Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55963
Babysitting Graph
Students are given a graph that models the hourly earnings of a babysitter and are asked to interpret ordered pairs in context.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, proportion, rate, unit rate, ordered pair
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_BabysittingGraph_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 Babysitting Graph worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to interpret ordered pairs in the context of the problem or provides only partial interpretations.
Examples of Student Work at this Level
The student:
Says that (0, 0) is where the graph starts and (6, 45) is the highest point on the graph.
page 1 of 3 Says that (0, 0) is the origin and (6, 45) is the “stop point.” Provides incorrect or incomplete interpretations.
Questions Eliciting Thinking
Can you explain what the x-axis and the y-axis represent in the context of the problem?
What does the first coordinate in an ordered pair represent in this problem? What does the second coordinate in an ordered pair represent in this problem?
What does the graph tell you about the relationship between the number of hours Sandy babysits and how much she earns?
Instructional Implications
If necessary, review graphing in the coordinate plane. Using the problem context and graph in this task, make explicit the variables represented on each axis and how the
graph shows the relationship between them. Model interpreting an ordered pair by saying, “When Sandy babysits 6 hours, she earns $45.” Ask the student to use the
graph to find Sandy’s earnings for 2 hours of babysitting and the number of hours of babysitting for which Sandy would earn $30. Then ask the student to interpret the
ordered pair (5, 37.50).
Then provide additional problem contexts and graphs of proportional relationships and ask the student to interpret given ordered pairs including (0, 0) and the point whose
x-coordinate is one. Guide the student to observe that the y-coordinate of the point whose x-coordinate is one is both a unit rate and the constant of proportionality.
Making Progress
Misconception/Error
The student is unable to use the graph to find the hourly rate.
Examples of Student Work at this Level
The student:
Incorrectly identifies a point on the graph and uses it to determine the hourly rate.
Identifies the point (2, 15) [or (15, 2)] and determines the hourly rate is $15.
Questions Eliciting Thinking
Where on the graph did you look to find the charge per hour?
What does an hourly rate or hourly payment for work mean?
If we wanted to write an ordered pair to represent Sandy’s hourly rate, what would its x-coordinate be?
Instructional Implications
If necessary, explain what hourly rate means and that the hourly rate is the y-coordinate of the point whose x-coordinate is one. Use rate language to interpret this point,
(e.g., say, “Sandy’s hourly rate of $7.50 means that for each hour that she babysits, she earns $7.50.”). Provide additional problem contexts and graphs of proportional
relationships and ask the student to interpret given ordered pairs including (0, 0) and the point whose x-coordinate is one. Guide the student to observe that the ycoordinate of the point whose x-coordinate is one is both a unit rate and the constant of proportionality.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
page 2 of 3 Examples of Student Work at this Level
The student explains that the ordered pair (0, 0) means that when Sandy babysits for zero hours, she earns zero dollars; (6, 45) means that Sandy earns $45 for 6 hours of
babysitting; and Sandy charges $7.50 per hour.
Questions Eliciting Thinking
You wrote “6 hours and 45 dollars” on your paper. Can you tell me what this means in the context of this problem?
Do you know what the constant of proportionality is in this problem?
Can you represent the relationship between the number of hours Sandy babysits and how much she earns with an equation?
Why do you suppose the negative part of the graph was not shown?
If you had not been told the amount Sandy earns from babysitting is proportional to the number of hours she works, could you have determined this just from the graph?
Instructional Implications
Give a verbal description of a proportional relationship and challenge the student to represent the relationship with a table, graph, and equation. Encourage the student to
identify the constant of proportionality and to describe its meaning in context.
Challenge the student to write an equation representing the proportional relationship displayed in the graph. Consider implementing MFAS task Writing An Equation
(7.RP.1.2).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Babysitting Graph 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
MAFS.7.RP.1.2:
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.
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 3 of 3