Download Computing Unit Rates

Computing Unit Rates
Resource ID#: 55436
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to compute and interpret unit rates in two different ways from values that
include fractions and mixed numbers.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, ratio, rate, unit rate
Instructional Component Type(s): Formative Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ComputingUnitRates_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 Computing Unit Rates
worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student writes ratios that are not unit rates.
Examples of Student Work at this Level
The student:

Writes the ratio using the given values, and then reverses the order to get a second ratio (e.g.,
to
an

Changes the ratio
to
to decimal form, then puts the number one under each part of the gear ratio, fo
Questions Eliciting Thinking
What is a ratio? What two quantities are being compared in this problem? How are they being compared?
Do you know what a unit rate is?
What do you think the ratio
to
How would you interpret the ratio
means in the context of this problem?
? (Ask only if the student wrote such a ratio.)
Instructional Implications
Review the concept of ratio and point out that the associated quantities in ratios may or may not contain the sam
rates and unit rates. Model how to determine unit rates from given rates. Be sure the student understands the con
Consider implementing CPALMS lesson plan It’s Carnival Time! (Resource ID: 47394), and then assessing the
Next, model finding unit rates with quantities that include fractions and mixed numbers. Review operations with
describing the meaning.
Consider implementing MFAS tasks Unit Rate Area (7.RP.1.1) and Unit Rate Length (7.RP.1.1).
Moving Forward
Misconception/Error
The student is unable to determine the second unit rate.
Examples of Student Work at this Level
The student correctly writes 3 to 1 for the first unit rate, but:

Reverses it and writes 1 to 3 for the second unit rate.

Cannot determine the second unit rate.
Questions Eliciting Thinking
Can you tell me what the rate 3:1 means? Can you rewrite this rate so that it tells us how many times the larger g
Do ratios and rates have to contain only whole numbers?
Instructional Implications
Clarify the definition of unit rate as a comparison of some quantity to one unit of another quantity. Emphasize th
describing the meaning of unit rates in context. Using a table, tape diagram or double number line, model how to
Consider implementing MFAS tasks Explaining Rates (6.RP.1.2) and Unit Rate Length (7.RP.1.1).
Almost There
Misconception/Error
The student is unable to correctly interpret the unit rates in the context of the problem.
Examples of Student Work at this Level
The student:

Explains the procedure used for calculating the unit rates rather than interpreting them in the context of t

Does not use ratio language when interpreting the rates and says, "The smaller gear turns three times and
Questions Eliciting Thinking
What does 3:1 mean in the context of this problem?
How are the gears related? What does 3:1 mean about the relationship between how the gears turn?
Instructional Implications
Model explaining the meaning of rates in the context of problems. Use unit rate language (e.g., "for each one," "
When the student is ready, consider editing the worksheet to include different rational values and then implemen
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:
to 1 or 0.3333… to 1 and

Writes both unit rates correctly: 3 to 1 and

Explains that the smaller gear turns three times for each one turn of the larger gear and the larger gear tur
Questions Eliciting Thinking
How did you determine the unit rates?
If a student said the unit rates are 3:1 and 1:3, what did that student do wrong? Why?
Why does the second part of the ratio have to be one?
Instructional Implications
Have the student use the unit rate to solve problems (e.g., "How many times will the smaller gear rotate when th
Pair the student with a Moving Forward student. Have the student explain to the Moving Forward partner how t
Challenge the student with the following problem: If Gear A turns n times for every one turn of Gear B, then ho
ACCOMMODATIONS & RECOMMENDATIONS

Special Materials Needed:
o
Computing Unit Rates 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
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.RP.1.1:
Description
Compute unit rates associated with ratios of fractions, including
ratios of lengths, areas and other quantities measured in like or
different units. For example, if a person walks 1/2 mile in each
1/4 hour, compute the unit rate as the complex fraction 1/2/1/4
miles per hour, equivalently 2 miles per hour.