Unlocking Equivalent Ratios: A Flavorful Approach

Mathematics Grades 7th Grade 5:45 Video
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Lesson Description

Explore equivalent ratios using real-world examples like dipping sauces and paint mixtures. Learn how to identify and create equivalent ratios to solve problems.

Video Resource

Understanding equivalent ratios

Khan Academy

Duration: 5:45
Watch on YouTube

Key Concepts

  • Ratio
  • Equivalent Ratio
  • Proportional Reasoning

Learning Objectives

  • Define ratio and equivalent ratio.
  • Identify equivalent ratios using multiplication.
  • Apply equivalent ratios to solve real-world problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they know about ratios. Use relatable examples, like the ratio of students to teachers in the class. Introduce the concept of equivalent ratios and explain that they represent the same proportional relationship.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Understanding Equivalent Ratios'. Encourage students to take notes on key vocabulary and examples. Pause the video at key points to clarify any confusion.
  • Guided Practice (15 mins)
    Work through similar examples as in the video, such as recipes that need to be doubled or scaled down. Emphasize the importance of multiplying both parts of the ratio by the same factor to maintain equivalence. Use the examples to model how to set up ratios correctly and solve for missing quantities.
  • Independent Practice (15 mins)
    Provide students with practice problems where they need to determine if ratios are equivalent, create equivalent ratios, and solve problems using equivalent ratios. Problems can involve scenarios with different units to enhance complexity.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and learning objectives. Administer a short quiz (multiple choice and/or fill-in-the-blank) to assess student understanding. Preview the next lesson on proportions.

Interactive Exercises

  • Ratio Table Challenge
    Create ratio tables with missing values and have students fill them in to create equivalent ratios.
  • Real-World Ratio Matching
    Provide cards with real-world scenarios involving ratios and cards with corresponding equivalent ratios. Have students match the cards.

Discussion Questions

  • What does it mean for two ratios to be equivalent?
  • How can you determine if two ratios are equivalent?
  • Give an example of when you might use equivalent ratios in everyday life.

Skills Developed

  • Proportional Reasoning
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

Which of the following ratios is equivalent to 3:5?

Correct Answer: 6:10

Question 2:

If a recipe calls for 2 cups of flour for every 3 eggs, how many cups of flour are needed for 9 eggs?

Correct Answer: 6 cups

Question 3:

What number can you multiply both parts of the ratio 4:7 by to get the equivalent ratio 12:21?

Correct Answer: 3

Question 4:

Which ratio represents the same proportion as 10/15?

Correct Answer: 2/3

Question 5:

A map scale is 1 inch = 25 miles. If two cities are 4 inches apart on the map, what is the actual distance between them?

Correct Answer: 100 miles

Question 6:

If the ratio of boys to girls in a class is 2:3, what fraction of the class are boys?

Correct Answer: 2/5

Question 7:

Which of these ratios is NOT equivalent to 1:4?

Correct Answer: 5:15

Question 8:

A store sells apples at a rate of 3 for $2. How much would 9 apples cost?

Correct Answer: $6

Question 9:

If a car travels 120 miles in 2 hours, what is its rate in miles per hour?

Correct Answer: 60 mph

Question 10:

Which ratio is equivalent to 0.5:1?

Correct Answer: 1:2

Fill in the Blank Questions

Question 1:

A _______ is a comparison of two quantities.

Correct Answer: ratio

Question 2:

Ratios that represent the same relationship are called _______ ratios.

Correct Answer: equivalent

Question 3:

To find an equivalent ratio, you can _______ or divide both parts of the ratio by the same number.

Correct Answer: multiply

Question 4:

If 4:5 = 8:x, then x = _______.

Correct Answer: 10

Question 5:

The ratio 12/16 simplified to its lowest terms is _______.

Correct Answer: 3/4

Question 6:

If one pizza costs $10, then three pizzas will cost $_______.

Correct Answer: 30

Question 7:

The scale on a map is 1 inch = 50 miles. If two cities are 3 inches apart on the map, the actual distance is _______ miles.

Correct Answer: 150

Question 8:

In the ratio 7:9, the number 7 is called the _______ term.

Correct Answer: first

Question 9:

If a basketball team wins 6 out of 8 games, the ratio of wins to total games is _______.

Correct Answer: 6/8

Question 10:

The concept of finding equivalent ratios is called _______ reasoning.

Correct Answer: proportional

Educational Standards

7.A.2.3:Use proportional reasoning to solve problems involving ratios. 7.A.2.4:Use proportional reasoning to assess the reasonableness of solutions. 7.N.1.2:Recognize and generate equivalent representations of rational numbers, including equivalent fractions.

Teaching Materials

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