Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 60566
Identifying Constant of Proportionality in Equations
Students are asked to identify and explain the constant of proportionality in three different equations.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rate, unit rate, constant of proportionality, equation
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_IdentifyingConstantOfProportionalityInEquations_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Identifying Constant of Proportionality in Equations worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly identify the constant of proportionality.
Examples of Student Work at this Level
The student:
Identifies a variable as the constant (e.g., identifies s as the constant of proportionality given P = 4s).
Identifies a term of the equation as the constant of proportionality (e.g., identifies 4s as the constant of proportionality given P = 4s).
Does not identify a constant of proportionality but attempts to show or explain how the variables are related.
page 1 of 4 Questions Eliciting Thinking
What does the constant of proportionality mean?
What does the equation of a proportional relationship look like? Which part is the constant of proportionality?
How is perimeter of a square found? What is the meaning of the four in the formula?
Instructional Implications
Make explicit the difference between a variable and a constant. Introduce the concept of the constant of proportionality and its role in describing the relationship between
variables that are proportionally related. Help the student recognize that if there is a proportional relationship between the variables, then there is a constant factor that
relates the pairs of associated values. In other words, the value of one variable can always be found by multiplying the value of the other variable by the constant of
proportionality. Demonstrate this with a table of values for one of the proportional relationships in this task. Then relate the constant of proportionality to the equation.
Show the student that proportional relationships can be modeled by equations of the form y = cx where c is the constant of proportionality. Provide additional opportunities
for the student to find and interpret the constant of proportionality in equations.
Making Progress
Misconception/Error
The student is able to identify the constant of proportionality but cannot explain its meaning in context.
Examples of Student Work at this Level
The student correctly identifies the constant of proportionality in each equation but:
Does not attempt any explanation.
Does not explain adequately.
page 2 of 4 Questions Eliciting Thinking
You identified the constant of proportionality correctly. How did you determine your answer?
Is the constant of proportionality the same as the unit rate? What is a unit rate?
What does the constant of proportionality tell you about the relationship between the variables?
Instructional Implications
Assist the student in understanding the constant of proportionality as a number by which the value of one variable can always be multiplied to find the corresponding value
of the other variable in a proportional relationship. Assist the student in using the context of the proportional relationship to explain the relationship between the variables in
terms of the constant of proportionality. Model an explanation of the constant of proportionality for the first problem and ask the student to develop explanations for the
two remaining problems. Give the student additional opportunities to identify the constant of proportionality in equations and explain their meaning in context.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly identifies and explains the constant of proportionality in each problem:
The student identifies four as the constant of proportionality because it is the factor by which you multiply the length of a side to get the perimeter of a square (because
there are four congruent sides to a square). The student explains that the perimeter will increase by four units for every one unit that the side increases.
The student identifies
as the constant of proportionality because it is the factor by which you multiply the diameter of a circle to get its circumference. The student
explains that the circumference will increase by
The student identifies
radius will increase by
for every one unit that the diameter increases.
as the constant of proportionality because it is the factor by which you multiply the diameter to get the radius. The student explains that the
unit for every one unit the diameter increases.
Questions Eliciting Thinking
The circumference of a circle is proportional to its radius. This relationship can be expressed by the equation C =
. What is the constant of proportionality and what
does it mean?
If you graphed these equations what would they look like?
Which point on the graph has the constant of proportionality as one of its coordinates?
Instructional Implications
Pair the student with a Making Progress partner. Provide the pair with a set of equations that represent proportional relationships. Challenge the pair to identify the constant
of proportionality in each equation and explain its meaning in context. Encourage the pair to compare their answers and reconcile any differences.
Consider using the MFAS task Serving Size (7.RP.1.2).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Identifying Constant of Proportionality in Equations worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
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.
page 3 of 4 MAFS.7.RP.1.2:
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.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
Students in grade 7 grow in their ability to recognize, represent, and analyze proportional relationships in various
ways, including by using tables, graphs, and equations.
page 4 of 4