Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55015
Solving Formulas for a Variable
Students are given the slope formula and the slope-intercept equation and are asked to solve for specific variables.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, literal equations, slope formula, slope-intercept equation, solving, rearranging, variable
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_SolvingFormulasForAVariable_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 Solving Formulas for a Variable worksheet.
2. The teacher asks follow-up questions as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to apply strategies used in solving equations when rewriting literal equations.
Examples of Student Work at this Level
The student does not understand how to apply inverse properties in literal equations. The student:
Manipulates symbols without any mathematical justification.
page 1 of 4 Attempts to apply properties of equality but is unable to correctly rewrite expressions.
Questions Eliciting Thinking
Suppose you were to solve this equation, a = b + c, for b. What would you do?
What do you know about the properties of equality? For example, what is the Addition Property of Equality? How can it be used to solve equations?
Instructional Implications
Review the four basic operations (i.e., add, subtract, multiply, and divide) and give the student the opportunity to determine the inverse of each. Provide feedback as
needed.
Review the reasoning that is used in solving equations and assist the student in applying it to formulas. Begin with simple three-variable formulas that require only one step
to solve, and then introduce the student to two-step and multistep problems.
Consider implementing MFAS tasks Literal Equations (A-CED.1.4) and Solving Literal Equations (A-CED.1.4) if not used previously.
Moving Forward
Misconception/Error
The student makes errors when solving literal equations that contain grouping symbols.
Examples of Student Work at this Level
The student:
Adds 6 to 5(d – 6) getting 5d.
Rewrites
as k + 6.
Is unable to correctly apply equation solving strategies to solve the third equation for
.
Questions Eliciting Thinking
Suppose you first distributed the 5 in the expression 5(d – 6)? If you then add 6, will you get 5d?
Is (k + 30)/5 equal to k/5 + 30/5? Is k/5 + 30/5 equal to k + 6?
Can you explain how you solved for
in the third problem?
page 2 of 4 Instructional Implications
Assist the student in identifying and correcting his or her error(s). Make explicit the application of properties of equality in solving the equations and relate solving literal
equations to solving linear equations in one variable. Give the student other multistep literal equations that include parentheses and fractions bars as grouping symbols and
ask the student to solve for variables within the grouping symbols. Provide feedback as needed.
Almost There
Misconception/Error
The student makes an error in writing mathematics.
Examples of Student Work at this Level
The student correctly solves each literal equation for the specified variable but:
Does not enclose the expression
Copies the numerator
in parentheses and writes a final answer of
as
=
+
and then continues solving correctly.
Writes subscripts as exponents.
Rewrites
as
.
Questions Eliciting Thinking
Do
and
mean the same thing? How should you have written this expression?
I see that you changed
to
. Did you have a reason for doing that?
What is the difference between a subscript and an exponent? Do they mean the same thing?
Is
equal to
?
Instructional Implications
Provide feedback to the student concerning the specific error made and allow the student to correct his or her work. Provide additional opportunities to solve multistep
equations for specified variables.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
For each problem, the student shows mathematically correct work to solve for the specified variable. The student’s final answers are (or are equivalent to):
1.
2.
3.
page 3 of 4 Questions Eliciting Thinking
Are there other ways you could solve these equations for the specified variables?
Is there more than one right answer for these problems? How is the final answer related to the strategy used to solve for the variable?
Instructional Implications
Challenge the student to write at least two correct forms of the answer for each equation.
Ask the student to justify each step in the process of solving by citing the relevant postulate, property, or theorem to support each step.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Solving Formulas for a Variable 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.912.A-CED.1.4:
Description
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example,
rearrange Ohm’s law V = IR to highlight resistance R. ★
page 4 of 4