Decoding Rates: Mastering Unit Rates and Proportional Reasoning

Mathematics Grades 7th Grade 4:30 Video
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Lesson Description

Learn to solve rate problems by finding unit rates and using proportional reasoning. This lesson covers calculating unit costs and applying them to solve real-world problems.

Video Resource

Rate problems

Khan Academy

Duration: 4:30
Watch on YouTube

Key Concepts

  • Rate
  • Unit Rate
  • Proportional Reasoning

Learning Objectives

  • Students will be able to calculate unit rates from given information.
  • Students will be able to apply unit rates to solve proportional reasoning problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a rate and asking students for real-world examples of rates (e.g., miles per hour, cost per item). Briefly discuss the importance of rates in everyday life.
  • Video Explanation (15 mins)
    Play the Khan Academy video "Rate problems". Pause at key points to explain the steps and ensure understanding. Emphasize the strategy of finding the unit rate as a problem-solving technique. Encourage students to ask questions.
  • Guided Practice (15 mins)
    Work through additional examples similar to those in the video. Model the process of identifying the rate, finding the unit rate, and using the unit rate to solve for the unknown. Encourage student participation by asking them to suggest steps or solve parts of the problem.
  • Independent Practice (10 mins)
    Assign practice problems for students to solve individually. Circulate to provide assistance and answer questions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and strategies covered in the lesson. Administer a short quiz to assess student understanding.

Interactive Exercises

  • Rate Calculation Challenge
    Divide students into small groups and present them with a series of rate problems. Each group must calculate the unit rate and solve the problem. The group with the correct answers in the shortest time wins.

Discussion Questions

  • What is a rate? Can you give some examples?
  • Why is it helpful to find the unit rate when solving rate problems?
  • How can you tell if a problem involves a proportional relationship?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Proportional reasoning

Multiple Choice Questions

Question 1:

What is the first step in solving most rate problems, according to the video?

Correct Answer: Find the unit rate.

Question 2:

If 3 apples cost $2.25, what is the cost of one apple (the unit rate)?

Correct Answer: $0.75

Question 3:

Lynnette can wash 95 cars in 5 days. How many cars can she wash in 1 day?

Correct Answer: 19 cars

Question 4:

If a train travels 240 miles in 4 hours, what is its speed in miles per hour?

Correct Answer: 60 mph

Question 5:

At the market, 8 batteries cost $10. How much does one battery cost?

Correct Answer: $1.25

Question 6:

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 7:

A store sells 5 candy bars for $3. What is the unit price per candy bar?

Correct Answer: $0.60

Question 8:

If a plant grows 2 inches per week, how many inches will it grow in 6 weeks?

Correct Answer: 12 inches

Question 9:

What does 'per' usually indicate in rate problems?

Correct Answer: Division

Question 10:

If you know the cost of one item, how do you find the cost of multiple items?

Correct Answer: Multiply

Fill in the Blank Questions

Question 1:

A _______ is a ratio that compares two different quantities.

Correct Answer: rate

Question 2:

A _______ _______ is a rate with a denominator of 1.

Correct Answer: unit rate

Question 3:

If 4 notebooks cost $6, then one notebook costs $_______.

Correct Answer: 1.50

Question 4:

Lynnette can wash 95 cars in 5 days. Therefore, she washes _______ cars per day.

Correct Answer: 19

Question 5:

At the market, 8 batteries cost $10. Six batteries would cost $_______.

Correct Answer: 7.50

Question 6:

The process of using ratios to solve problems is called _______ _______.

Correct Answer: proportional reasoning

Question 7:

If a car travels 150 miles in 3 hours, its average speed is _______ miles per hour.

Correct Answer: 50

Question 8:

If 5 pencils cost $2.50, the unit cost per pencil is $_______.

Correct Answer: 0.50

Question 9:

To find the unit rate, you usually _______ the numerator by the denominator.

Correct Answer: divide

Question 10:

If one ticket costs $12, then 3 tickets cost $_______.

Correct Answer: 36

Educational Standards

7.A.1:Explain the concept of proportionality in mathematical models and situations and distinguish between proportional and non-proportional relationships. 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.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).

Teaching Materials

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