Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 60910
Write and Solve an Equation
Students are asked to write and solve a two-step equation to model the relationship among variables in a given scenario.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, two-step equation, solve, equation
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WriteAndSolveAnEquation_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 problem on the Write and Solve an Equation worksheet.
1. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is not able to solve a real-world problem by reasoning about the quantities.
Examples of Student Work at this Level
The student attempts a computational strategy to solve the problem but misinterprets the conditions stated in the problem. The student does not attempt to write an
equation.
page 1 of 4 Questions Eliciting Thinking
Can you restate the problem in your own words?
What are you asked to find? What information are you given?
Can you explain how to determine the amount Elijah has paid so far?
Instructional Implications
Guide the student to determine the unknown quantity in the problem and represent it with a variable. Explain the relationship among all quantities given or described. Ask
the student to determine the total amount of money Elijah would pay after one, two, three, and four months of membership. Assist the student in using these calculations
to develop an equation that models the relationship among the quantities given in the problem. Provide additional opportunities to model relationships among quantities with
equations. Begin with situations that can be modeled by equations of the form x + p = q and px = q (6.EE.2.7). Then progress to situations leading to equations of the
form px + q = r and p(x + q) = r.
Review solving equations of the form x + p = q and px = q (6.EE.2.7) and equations of the form px + q = r and p(x + q) = r. Provide additional opportunities to solve word
problems by writing and solving equations of the form x + p = q, px = q, px + q = r, and p(x + q) = r, where p, q, and r are rational numbers.
Moving Forward
Misconception/Error
The student is not able to write an equation to represent the given quantities in a real-world problem.
Examples of Student Work at this Level
The student:
Correctly uses a computational strategy to solve the problem and does not write an equation.
Misinterprets the conditions stated in the problem and writes an incorrect equation such as 55n = 115 or 30m = 90.
Correctly uses a computational strategy but writes an incorrect equation.
Questions Eliciting Thinking
What do you think is meant by “write an equation?”
What are you asked to find in this problem? If you represent it with a variable, can you write an equation that models the relationship among the quantities described in the
problem?
Instructional Implications
Work with the student on modeling relationships among quantities with equations. Begin with situations that can be modeled by equations of the form x + p = q and px =
q (6.EE.2.7). Then progress to situations leading to equations of the form px + q = r and p(x + q) = r. Ask the student to explicitly describe the meaning of any variables
used in the equations. 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 months of membership, then 30x represents the cost of the monthly fees paid for x months, and 30x + 25 represents the total cost
of gym membership which gives rise to the equation 30x + 25 = 115.
Use the student’s numerical work, if possible, as a starting point for the development of an equation. For example, if the student completed a series of computations, such
as 30(1) + 25 = 55; 30(2) + 25 = 85; 30(3) + 25 = 115, ask the student to justify the form of the computations. Then guide the student to replace the varying quantity
in parentheses with a variable to write the equation.
If necessary, review solving equations of the form x + p = q and px = q (6.EE.2.7) and equations of the form px + q = r and p(x + q) = r. Provide additional opportunities
to solve word problems by writing and solving equations of the form x + p = q, px = q, px + q = r, and p(x + q) = r, where p, q, and r are rational numbers.
Consider using the MFAS task Writing Real World Expressions (6.EE.2.6) and various MFAS 6.EE.2.7 tasks for additional assessment.
page 2 of 4 Almost There
Misconception/Error
The student is unable to use the equation to solve the problem.
Examples of Student Work at this Level
The student writes the correct equation but then:
Solves it numerically by guess and check and/or working backwards.
Solves it incorrectly, such as combining unlike terms of 25 and 30m to get 55m.
Writes mathematically incorrect statements while solving (e.g., 30 × 3 = 90 + 25 = 115 or 115 ­ 25 = 90 ÷ 3 = 30).
Gives the numerical answer of “3” with no context of “months.”
Misinterprets the answer as $3 per month.
Makes mathematical errors in the solution process.
Questions Eliciting Thinking
Can you solve your equation?
What would the solution of your equation indicate about the answer to the question posed in this problem?
Could you have written an equation without having solved the problem first?
Instructional Implications
Explain to the student that writing and solving an equation is an effective strategy for solving mathematical problems. In this problem, the objective in writing and solving
the equation is to answer the question posed in the problem. Ask the student to solve his or her equation and explain what the solution means in the context of the
problem. If needed, review solving equations of the form px + q = r.
Provide additional opportunities to solve word problems by writing and solving equations of the form px + q = r, where p, q, and r are rational numbers. Have the student
explain the meaning of the variable in context and the significance of the solution in solving the word problem.
Consider implementing the MFAS task Algebra or Arithmetic? (7.EE.2.4).
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 and solves an equation to determine Elijah paid for three months at the gym.
The student may use any variable when writing an equation such as:
page 3 of 4 25 + 30m = 115
115 = 30m + 25
Questions Eliciting Thinking
What does the variable stand for?
What does the solution mean?
Is there only one solution?
How would changing the initial fee change the equation?
How would the equation change if you knew the number of months is five but you had to find how much he pays each month?
Instructional Implications
Challenge the student with problem contexts that require multistep equations to solve.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Write and Solve an Equation 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 4 of 4