A Hawaiian kapa artist explains how she uses area and measurements as part of her art-making process in this video from the Center for Asian American Media. In the accompanying classroom activity, students watch the video and learn how the artist finds the area of cloth that she can create with one cup of tree bark fiber. Next, students find how many cups of tree bark fiber they would need for kapa cloth to cover various surfaces around the classroom. To get the most from this lesson, students should have experience using a constant of proportionality to find proportional relationships.

Learn how to calculate the area of paintings and shapes as graffiti artist Scape Martinez uses math to plan the supplies required for his artwork in this video from the Center for Asian American Media. In the accompanying classroom activity, students learn how to calculate the area of a large letter to be painted, create their own design, and determine how much spray paint they would need to paint it. To get the most from this lesson, students should know how to find the area of shapes and be able to use a constant of proportionality to find proportional relationships.

Video tutorial demonstrates how to graph the equation of a line that represents a proportional relationship given a unit rate. [4:30]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Explore how to graph the equation of a line that represents a proportional relationship given a table. [1:10]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Video lesson shows how to graph the equation of a line that represents a proportional relationship given an equation. [3:08]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Watch a student think through a problem about how the area of a rectangle changes when both sides are increased by the same scale factor and use online tools to demonstrate understanding of concepts related to area and scale factors in this interactive from KET. Students use the Notes tool to respond to the video. They then complete a Visualize It! activity, a quiz, and a Chart It! activity to demonstrate their learning.

Learn how to calculate sale price when combining two "percent-off" discounts in this video from KQED. In the accompanying classroom activity, students develop and share a variety of strategies, including modeling with a 10 x 10 grid to determine a total discount and sale price when two percent-off discounts are combined. They compare their strategies with the approach demonstrated in a video. To get the most out of the activity, students should be comfortable calculating discount as a percent off a dollar amount (e.g., 20% off an item priced at $50) and familiar with the concept of a ratio.

Explore firearm deaths in the United States in 2010 by type, race, and age group in this interactive from KQED. In the accompanying classroom activity, students are presented with a simple question: Is America a safe place to live? In forming a response, students examine data in pie charts and bar graphs and try to figure out what story the data tell. They also list questions whose answers would help them come to a better understanding of the issue of gun violence in America.

Proportional Relationships

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Understand what a rate and ratio are.
Make a ratio table.
Make a graph using values from a ratio table.

Lesson Flow

Students start the unit by predicting what will happen in certain situations. They intuitively discover they can predict the situations that are proportional and might have a hard time predicting the ones that are not. In Lessons 2–4, students use the same three situations to explore proportional relationships. Two of the relationships are proportional and one is not. They look at these situations in tables, equations, and graphs. After Lesson 4, students realize a proportional relationship is represented on a graph as a straight line that passes through the origin. In Lesson 5, they look at straight lines that do not represent a proportional relationship. Lesson 6 focuses on the idea of how a proportion that they solved in sixth grade relates to a proportional relationship. They follow that by looking at rates expressed as fractions, finding the unit rate (the constant of proportionality), and then using the constant of proportionality to solve a problem. In Lesson 8, students fine-tune their definition of proportional relationship by looking at situations and determining if they represent proportional relationships and justifying their reasoning. They then apply what they have learned to a situation about flags and stars and extend that thinking to comparing two prices—examining the equations and the graphs. The Putting It Together lesson has them solve two problems and then critique other student work.

Gallery 1 provides students with additional proportional relationship problems.

The second part of the unit works with percents. First, percents are tied to proportional relationships, and then students examine percent situations as formulas, graphs, and tables. They then move to a new context—salary increase—and see the similarities with sales taxes. Next, students explore percent decrease, and then they analyze inaccurate statements involving percents, explaining why the statements are incorrect. Students end this sequence of lessons with a formative assessment that focuses on percent increase and percent decrease and ties it to decimals.

Students have ample opportunities to check, deepen, and apply their understanding of proportional relationships, including percents, with the selection of problems in Gallery 2.

Students explore the idea that not all straight lines are proportional by comparing a graph representing a stack of books with a graph representing a stack of cups. They recognize that all proportional relationships are represented as a straight line that passes through the origin.Key ConceptsNot all graphs of straight lines represent proportional relationships.There are three ways to tell whether a relationship between two varying quantities is proportional:The graph of the relationship between the quantities is a straight line that passes through the point (0, 0).You can express one quantity in terms of the other using a formula of the form y = kx.The ratios between the varying quantities are constant.Goals and Learning ObjectivesUnderstand when a graph of a straight line is and when it is not a proportional relationship.Recognize that a proportional relationship is shown on a graph as a straight line that passes through the origin (0, 0).Make a table of values to represent two quantities that vary.Graph a table of values representing two quantities that vary.Describe what each variable and number in a formula represents.

Students interpret verbal descriptions of situations and determine whether the situations represent proportional relationships.Key ConceptsIn a proportional relationship, there has to be some value that is constant.There are some relationships in some situations that can never be proportional.Goals and Learning ObjectivesIdentify verbal descriptions of situations as being proportional relationships or notUnderstand that some relationships can never be proportionalUnderstand that for two variable quantities to be proportional to one another, something in the situation has to be constant

Students watch a video showing three different ways to solve a problem involving a proportional relationship, and then they use each method to solve a similar problem. Students describe each approach, including the mathematical terms associated with each.Key ConceptsThree methods for solving problems involving proportional relationships include:Setting up a proportion and solving for the missing valueFinding the unit rate and multiplyingWriting and solving a formula using the constant of proportionalityGoals and Learning ObjectivesSolve a problem involving a proportional relationship in three different ways: set up a proportion and solve for a missing value, use a unit rate, and use the constant of proportionality to write and solve a formula.

In this lesson, students will learn how to solve percent of change problems.

In this lesson, students will learn how to identify proportional relationships from tables, graphs, and equations. They will also learn how to identify the unit rate and write an equation to represent proportional relationships.

In this lesson on ratios, students explore how ratios can be used to demonstrate rates by exploring proportional relationships.

Video explores how to compare a rate given in an equation to a rate shown on a graph. [1:24]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Video explores rates and proportional relationships using a gas mileage problem. [3:18]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

Using this infographic, learn how wage equity today compares with data from 50 years ago, at the dawn of the equal pay movement. The accompanying classroom activity invites students to explore the change in the gender wage gap from 1965 to 2010. First, students will learn how the wage gap can be calculated from different median salaries for men and women. Then, students will consider the real monetary impact of increasing equity in wages-and will look to the graph for clues about when the wage gap will be eliminated, if at all.

In this Cyberchase media gallery, learn about ratio and proportion and how to use an algebraic shortcut to solve proportion problems. In the accompanying classroom activity, students play a game called the "Pom-Pom Nose Push," in which they collect data and determine the ratio of time to distance.