Understanding Proportional Relationships
Common Core State Standards
Math 
Math 
7 
Grade 7 
RP 
Ratios & Proportional Relationships 
A 
Analyze proportional relationships and use them to solve realworld and mathematical problems 
2 
Recognize and represent proportional relationships between quantities. a. 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. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. 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. d. 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. 
Download Common Core State Standards (PDF 1.2 MB) 
Common Core State Standards
Math 
Math 
Practice 
Mathematical Practice Standards 
MP1 
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 
Download Common Core State Standards (PDF 1.2 MB) 

Lesson Idea  Common CoreUnderstanding TransformationsGrade 912 / Math / GeometryMath.HSG.CO.A.4 / Math.HSG.CO.A.5
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Lesson Idea  Common CoreCommon Issues with TransformationsGrade 912 / Math / GeometryMath.HSG.CO.A.4 / Math.HSG.CO.A.5
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Lesson Idea  Common CoreDeepening Understanding of TransformationsGrade 912 / Math / GeometryMath.HSG.CO.A.4 / Math.HSG.CO.A.5
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Lesson Idea  Common CoreCollaborative Work with TransformationsGrades 912 / Math / GeometryMath.HSG.CO.A.4 / Math.HSG.CO.A.5
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Lesson Idea  Common CoreCommon Issues with Proportional RelationshipsGrade 7 / Math / CollaborationMath.7.RP.A.2 / Math.Practice.MP1
 180
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Lesson Idea  Common CoreDeepening Understanding: Proportional RelationshipsGrade 7 / Math / AssessmentMath.7.RP.A.2 / Math.Practice.MP1
 27
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Lesson Idea  Common CoreReviewing Linear Equations in Two VariablesGrades 812 / Math / AssessmentMath.A.REI.1 / Math.A.CED.2 / Math.Practice.MP2
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Lesson Idea  Common CoreCommon Issues with Linear EquationsGrades 812 / Math / ReasoningMath.A.REI.1 / Math.A.CED.2 / Math.Practice.MP2
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Lesson Idea  Common CoreDeepening Understanding: Linear EquationsGrades 812 / Math / AssessmentMath.A.REI.1 / Math.A.CED.2 / Math.Practice.MP2
 5
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Lesson Idea  Common CoreLearning from Mistakes: Linear EquationsGrade 812 / Math / EquationsMath.A.REI.1 / Math.Practice.MP2 / Math.Practice.MP3
 24
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Lesson Idea  Common CoreCollaborative Work with Proportional RelationshipsGrade 7 / Math / CollaborationMath.7.RP.A.2 / Math.Practice.MP1
 3
 Lesson Objective
 Recognize proportional relationships between two quantities
 Length
 8 min
 Questions to Consider
 How does Ms. Walker encourage her students to take responsibility for their learning?
 Why does Ms. Walker use feedback questions instead of comments when responding to student work?
 What is powerful about grade level teachers looking at student work together?
 Common Core Standards
 Math.7.RP.A.2, Math.Practice.MP1
Teacher & School Info

Teri Walker

Jenny Barrett

Ann Shannon
 School Details
 Twenhofel Middle School Independence, KY
 Population
 734 students
 District Spending
 $7,416
Supporting Materials

Understanding Proportional Relationships Transcript

MAP Lesson Materials

Ann Shannon's Website

Common Core Math Playlist: Engaging Students with “Productive Struggle”