Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 60917
Write, Solve and Graph an Inequality
Students are asked to write, solve, and graph a two-step inequality.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, two-step inequality, graph, solve inequality
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WriteSolveAndGraphAnInequality_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 Write, Solve, and Graph an Inequality worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student cannot write a meaningful inequality to represent the given constraints.
Examples of Student Work at this Level
The student:
Uses a direct numerical approach to solve rather than writing an inequality.
page 1 of 6 Writes an expression or equation instead of an inequality.
Does not use a variable in the inequality statement, writing
+ 32 = -109.3.
Uses the given value of -109.3 twice or in the wrong place in the inequality, writing
Reverses the positions of the Fahrenheit temperature and Celsius variable, writing
(-109.3) + 32 = -109.3.
(-109.3) + 32 = C.
Questions Eliciting Thinking
What does it mean to write an inequality?
Is the problem going to have one or more than one solution? What symbol can you use to show this?
Do you know the Celsius temperature or do you know the Fahrenheit temperature? Which are you solving for? What variable should you use and where does it go?
Instructional Implications
Work with the student on modeling relationships among quantities with inequalities. Begin with situations that can be modeled by one-step inequalities. Then progress to
situations leading to two-step inequalities. Ask the student to explicitly describe the meaning of any variables used in the inequality. Emphasize the relationship between
algebraic expressions and the quantities they represent in the context of the situations in which they arise. For example, if x represents the number of degrees Celsius, then
x + 32 represents the degrees Fahrenheit.
Use the student’s numerical work, if possible, as a starting point for the development of an inequality. For example, if the student completed a series of computations, such
as ­109.3 – 32 = ­141.3; ­141.3(5) = ­706.5; ­706.5 ÷ 9 = ­78.5, guide the student to replace the final answer, ­78.5, with a variable and work backwards to develop the
inequality.
If necessary, review solving one-step and two-step equations and inequalities. Provide additional opportunities to solve word problems by writing, solving, and graphing
inequalities involving rational numbers.
Moving Forward
Misconception/Error
The student is unable to solve the inequality.
Examples of Student Work at this Level
The student correctly writes an inequality to represent the problem situation but is unable to correctly solve the inequality. The student:
page 2 of 6 Changes the inequality to an equation in some step of the solution process.
Makes one or more errors, including errors with rational number or integer operations.
“Drops” the variable C rather than solving for it.
Uses an incorrect method to solve the inequality (e.g., dividing only some of the terms by
in the first step).
Uses a “guess­and­check” or a work­backwards numerical approach to solve the inequality, rather than solving the inequality algebraically.
Questions Eliciting Thinking
What does the inequality symbol mean? Does an equal sign have the same meaning?
What steps did you take to solve this? Are they the same steps you would take to solve a two-step equation?
How should you add/subtract decimals? How do you multiply/divide decimals?
Instructional Implications
Provide direct feedback on any errors that the student might have made and allow the student to correct them. Review solving one-step and two-step equations and
inequalities. Provide additional opportunities to solve word problems by writing, solving, and graphing inequalities involving rational numbers. Remind the student to use
substitution to check solutions in the original inequality.
Review operations with rational numbers and provide frequent opportunities to add, subtract, multiply, and divide rational numbers in a variety of forms. Explain that dividing
by a fraction is equivalent to multiplying by the reciprocal of the fraction. Using the inequality in this task, demonstrate how this idea can be used in the process of solving.
Suggest using two steps to multiply both sides of
C
-141.3 by
(e.g., by first multiplying both sides of the inequality by five, then dividing each side of the inequality
by nine).
Consider implementing the MFAS tasks Rational Addition and Subtraction (7.NS.1.1) or Applying Rational Number Properties (7.NS.1.2) to provide additional review for
students struggling with rational number operations.
Making Progress
Misconception/Error
The student is unable to correctly graph the inequality.
Examples of Student Work at this Level
The student correctly writes and solves the inequality but makes an error when graphing the solution by:
Scaling the number line improperly.
page 3 of 6 Giving the positive and negative numbers different scales.
Using an open rather than a closed circle (or uses no circle at all).
Graphing x
-109.3 rather than x
-78.5.
Not shading the number line to indicate all possible solution values.
Not giving the number line a numerical scale at all.
Questions Eliciting Thinking
On the number line, do the negative numbers get larger as you move to the right or to the left?
What does an open or closed circle indicate on a graph? How do you choose which one to use?
How do you decide which direction to shade? What does the arrow mean on the graph of an inequality? Is there a way to use a specific value to check if your shading is
correct?
What does the inequality symbol mean? Does it include numbers that are greater than or less than the given number? Does it also include the exact value of the given
number? How can you show this on the graph?
Instructional Implications
Provide instruction on graphing inequalities on the number line. Be sure the student understands the conventions in graphing inequalities and their meaning (e.g., the use of
an open versus closed dot, the direction of shading, and the arrow). If necessary, provide instruction on the meaning of the inequality symbols. Have the student graph a
variety of inequalities (including some with the variable written to the right of the inequality symbol) and write inequalities to match given graphs.
Review what it means for a number to be a solution of an inequality. Give an example of an inequality and provide a set of numbers, some of which are not solutions.
Demonstrate how to use substitution to test numbers to determine whether or not they are solutions. Guide the student to graph “all solutions” by shading those in the
solution set that make the inequality true.
Almost There
Misconception/Error
The student makes minor errors in writing, solving, or graphing the inequality.
Examples of Student Work at this Level
The student makes one minor error but all other work is correct given the error. For example, the student:
Makes a calculation error in some step of the problem.
page 4 of 6 Changes
to a decimal incorrectly.
Drops the negative symbol during some step of the problem.
Misinterprets the answer as having only one solution, writing “the temperature must be ­78.5.”
Reverses the inequality symbol in the initial equation.
Partially solves the inequality using a numerical approach before writing it.
Questions Eliciting Thinking
Can you review your work and look for any errors with your calculations?
What does the inequality mean? How many solutions does it represent?
Can you write the inequality without first solving for C?
Instructional Implications
Provide direct feedback to the student concerning any error made and allow the student to revise his or her work accordingly. If necessary, ask the student to use the
graph to find an example of a solution and to substitute this solution into the original inequality to determine if it satisfies the inequality. Provide additional opportunities to
solve inequalities with rational coefficients and remind the student to check solutions.
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 writes the inequality
C + 32
-109.3, solves it to get C
­78.5° , scales the number line appropriately, and graphs the solutions using a closed dot at ­
78.5 and shading to the left.
page 5 of 6 Questions Eliciting Thinking
What does the solution mean?
Is there only one solution? If not, what are some examples of other solutions?
Is -78 a solution? Is -79 a solution? Is -78.5 a solution?
Instructional Implications
Introduce the student to compound inequalities. Give the student a statement such as, “The various routes that Kelvin can drive to work range from 8.2 miles to 9.7 miles
in length,” and ask the student to represent the lengths, m, as a compound inequality (e.g., in the form 8.2
m
9.7 or in the form m
8.2 and m
9.7). Guide the
student to graph the inequality on the number line and verbally describe the values that satisfy it. Gradually increase the complexity of the problem so the student must first
write and solve a one- or two-step inequality for a given context.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Write, Solve, and Graph an Inequality 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.EE.2.4:
Description
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and
inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific
rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution,
identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54
cm. Its length is 6 cm. What is its width?
b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific
rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For
example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at
least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, students
solve the equations fluently. This will require fluency with rational number arithmetic (7.NS.1.1–1.3), as well as
fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients
(7.EE.1.1).
Examples of Opportunities for In-Depth Focus
Work toward meeting this standard builds on the work that led to meeting 6.EE.2.7 and prepares students for the
work that will lead to meeting 8.EE.3.7.
page 6 of 6