Common Issues with Proportional Relationships

Grade 7 / Math / Collaboration
CCSS: Math.7.RP.A.2 Math.Practice.MP1

Common Core State Standards

Math

Math

7

Grade 7

RP

Ratios & Proportional Relationships

A

Analyze proportional relationships and use them to solve real-world 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)
Engaging Students with "Productive Struggle" Series
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Lesson Objective
Determine if two quantities are in a proportional relationship
Length
10 min
Questions to Consider
Why does Ms. Walker have the students work in pairs?
How does Ms. Walker support students’ thinking and reasoning?
In what ways are the students owning the learning in this lesson?
Common Core Standards
Math.7.RP.A.2, Math.Practice.MP1

Supporting Materials

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  • Common Issues with Proportional Relationships Transcript

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Lesson Idea (Common Core) Common Issues with Proportional Relationships

Grade 7 / Math / Collaboration

Common Issues with Proportional Relationships