Standard 4: Analyze and represent two-variable proportional relationships.

General Information
Number: MA.7.AR.4
Title: Analyze and represent two-variable proportional relationships.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 7
Strand: Algebraic Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.7.AR.4.AP.1
Given a table or a graph, determine whether two quantities have a proportional relationship.
MA.7.AR.4.AP.2
Identify the constant of proportionality when given a table or graph of a proportional relationship.
MA.7.AR.4.AP.3
Given a table or equation, graph a proportional relationship.
MA.7.AR.4.AP.4
Given a table representation of a proportional relationship, translate the relationship into an equation or a graph.
MA.7.AR.4.AP.5
Solve simple real-world problems involving proportional relationships.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Formative Assessments

Identifying Constant of Proportionality in Equations:

Students are asked to identify and explain the constant of proportionality in three different equations.

Type: Formative Assessment

Teacher to Student Ratios:

Students are asked to graph four ordered pairs given in context and decide if the variables they represent are proportionally related.

Type: Formative Assessment

Constant of Proportionality Trip:

Students are asked to identify and explain the constant of proportionality given a verbal description and a diagram representing a proportional relationship.

Type: Formative Assessment

Writing An Equation:

Students are asked to write an equation to represent a proportional relationship depicted in a graph.

Type: Formative Assessment

Graphs of Proportional Relationships:

Students are asked to identify the graph of a proportional relationship.

Type: Formative Assessment

Babysitting Graph:

Students are given a graph that models the hourly earnings of a babysitter and are asked to interpret ordered pairs in context.

Type: Formative Assessment

Finding Constant of Proportionality:

Students are asked to determine the constant of proportionality using a table and a graph.

Type: Formative Assessment

Deciding If Proportional:

Students decide if two variables are proportionally related based on data given in a table.

Type: Formative Assessment

Serving Size:

Students are given the number of calories in a serving of oatmeal and are asked to write an equation that models the relationship between the size of the serving and the number of calories.

Type: Formative Assessment

Lesson Plans

Clean It Up:

Students will help a volunteer coordinator choose cleanup projects that will have the greatest positive impact on the environment and the community.  They will apply their knowledge of how litter can impact ecosystems along with some math skills to make recommendations for cleanup zones to prioritize.  Students will explore the responsibilities of citizens to maintain a clean environment and the impact that litter can have on society in this integrated Model Eliciting Activity.  

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.  Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Is My Backpack Too Massive?:

This lesson combines many objectives for seventh grade students. Its goal is for students to create and carry out an investigation about student backpack mass. Students will develop a conclusion based on statistical and graphical analysis.

Type: Lesson Plan

Cricket Songs:

Using a guided-inquiry model, students in a math or science class will use an experiment testing the effect of temperature on cricket chirping frequency to teach the concepts of representative vs random sampling, identifying directly proportional relationships, and highlight the differences between scientific theory and scientific law.

Type: Lesson Plan

Are Corresponding Leaf Veins Proportional to Leaf Height?:

Students will measure the length of different sized leaves and corresponding veins to determine proportionality.  Students will graph their results on a coordinate grid and write about their results. 

Type: Lesson Plan

From Tables to Graphs and Back!:

Students will match corresponding sets of tables, graphs and linear equations in order to deepen their understanding of multiple representations of the relationships between dependent and independent variables.

Type: Lesson Plan

Water Troubles:

This Model Eliciting Activity (MEA) presents students with the real-world problem of contaminated drinking water.  Students are asked to provide recommendations for a non-profit organization working to help a small Romanian village acquire clean drinking water.  They will work to develop the best temporary strategies for water treatment, including engineering the best filtering solution using local materials.  Students will utilize measures of center and variation to compare data, assess proportional relationships to make decisions, and perform unit conversions across different measurement systems.

Type: Lesson Plan

The Speeding Ticket: Part 2 - Graphing Linear Functions:

This lesson allows the student to learn about dependent and independent variables and how to make the connection between the linear equation, a linear function, and its graph. The student will learn graphing relationships and how to identify linear functions.

Type: Lesson Plan

The Speeding Ticket (Part 1: Solving Linear Equations with One Variable):

"The Speeding Ticket" lesson uses real world application to create and solve linear equations and tables with one variable numerically, verbally, and algebraically. The student will also learn the relationship between the independent and dependent variables.

Type: Lesson Plan

Math in Mishaps:

Students will explore how percentages, proportions, and solving for unknowns are used in important jobs. This interactive activity will open their minds and address the question, "When is this ever used in real life?"

Type: Lesson Plan

Perspectives Video: Experts

Statistical Sampling Results in setting Legal Catch Rate :

Fish Ecologist, Dean Grubbs, discusses how using statistical sampling can help determine legal catch rates for fish that may be endangered.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Unit Rate: Spring Water Bottling:

Nestle Waters discusses the importance of unit rate in the manufacturing process of bottling spring water.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Fishery Independent vs Dependent Sampling Methods for Fishery Management:

NOAA Scientist Doug Devries discusses the differences between fishery independent surveys and fishery independent surveys.  Discussion includes trap sampling as well as camera sampling. Using graphs to show changes in population of red snapper.

Type: Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Calories, Distance, and Rowing Rates:

Food is fuel, especially important when your body is powering a boat across the ocean.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Calories, Exercise, and Metabolism Rates:

How much food do you need to cross the Pacific in a kayak? Get a calculator and a bag of almonds before you watch this.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Idea

Robot Mathematics: Gearing Ratio Calculations for Performance:

A science teacher demonstrates stepwise calculations involving multiple variables for designing robots with desired characteristics.

Type: Perspectives Video: Teaching Idea

Tutorials

Proportion Word Problem:

This introductory video demonstrates the basic skill of how to write and solve a basic equation for a proportional relationship. 

Type: Tutorial

Interpreting Graphs of Proportional Relationships:

This video shows how to recognize and understand graphs of proportional relationships to find the constant of proportionality.

Type: Tutorial

Solving a Proportion with an Unknown Variable :

Here's an introductory video explaining the basic reasoning behind solving proportions and shows three different methods for solving proportions which you will use later on to solve more difficult problems. 

Type: Tutorial

Setting up Proportions to Solve Word Problems:

This introductory video shows some basic examples of writing two ratios and setting them equal to each other. This is just step 1 when solving word problems with proportions. 

Type: Tutorial

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast

Tutorials

Proportion Word Problem:

This introductory video demonstrates the basic skill of how to write and solve a basic equation for a proportional relationship. 

Type: Tutorial

Interpreting Graphs of Proportional Relationships:

This video shows how to recognize and understand graphs of proportional relationships to find the constant of proportionality.

Type: Tutorial

Solving a Proportion with an Unknown Variable :

Here's an introductory video explaining the basic reasoning behind solving proportions and shows three different methods for solving proportions which you will use later on to solve more difficult problems. 

Type: Tutorial

Setting up Proportions to Solve Word Problems:

This introductory video shows some basic examples of writing two ratios and setting them equal to each other. This is just step 1 when solving word problems with proportions. 

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Perspectives Video: Expert

Using Statistics to Estimate Lionfish Population Size:

It's impossible to count every animal in a park, but with statistics and some engineering, biologists can come up with a good estimate.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Sampling Bird Populations to Track Environmental Restoration:

Sometimes scientists conduct a census, too! Learn how population sampling can help monitor the progress of an ecological restoration project.

Type: Perspectives Video: Professional/Enthusiast