Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 123010
Writing Absolute Value Equations
Students are asked to solve a set of absolute value equations.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Keywords: MFAS, absolute value, equation, word problem
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WritingAbsoluteValueEquations_Worksheet.docx
MFAS_WritingAbsoluteValueEquations_Worksheet.pdf
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 Writing Absolute Value Equations worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand how to write absolute value equations.
Examples of Student Work at this Level
The student does not write either equation correctly.
page 1 of 3 Questions Eliciting Thinking
Can you explain why you wrote your equation the way you did?
You wrote the equation in more than one way. Are the two ways equivalent?
How would you write “the absolute value of 25”? How can you write the absolute value of an unknown number?
Instructional Implications
Review the concept of absolute value and how it is written. Emphasize that the concept of absolute value can be used to describe the difference between two numbers.
Model using absolute value to represent distances between values on the number line. For example, represent a number’s distance from zero as |x – 0| or |x|. Explain that
distance is usually represented by a positive number, so if x is unknown, its distance from zero is best represented as |x| which represents a nonnegative value. Generalize
this explanation to the distance between two numbers on the number line, for example, x and 12. Explain that x could be greater than 12 or x could be less than 12. Either
way, |x – 12| (or |12 – x|) represents the distance between x and 12.
Provide examples of absolute value equations and ask the student to solve them. Ensure that the student uses absolute value notation correctly and represents solutions of
absolute value equations appropriately (e.g., as x = 3 or x = -3 rather than |x| = ±3).
Next, introduce the student to contexts in which absolute value is needed to represent described quantities, similar to the second problem on the worksheet. Model using
absolute value to represent such quantities. Provide additional contexts and ask the student to write expressions or equations to model quantities or relationships described.
Moving Forward
Misconception/Error
The student is unable to represent a difference using absolute value.
Examples of Student Work at this Level
The student correctly writes and solves the absolute value equation described in the first problem. However, the student is unable to correctly write an absolute value
equation to represent the described difference.
Questions Eliciting Thinking
Can you reread the first sentence of the second problem? A difference is described between two values. What are these two values? What is the difference?
Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees?
Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?
Instructional Implications
Model using absolute value to represent differences between two numbers. For example, represent the difference between x and 12 as |x – 12| or |12 – x|. Emphasize
that each expression simply means the difference between x and 12. Evaluate the expression |x – 12| for a sample of values some of which are less than 12 and some of
which are greater than 12 to demonstrate how the expression represents the difference between a particular value and 12.
Guide the student to write an equation to represent the relationship described in the second problem. Ask the student to solve the equation and provide feedback. Then
explain why the equation the student originally wrote does not model the relationship described in the problem. For example, explain that an equation such as | | = 74 – 6
means that the difference between some value
and zero is 74 – 6 or 68 so that = 68 or
the problem to see if each fits the condition given in the problem (i.e., the difference between
= -68. Ask the student to consider these two solutions in the context of
and 74 is six).
Provide additional opportunities for the student to write and solve absolute value equations.
Almost There
Misconception/Error
The student correctly writes both equations but errs in solving the first equation or writing its solutions.
Examples of Student Work at this Level
The student:
Finds only one of the solutions of the first equation.
Writes the solutions of the first equation using absolute value symbols.
page 2 of 3 Questions Eliciting Thinking
How many solutions can an absolute value equation have? Do you think you found all of the solutions of the first equation?
What are the solutions of the first equation? Should you use absolute value symbols to show the solutions?
Instructional Implications
Provide feedback to the student concerning any errors made. If needed, clarify the difference between an absolute value equation and the statement of its solutions.
Consider implementing MFAS task Solving Absolute Value Equations (A-CED.1.1).
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 writes and solves the first equation: |x| = 17.4 so that x = 17.4 or x = -17.4. The student correctly writes the second equation as |
– 74| = 6 or
|74 – | = 6.
Questions Eliciting Thinking
Why was it necessary to use absolute value to write this equation?
How many solutions do you think this equation has? Why are there two solutions? What would they mean in this context?
Instructional Implications
Ask the student to solve the second equation and interpret the solutions in the context of the problem.
Ask the student to identify and write as many equivalent forms of the equation as possible. Then have the student solve each equation to show that they are equivalent.
Consider implementing MFAS task Writing Absolute Value Inequalities (A-CED.1.1).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
• Writing Absolute Value Equations worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.A-CED.1.1:
Description
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear
and quadratic functions, and simple rational, absolute, and exponential functions. ★
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