7A11
7.A.1.1 Identify a relationship between two varying quantities, x, and y, as proportional if it can be expressed in the form y/x = k or y= kx; distinguish proportional relationships from nonproportional relationships.
In a Nutshell
A relationship is proportional if one compared quantity divided by the other produces a constant rate of change, which is noted as a constant of proportionality (k). Another way relationships can be proportional is if one compared quantity multiplied by the constant of proportionality produces the other compared quantity each time ( y=kx).
Student Actions

Teacher Actions


Develop a Productive Mathematical Disposition by looking for and making use of patterns to identify proportional, inversely proportional, and other types of relationships as a strategy for becoming resilient and effective problem solvers.

Develop the ability to communicate mathematically explaining why a relationship is proportional.
 Develop Accurate and Appropriate Procedural Fluency when choosing the most appropriate and efficient procedures to express a proportional relationship in the form y/x=k or y=kx.


Implement tasks that promote reasoning and problemsolving with possibilities for students to explore patterns of relationships between quantities and develop problemsolving strategies for distinguishing between proportional and nonproportional relationships.

Elicit and use evidence of student thinking when students compare and connect mathematical representations of proportional relationships, such as graphs, equations, and tables, to determine if proportional relationships exist.
 Pose purposeful questions that allow students to explain their thinking about why the relationship between quantities is proportional.

Key Understandings

Misconceptions


A constant of proportionality indicates a proportional relationship between quantities.

The constant of proportionality can be found by dividing two compared values (quantities) with the equation y/x=k and checking for a constant multiple or divisor between compared values (quantities)
 The equation for any proportional relationship is expressed y= kx, where x and y represent the related quantities (compared values) and k is the constant of proportionality.


Students may believe values must be multiples of one another in order for there to be a proportional relationship.

Students may believe that any relationship between numbers is proportional.

Students may incorrectly compare values (quantities) when dividing. For example, x/y=k

Students may not be able to distinguish which value (quantity) represents independent (x) and dependent (y) when determining a constant of proportionality.

Knowledge Connections

Prior Knowledge

Leads to


Identify and use ratios to compare and relate quantities in multiple ways. (6.N.3.1)

Determine the unit rate for ratios. (6.N.3.2)

Apply the relationship between ratios, equivalent fractions, and unit rates to solve problems. (6.N.3.3)

Multiply and divide fractions and decimals using efficient and generalizable procedures. (6.N.4.3)


Identify, describe, and analyze linear relationships between two variables. (PA.A.2.2)

Use substitution to simplify and evaluate algebraic expressions. (PA.A.3.1)

Sample Assessment Items

The Oklahoma State Department of Education is releasing sample assessment items to illustrate how state assessments might be designed to measure specific learning standards/objectives. These examples are intended to provide teachers and students with a clearer understanding of how the state assesses Oklahoma's academic standards and their objectives. It is important to note that these sample items are not intended to be used for diagnostic or predictive purposes. Ways to incorporate the items.

OKMath Framework Introduction
7th Grade Introduction
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