Solving Proportion Word Problems: Hot Dogs and Algebra!

Algebra 1 Grades High School 4:57 Video
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Lesson Description

Learn how to set up and solve proportion problems using the concept of constant ratios. This lesson uses a fun hot dog eating contest scenario to illustrate the application of proportions in real-world situations.

Video Resource

Proportion word problem (example 2) | 7th grade | Khan Academy

Khan Academy

Duration: 4:57
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Key Concepts

  • Proportions
  • Ratios
  • Constant Rate
  • Solving for unknowns

Learning Objectives

  • Students will be able to set up a proportion from a word problem.
  • Students will be able to solve proportions using algebraic manipulation.
  • Students will be able to interpret the solution of a proportion problem in the context of the original problem.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students if they have ever encountered proportions in everyday life (e.g., scaling recipes, calculating travel time). Briefly review the definition of a proportion as an equality of two ratios. Introduce the hot dog eating contest scenario as an engaging way to explore proportions.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Proportion word problem (example 2) | 7th grade | Khan Academy'. Instruct students to take notes on the problem setup, the different methods used to solve the proportion, and the importance of maintaining consistent units.
  • Guided Practice (10 mins)
    Work through the hot dog problem again, step-by-step, on the board. Emphasize the two different ways the proportion can be set up (hot dogs per minute vs. minutes per hot dog) and show how both lead to the same answer. Discuss the concept of 'constant pace' and its importance in setting up the proportion.
  • Independent Practice (10 mins)
    Provide students with similar proportion word problems to solve independently. Encourage them to try both methods of setting up the proportion and compare their answers. Circulate to provide assistance and answer questions.
  • Wrap-up and Discussion (3 mins)
    Review the key concepts of the lesson: proportions, ratios, constant rate. Answer student questions and prepare them for the quiz.

Interactive Exercises

  • Proportion Station
    Set up stations around the room with different proportion word problems. Students rotate through the stations, working in pairs to solve each problem. Each station focuses on different real-world applications of proportions (e.g., map scales, mixing solutions, calculating percentages).

Discussion Questions

  • Why is it important to keep the units consistent when setting up a proportion?
  • Can you think of other real-world scenarios where proportions are used?
  • What are some different strategies for solving a proportion equation?

Skills Developed

  • Problem-solving
  • Algebraic manipulation
  • Critical thinking
  • Ratio and proportional reasoning

Multiple Choice Questions

Question 1:

What is a proportion?

Correct Answer: An equation stating that two ratios are equal.

Question 2:

If 3 apples cost $2, how much will 9 apples cost if the price is proportional?

Correct Answer: $6

Question 3:

In a proportion problem, why is it important to maintain consistent units?

Correct Answer: To ensure that the ratios are truly equal.

Question 4:

What does 'constant pace' mean in the context of the hot dog eating problem?

Correct Answer: Mika eats at the same rate.

Question 5:

Which of the following is a valid way to set up a proportion for the problem: If 5 books cost $20, how much do 8 books cost?

Correct Answer: 5/20 = 8/x

Question 6:

Solving a proportion involves what algebraic technique?

Correct Answer: Solving for an unknown variable.

Question 7:

If a map has a scale of 1 inch = 25 miles, and two cities are 4 inches apart on the map, how far apart are they in reality?

Correct Answer: 100 miles

Question 8:

In the hot dog problem, what were the two different ratios that were set equal to each other?

Correct Answer: Hot dogs per minute and minutes per hot dog

Question 9:

If y is proportional to x and y = 12 when x = 3, what is the value of y when x = 5?

Correct Answer: 24

Question 10:

What is the reciprocal of 2/5?

Correct Answer: 5/2

Fill in the Blank Questions

Question 1:

A _______ is an equation that states that two ratios are equal.

Correct Answer: proportion

Question 2:

To solve a proportion, you need to isolate the _______ variable.

Correct Answer: unknown

Question 3:

Maintaining consistent _______ is crucial when setting up a proportion.

Correct Answer: units

Question 4:

The hot dog problem used the concept of a _______ pace to set up the proportion.

Correct Answer: constant

Question 5:

Multiplying a number by its _______ results in 1.

Correct Answer: reciprocal

Question 6:

If 2 shirts cost $30, then 4 shirts cost $_______.

Correct Answer: 60

Question 7:

A ratio compares two _______ or quantities.

Correct Answer: numbers

Question 8:

The video showed that you can solve the hotdog problem by setting up the proportion as hotdogs per minute or _______ per hotdog.

Correct Answer: minutes

Question 9:

Cross-_______ can be used as a method of solving proportions.

Correct Answer: multiplication

Question 10:

If one variable increases as the other decreases, the proportion is an _______ proportion.

Correct Answer: inverse

Educational Standards

A1.A.1:Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context. A1.A.3.1:Solve equations involving several variables for one variable in terms of the others. A1.A.4:Analyze real-world and mathematical problems involving linear equations.

Teaching Materials

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