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

Guiding Grids: Math inspired self-portraits:

Students will create a proportional self portrait from a photo using a gridded drawing method and learn how a grid system can help accurately enlarge an image in a work of art. Students will use the mathematical concepts of scale, proportion and ratio, to complete their artwork.

Type: Lesson Plan

Smith Valley Farms Horse Pedigrees:

The owner of newly opened Smith Valley Farms is looking to breed the next generation of top race horses. In this MEA, students will study race horse pedigrees as well as horse racing data to determine which is the best stallion to breed with a filly. Students will have to read a horse pedigree, calculate percentages based on a data table, and complete Punnett squares to determine genetic probability.

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

How Fast Can One Travel on a Bicycle?:

Students investigate how the pedal and rear wheel gears affect the speed of a bicycle. A GeoGebra sketch is included that allows a simulation of the turning of the pedal and the rear wheel. A key goal is to provide an experience for the students to apply and integrate the key concepts in seventh-grade mathematics in a familiar context.

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

Building Graduation Caps:

Students will apply skills from the Geometry Domain to build graduation caps for themselves using heavyweight poster paper. They will also apply some basic mathematical skills to determine dimensions and to determine minimum cost. Some of the Geometric skills reinforced in Building Graduation Caps: Cooperative Assignment are finding area, applying the concept of similarity, and the application of the properties of parallelograms. Other skills also involved in this application are measuring, and statistical calculations, such as finding the mean and the range. In addition to the hands-on group project that takes place during the lesson, there is the Prerequisite Skills Assessment: Area that should be administered before the group activity and a home-learning activity. Building Graduation Caps: Individual Assignment is the home-learning assignment; it is designed to reinforce the skills learned in the group activity.

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

Running and Rising:

In this lesson students will graph and compare two proportional relationships from different representations in contextual problems and be introduced to the constant of proportionality as the unit rate.

Type: Lesson Plan

When Pigs Fly:

In this lesson students will explore probability and likelihood that an event will occur. They will place both serious and silly events on a number line, once they have assigned a value to that event. They will work with a group and then justify their classifications to their peers.

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

Practically Probable:

In this lesson, students will differentiate between likely and unlikely event, as well as learn the difference between dependent and independent events. Finally, they learn how to compute theoretical probabilities in simple experiments.

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

What's the Going Rate?:

Students discover that the unit rate and the slope of a line are the same, and these can be used to compare two different proportional relationships. Students compare proportional relationships presented in table and graph form.

Type: Lesson Plan

Who goes faster, earns more, drives farthest?:

Given a proportional relationship, students will determine the constant of proportionality, write an equation, graph the relationship, and interpret in context.

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]

Download the CPALMS Perspectives video student note taking guide.

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

Problem-Solving Tasks

Art Class, Variation 1:

Students are asked to use ratios and proportional reasoning to compare paint mixtures numerically and graphically.

Type: Problem-Solving Task

Art Class, Variation 2:

Giving the amount of paint in "parts" instead of a specific standardized unit like cups might be confusing to students who do not understand what this means. Because this is standard language in ratio problems, students need to be exposed to it, but teachers might need to explain the meaning if their students are encountering it for the first time.

Type: Problem-Solving Task

Coffee by the Pound:

Students will answer questions about unit price of coffee, make a graph of the information, and explain the meaning of constant of proportionality/slope in the given context.

Type: Problem-Solving Task

Chocolate Bar Sales:

In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations. In the later part of the problem, the numbers are big enough so that using the formula is the most efficient way to solve the problem; however, creative use of the table or graph will also work.

Type: Problem-Solving Task

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

Problem-Solving Tasks

Art Class, Variation 1:

Students are asked to use ratios and proportional reasoning to compare paint mixtures numerically and graphically.

Type: Problem-Solving Task

Coffee by the Pound:

Students will answer questions about unit price of coffee, make a graph of the information, and explain the meaning of constant of proportionality/slope in the given context.

Type: Problem-Solving Task

Chocolate Bar Sales:

In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations. In the later part of the problem, the numbers are big enough so that using the formula is the most efficient way to solve the problem; however, creative use of the table or graph will also work.

Type: Problem-Solving Task

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

Problem-Solving Tasks

Art Class, Variation 1:

Students are asked to use ratios and proportional reasoning to compare paint mixtures numerically and graphically.

Type: Problem-Solving Task

Art Class, Variation 2:

Giving the amount of paint in "parts" instead of a specific standardized unit like cups might be confusing to students who do not understand what this means. Because this is standard language in ratio problems, students need to be exposed to it, but teachers might need to explain the meaning if their students are encountering it for the first time.

Type: Problem-Solving Task

Coffee by the Pound:

Students will answer questions about unit price of coffee, make a graph of the information, and explain the meaning of constant of proportionality/slope in the given context.

Type: Problem-Solving Task

Chocolate Bar Sales:

In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations. In the later part of the problem, the numbers are big enough so that using the formula is the most efficient way to solve the problem; however, creative use of the table or graph will also work.

Type: Problem-Solving Task