Unlocking Rates: Mastering Ratios in the Real World

Mathematics Grades 7th Grade 5:29 Video
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Lesson Description

Explore the relationship between ratios and rates, understand real-world applications, and learn to quantify change and comparisons.

Video Resource

Introduction to rates | Ratios, rates, and percentages | 6th grade | Khan Academy

Khan Academy

Duration: 5:29
Watch on YouTube

Key Concepts

  • Definition of Rate
  • Relationship between Ratios and Rates
  • Real-World Applications of Rates

Learning Objectives

  • Define 'rate' and provide examples from everyday life.
  • Explain the connection between ratios and rates, and how they are related.
  • Apply the concept of rates to solve practical problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they understand by the term 'rate'. Discuss examples like speed limits or hourly wages. Briefly introduce the video and its learning objectives.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Introduction to rates'. Instruct students to take notes on the key definitions and examples provided.
  • Guided Discussion (8 mins)
    After the video, facilitate a class discussion using the discussion questions. Encourage students to share their understanding of rates and provide additional examples.
  • Interactive Exercises (10 mins)
    Engage students in the interactive exercises. This involves creating their own rate problems based on real-life scenarios and solving them, solidifying their understanding. Have them explain their reasoning.
  • Wrap-up and Assessment (5 mins)
    Summarize the key points of the lesson. Administer the multiple choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Rate Problem Creation
    Students create their own rate problems based on scenarios such as the cost of groceries per item, the distance traveled by a cyclist per minute, or the number of words typed per minute. They then exchange problems and solve them.

Discussion Questions

  • What are some examples of rates you encounter in your daily life, besides the ones mentioned in the video?
  • How are rates and ratios similar, and how are they different?
  • Why is it important to understand rates when dealing with real-world situations?

Skills Developed

  • Critical Thinking
  • Problem-Solving
  • Analytical Skills

Multiple Choice Questions

Question 1:

What is a rate?

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

Question 2:

Which of the following is an example of a rate?

Correct Answer: The price of apples at $2 per pound.

Question 3:

If you earn $12 per hour, how much will you earn in 5 hours?

Correct Answer: $60

Question 4:

What does 'miles per hour' (MPH) measure?

Correct Answer: The distance covered in a specific amount of time.

Question 5:

A dessert has 150 calories per serving. If you eat 2.5 servings, how many calories did you consume?

Correct Answer: 375 calories

Question 6:

Which of the following statements correctly describes the relationship between ratios and rates?

Correct Answer: A rate is a specific type of ratio that compares different units.

Question 7:

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

Correct Answer: 60 mph

Question 8:

Which of these is NOT a rate?

Correct Answer: Apples per oranges

Question 9:

Why are rates important in mathematics?

Correct Answer: They allow us to quantify how fast things are happening and compare different scenarios.

Question 10:

If you read 30 pages in one hour, what is your reading rate?

Correct Answer: 1 page per 30 minutes

Fill in the Blank Questions

Question 1:

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

Correct Answer: rate

Question 2:

If you are paid $15 per hour, then '$15 per hour' is an example of a(n) ______.

Correct Answer: rate

Question 3:

If a recipe requires 2 cups of flour for every 1 cup of sugar, the ratio of flour to sugar is 2 to 1. We can also express this as a ______.

Correct Answer: rate

Question 4:

Rates help us to ______ how fast or slow things are happening.

Correct Answer: quantify

Question 5:

The rate 'miles per hour' (mph) tells us how many ______ are covered in one hour.

Correct Answer: miles

Question 6:

A rate that indicates the amount of something per single unit of something else is called a ________ rate.

Correct Answer: unit

Question 7:

The study of rates is especially important in ______ when analyzing slopes of lines.

Correct Answer: algebra

Question 8:

The rate of change in vertical direction relative to the horizontal direction of a line is called ________.

Correct Answer: slope

Question 9:

Calories per serving is an example of a rate that relates _________ to number of servings.

Correct Answer: calories

Question 10:

Differential calculus uses instantaneous _________ to see how fast something is happening at a given moment.

Correct Answer: rate

Educational Standards

7.A.2.1:Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations. 7.A.2.2:Solve multi-step problems with proportional relationships (e.g., distance-time, percent increase or decrease, discounts, tips, unit pricing, mixtures and concentrations, similar figures, other mathematical situations). 7.A.2.3:Use proportional reasoning to solve problems involving ratios.

Teaching Materials

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