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Recognize and represent proportional relationships between quantities.
  1. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  2. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  3. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
  4. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.


Standard #: MAFS.7.RP.1.2Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 7
Domain-Subdomain: Ratios & Proportional Relationships
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Formative Assessments
  • Identifying Constant of Proportionality in Equations # Students are asked to identify and explain the constant of proportionality in three different equations.
  • 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.
  • 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.
  • Writing An Equation # Students are asked to write an equation to represent a proportional relationship depicted in a graph.
  • Graphs of Proportional Relationships # Students are asked to identify the graph of a proportional relationship.
  • Babysitting Graph # Students are given a graph that models the hourly earnings of a babysitter and are asked to interpret ordered pairs in context.
  • Finding Constant of Proportionality # Students are asked to determine the constant of proportionality using a table and a graph.
  • Deciding If Proportional # Students decide if two variables are proportionally related based on data given in a table.
  • 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.
Lesson Plans
  • 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.
  • Radioactive Dating Lesson 1 # Read about a recent uncovering of mammoths to engage students in a discussion of radioactive dating. This is the first lesson in a unit of 4 lessons that integrates science, math, and computer science standards to teach the concept of half-lives and radioactive dating.
  • Irrigation Station # This STEM lesson, complete with a design challenge, helps students design, build, and test irrigation methods. Students will incorporate and develop math skills through solving proportions as they work in teams to solve an engineering challenge.
  • 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.
  • 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.
  • 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. 
  • Classifying Proportion and Non-proportion Situations # This lesson helps students determine whether two quantities are in a proportional relationship. Students analyze written and numerical situations to decide if quantities vary in direct proportion, distinguishing multiplicative relationships from additive ones. Through discussion and collaborative classification activities, students deepen their understanding of proportional relationships and the characteristics that define them.
  • Sampling and Estimating: Counting Trees # Students use data from a random sample to make predictions about a population. By counting trees in sample grid sections, they record data, apply proportional reasoning to estimate totals, and compare the accuracy of different estimates.
  • Back to the Past with the Geologic Time Scale # This lesson introduces the geologic time scale and the concept of time segments being divided by major events in Earth's history. It gives students an opportunity to place various fossils into appropriate periods, observe the change in the complexity of fossils and draw conclusions regarding the change. Students complete a brace map including the eras and periods showing their understanding of parts to the whole within the geologic time scale. On day 2, students research an organism of their choice and trace it back to their most basic relative. Students then create a final product, such as a brochure, timeline or a poster, demonstrating the change of the organism over time. Students will be provided with a rubric that will guide them while they work on the final product.
  • Drawing to Scale: A Garden # This lesson helps students apply proportional reasoning to solve real-world geometry problems involving scale drawings. Students interpret and use scale factors to relate dimensions on a plan to actual dimensions, calculate areas of geometric features, and reason about how changes in scale affect measurements. Through hands-on drawing tasks and collaborative problem solving, students deepen their understanding of the relationship between scale factor, proportional reasoning, and area in geometric contexts.
  • Comparing Strategies for Proportion Problems # In this lesson, students solve real-world problems involving proportions and apply their previous understanding of ratios. They explore different strategies such as using tables, scaling, unit rates, and equations to find solutions. Through discussion and comparison of methods, students strengthen their ability to reason proportionally and explain their thinking.
  • Making a Scale Drawing # Objective: Students will create a detailed scale drawing. Context: Students have used tools to measure length, solve proportions, and interpret scale drawings. They will continue to use ratio and proportion in the study of similar figures, percent, and probability.
  • Scientific calculations from a distant planet # Students will act as mathematicians and scientists as they use models, observations and space science concepts to perform calculations and draw inferences regarding a fictional solar system with three planets in circular orbits around a sun. Among the calculations are estimates of the size of the home planet (using a method more than 2000 years old) and the relative distances of the planets from their sun.
  • Are My Values Proportional? # Students will learn that a proportional relationship can be represented by a table, a graph, or an equation. They will also be able to determine the constant of proportionality from a table, graph, or equation.
  • Makeover, Home Edition Part III # This is the third part of the lesson, "Makeover, Home Edition". This lesson is designed to teach students how to put ideas into reality by creating and using scale drawings in the real world. In Part I (#48705) students determined backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into the backyard. In Part III (#49025) students will create a scale drawing of the backyard. Part IV (#49090) will focus on inserting a window and painting walls inside the house.
  • Makeover, Home Edition Part I # This is the first part of the lesson, "Makeover Home Edition." This lesson is designed to increase student engagement. Students must think critically about fencing in their new "dream" backyard by calculating the total fencing needed. They will choose the most cost-effective method of purchasing their fencing by comparing unit rates mathematically and graphically. CPALMS Lesson Part II (#48967) will concentrate on inserting a pool and patio into this backyard. Part III (#49025) will include the creation of a scale drawing of this backyard. Part IV (#49090) focuses on inserting a window and painting walls inside the house.
  • Let's Rate it! # The purpose of this lesson is to introduce rates of change to students, allowing them to explore how rates are formed, what rates are used for, and how rates can be used to solve real life problems.
  • 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?"
Perspectives Video: Professional/Enthusiasts
Problem-Solving Tasks
  • Art Class, Variation 1 # Students are asked to use ratios and proportional reasoning to compare paint mixtures numerically and graphically.
  • 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.
  • Buying Coffee # In this task, students determine a unit rate and use it to create a graph representing a proportional relationship between two quantities. As they graph the relationship, they interpret the unit rate as the constant of proportionality and recognize that proportional relationships are represented by straight lines through the origin on the coordinate plane.
  • Music Companies, Variation 1 # Students compare two offers to buy the same number of shares in a company. One offer is given as a total price and the other as a price per share. To solve, students calculate the unit rate (cost per share) for the first offer and then compare the two deals.
  • Robot Races # In this task, students analyze graphs that show how far three robots travel over time. They interpret what each labeled point means about a robot’s distance and time, decide whether the relationship between distance and time is proportional, and determine each robot’s speed by finding its constant of proportionality (unit rate) from the graph.
  • Sore Throats, Variation 1 # Students are asked to decide if two given ratios are equivalent.
Tutorials
Unit/Lesson Sequence
  • Direct and Inverse Variation # Lesson 1 of two lessons teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper tissues (to represent land) and drops of vegetable oil (to simulate a volume of oil). Lesson 2 teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of water poured into cylindrical containers of different sizes as compared to the area of the containers' bases." from Insights into Algebra 1 - Annenberg Foundation.
Virtual Manipulatives
  • Graphing Lines # This manipulative will help you to explore the world of lines. You can investigate the relationships between linear equations, slope, and graphs of lines.
  • Graphing Lines # Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the slope and various types of line equations can be explored.
MFAS Formative Assessments
  • Babysitting Graph # Students are given a graph that models the hourly earnings of a babysitter and are asked to interpret ordered pairs in context.
  • 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.
  • Deciding If Proportional # Students decide if two variables are proportionally related based on data given in a table.
  • Finding Constant of Proportionality # Students are asked to determine the constant of proportionality using a table and a graph.
  • Graphs of Proportional Relationships # Students are asked to identify the graph of a proportional relationship.
  • Identifying Constant of Proportionality in Equations # Students are asked to identify and explain the constant of proportionality in three different equations.
  • 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.
  • 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.
  • Writing An Equation # Students are asked to write an equation to represent a proportional relationship depicted in a graph.
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