 20 SUVs

Use the ratio of cars to motorcycles to demonstrate equivalent ratios:

40:10 = 4:1 = 8:2 = 20:5

Show how to create and use ratio tables to find missing values. For example:

Cars48121620
Motorcycles12345

Explain that all these ratios are equivalent because they represent the same relationship between cars and motorcycles.

Finally, demonstrate how to plot ratio pairs on a coordinate plane using the car to motorcycle ratio (4,1), (8,2), (12,3), (16,4), (20,5).

Use this Desmos activity to demonstrate plotting ratio pairs:

https://www.desmos.com/calculator/tikwghztdz

Review (10 minutes)

Use this video to review the basics of ratios:

https://www.media4math.com/library/1789/asset-preview

Assess (5 minutes)

Administer a 10-question quiz to assess student understanding of the lesson objectives. The quiz should include questions on identifying ratios, expressing ratios in different forms, working with ratio tables, and plotting ratio pairs.

Quiz

  1. Express the ratio of cars to SUVs in the parking lot in three different forms.
    40 cars
    10 motorcycles
    20 SUVs

     
  2. What is the part-to-whole ratio of motorcycles to all vehicles in the parking lot?

     
  3. If the ratio of cars to motorcycles is 4:1, how many cars are there if there are 15 motorcycles?

     
  4. Complete the equivalent ratio table for zebras to elephants: 3:2, 6:4, __:6, 12:__

     
  5. Suppose you were plotting the ratio pair (12,3). Which is the x-coordinate? Which is the y-coordinate?

     
  6. What is the simplified form of the ratio 20:70 (SUVs to total vehicles)?

     
  7. If the ratio of cars to SUVs is 2:1, and there are 30 cars, how many SUVs are there?

     
  8. Express the ratio of motorcycles to total vehicles as a simplified fraction.

     
  9. If the ratio of cars to parking attendants is 20:1, how many attendants are there if there are 40 cars?

     
  10. Create a ratio table for the ratio of cars to motorcycles (4:1), with 4 equivalent ratios.

     

Answers

  1. 40:20, 40 to 20, 2/1
  2. 10:70 or 1:7
  3. 60 cars
  4. 9:6, 12:8
  5. x: 12, y: 3
  6. 2:7
  7. 15 SUVs
  8. 10/70 or 1/7
  9. 2 attendants
  10. 4:1, 8:2, 12:3, 16:4 (or any other correct equivalent ratios)

 

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