Newspapers and Unit Rates: Cracking the Code!

Mathematics Grades 7th Grade 2:31 Video
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Lesson Description

Learn how to find unit rates using real-world examples, like delivering newspapers! This lesson breaks down the steps to calculate rates and apply them to everyday situations.

Video Resource

Solving unit rates problem | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy

Khan Academy

Duration: 2:31
Watch on YouTube

Key Concepts

  • Ratio
  • Rate
  • Unit Rate
  • Simplifying Fractions

Learning Objectives

  • Define and identify ratios and rates.
  • Calculate unit rates from given information.
  • Simplify fractions to find unit rates.
  • Apply unit rates to solve real-world problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what a 'rate' means to them in everyday language. Discuss examples like speed limits or price per item. Briefly introduce the concept of a 'unit rate' as a rate compared to one unit.
  • Video Viewing (7 mins)
    Play the Khan Academy video "Solving unit rates problem | Ratios, proportions, units, and rates | Pre-Algebra | Khan Academy". Encourage students to take notes on the steps involved in finding the unit rate.
  • Guided Practice (10 mins)
    Work through the newspaper delivery problem from the video, step-by-step, on the board. Emphasize the importance of correctly setting up the initial ratio and the process of simplifying the fraction to find the unit rate. Discuss why it's important to divide both the numerator and denominator by the same number.
  • Independent Practice (10 mins)
    Provide students with similar word problems to solve individually. For example: 'A car travels 240 miles in 4 hours. What is its speed in miles per hour?' or 'A store sells 5 apples for $2.50. What is the price per apple?'
  • Review and Closure (8 mins)
    Review the answers to the independent practice problems. Discuss any common errors or misconceptions. Reiterate the definition of a unit rate and its importance in real-world applications.

Interactive Exercises

  • Rate Matching Game
    Create a matching game where students match rates (e.g., 10 miles in 2 hours) with their corresponding unit rates (e.g., 5 miles per hour).
  • Real-World Rate Scavenger Hunt
    Have students find examples of rates in newspapers, magazines, or online (e.g., prices per ounce, miles per gallon) and calculate the unit rates.

Discussion Questions

  • What is the difference between a rate and a ratio?
  • Why is it helpful to find a unit rate?
  • Can you think of other real-world examples where unit rates are used?

Skills Developed

  • Problem-solving
  • Critical Thinking
  • Proportional Reasoning
  • Fraction Simplification

Multiple Choice Questions

Question 1:

What is a unit rate?

Correct Answer: A rate where the denominator is 1.

Question 2:

Jayda delivers 189 newspapers in 3 hours. What is her unit rate (newspapers per hour)?

Correct Answer: 63 newspapers per hour

Question 3:

A store sells 4 notebooks for $8. What is the price per notebook?

Correct Answer: $2

Question 4:

If a car travels 300 miles in 5 hours, what is its speed in miles per hour?

Correct Answer: 60 mph

Question 5:

Which of the following is NOT a unit rate?

Correct Answer: 3 cookies for every dollar

Question 6:

What operation is primarily used to find a unit rate?

Correct Answer: Division

Question 7:

A baker makes 24 cookies in 2 hours. What is the unit rate of cookies made per hour?

Correct Answer: 12 cookies/hour

Question 8:

A plant grows 15 cm in 5 days. What is the unit rate of growth per day?

Correct Answer: 3 cm/day

Question 9:

You read 120 pages in 4 hours. How many pages do you read per hour?

Correct Answer: 40 pages/hour

Question 10:

What does simplifying a fraction do to a unit rate?

Correct Answer: Makes it easier to understand

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 is a rate where the denominator is 1.

Correct Answer: unit

Question 3:

To find a unit rate, you often need to _______ a fraction.

Correct Answer: simplify

Question 4:

If you know the rate is 10 miles in 2 hours, the unit rate is ______ miles per hour.

Correct Answer: 5

Question 5:

Dividing both the numerator and the denominator by the same number ________ the fraction.

Correct Answer: simplifies

Question 6:

If 8 apples cost $4, then each apple costs $______.

Correct Answer: 0.50

Question 7:

A unit rate always compares a quantity to ______ unit.

Correct Answer: one

Question 8:

If a student completes 20 math problems in 40 minutes, the unit rate is 1 problem per ______ minutes.

Correct Answer: 2

Question 9:

The unit rate can also be called the constant of _________.

Correct Answer: proportionality

Question 10:

You can use proportional reasoning to check the ___________ of a unit rate solution.

Correct Answer: reasonableness

Educational Standards

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.

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