Mastering Proportions: Solving Word Problems with Ratios

Algebra 1 Grades High School 5:51 Video
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Lesson Description

Learn how to set up and solve proportion word problems by writing and manipulating ratios. This lesson covers multiple approaches to building proportions and applying them to real-world scenarios.

Video Resource

Setting up proportions to solve word problems | 7th grade | Khan Academy

Khan Academy

Duration: 5:51
Watch on YouTube

Key Concepts

  • Ratio
  • Proportion
  • Cross Multiplication

Learning Objectives

  • Students will be able to identify proportion word problems.
  • Students will be able to set up proportions from word problems using different ratio relationships.
  • Students will be able to solve proportions to find unknown values.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definitions of ratio and proportion. Explain that a proportion is an equation stating that two ratios are equal. Highlight the importance of understanding proportions in real-world problem-solving.
  • Video Viewing and Discussion (15 mins)
    Play the Khan Academy video 'Setting up proportions to solve word problems'. Pause at key points to discuss the different methods presented for setting up proportions. Emphasize that there isn't one single 'right' way, but consistency within a ratio is crucial.
  • Guided Practice (15 mins)
    Work through several example word problems as a class. For each problem, guide students through the following steps: 1. Identify the known quantities and the unknown quantity. 2. Determine the relationship between the quantities. 3. Set up a proportion using two equivalent ratios. 4. Solve the proportion using cross-multiplication or other methods. Discuss the importance of units and making sure they are consistent within each ratio.
  • Independent Practice (10 mins)
    Provide students with a set of word problems to solve independently. Encourage them to use the methods discussed in class and to check their answers.

Interactive Exercises

  • Proportion Match
    Present students with a list of word problems and a list of corresponding proportions (some correct, some incorrect). Students must match each word problem with the correct proportion and explain why the other options are incorrect.

Discussion Questions

  • Why is it important to maintain consistency in the units within each ratio?
  • Can you think of real-world examples where proportions are used?
  • What are some different ways you can set up a proportion to solve the same problem?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Mathematical reasoning

Multiple Choice Questions

Question 1:

Which of the following is a proportion?

Correct Answer: 1/2 = 4/8

Question 2:

If 3 apples cost $2, how can you set up a proportion to find the cost of 9 apples?

Correct Answer: 3/2 = 9/x

Question 3:

In a proportion, what must be true about the two ratios?

Correct Answer: They must be equal.

Question 4:

What is a ratio?

Correct Answer: A comparison of two quantities by division

Question 5:

If 5 pencils cost $1.50, which proportion can be used to find the cost of 15 pencils?

Correct Answer: 5/1.50 = 15/x

Question 6:

Which of these equations represents a valid method for solving proportions?

Correct Answer: Cross multiplication

Question 7:

If the ratio of boys to girls in a class is 2:3, and there are 10 boys, how would you find the number of girls (x)?

Correct Answer: 2/3 = 10/x

Question 8:

What is the first step in setting up a proportion word problem?

Correct Answer: Identify the known and unknown quantities

Question 9:

Is there only one correct way to set up a proportion for a given word problem?

Correct Answer: No, but the units need to be consistent

Question 10:

In the proportion a/b = c/d, which term is the unknown you might solve for?

Correct Answer: any of these

Fill in the Blank Questions

Question 1:

A proportion is an equation stating that two _______ are equal.

Correct Answer: ratios

Question 2:

In a proportion, you can use _______ _______ to solve for an unknown.

Correct Answer: cross multiplication

Question 3:

When setting up a proportion, the _______ must be consistent within each ratio.

Correct Answer: units

Question 4:

If 4 pencils cost $1, then 12 pencils will cost $______.

Correct Answer: 3

Question 5:

A _______ is a comparison of two quantities by division.

Correct Answer: ratio

Question 6:

Flipping both sides of an equation will result in a _______ proportion.

Correct Answer: valid

Question 7:

When using proportions to solve real-world problems, you need to _______ your answer.

Correct Answer: interpret

Question 8:

To solve 5/x = 10/2, _______ multiply and then divide to find x.

Correct Answer: cross

Question 9:

If you have 3/4 = 6/8, the numbers 3 and 8 are called _______ and they will _______ when multiplied

Correct Answer: extremes; equal

Question 10:

If 2 inches on a map represents 50 miles, 10 inches represents _______ miles.

Correct Answer: 250

Educational Standards

A1.A.1.1:Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, statistics) and interpret the solutions in the original context. A1.A.3.1:Solve equations involving several variables for one variable in terms of the others.

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