Download Writing System Equations

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 59705
Writing System Equations
Students are given word problems and asked to write a pair of simultaneous linear equations that could be used to solve them.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, linear equations, simultaneous equations, system of equations, real-world, solve equations
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_WritingSystemEquations_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 Writing System Equations worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand what it means to write a system of equations in two variables.
Examples of Student Work at this Level
The student:
Attempts to write one or two equations for each problem but does so incorrectly.
page 1 of 4 Attempts to find the missing values in each problem using a numerical approach.
Questions Eliciting Thinking
What are you asked to find in this problem? What are the unknown quantities? Can you assign a variable to each unknown quantity?
If there are two unknowns, how many variables should be in your equation? How many equations will you need to write in order to solve for the variables?
Instructional Implications
Review the definition of a system of linear equations in two variables and provide examples. Explain what it means for an ordered pair to be a solution of a single linear
equation in two variables as well as a solution of a system of linear equations in two variables. Provide an example of a system of equations along with its solution and ask the
student to show that the solution satisfies each equation in the system.
Explain to the student that a system of linear equations in two variables can be used to model and solve problems in which there are two unknown quantities that can be
related by linear equations. Using the first problem in this task, guide the student through the process of identifying and representing the unknown quantities and using
information given in the problem to write equations that relate these quantities. The student may find it helpful to organize information in a table before writing equations.
An example of such a table might look like this:
Then guide the student to write equations that relate the number of questions (f + e = 24) and the number of points (5f + 8e = 150). Be sure the student understands
what 5f and 8e represent in the context of the problem. Provide additional opportunities to write systems of equations from problem contexts.
The student may benefit from reviewing writing linear equations in one variable to represent problem situations. Consider implementing MFAS task Write and Solve an
Equation (7.EE.2.4).
Moving Forward
Misconception/Error
The student is unable to correctly write systems of equations for both problems.
Examples of Student Work at this Level
The student:
Correctly writes a system of equations for one of the problems but not both.
Writes equations that contains errors and cannot self-correct.
page 2 of 4 Is unable to determine a second equation for one of the systems.
Questions Eliciting Thinking
What are the unknowns in this problem? What do your variables represent?
How many independent equations must be written in order to solve for two variables?
What information is given in this problem that you could use to write two equations?
Your equations contain an error. Can you find and correct it?
Instructional Implications
Be sure the student understands that there are two unknowns in each problem and to solve for them, two independent equations involving these unknowns are needed.
Ask the student to explain the specific meaning of any variables used to represent the unknowns (e.g., f is the number of 5-point questions) and any variable expressions
(e.g., 5f is the number of points available for the 5-point questions). Provide feedback to the student with regard to any error(s) made and allow the student to revise
incorrect equations. Provide additional opportunities to write systems of equations from problem contexts.
Note: The Writing System Equations worksheet is editable and can be rewritten with new values and context to give the student further practice.
Almost There
Misconception/Error
The student writes what appears to be a correct system of equations related to the problem, but does not define the variables.
Examples of Student Work at this Level
The student writes two ostensibly correct equations related to the context of the problem, but does not define the variables. Upon questioning, the student struggles to
clearly explain the meaning of each of the variables.
Questions Eliciting Thinking
What does each variable represent in your equation?
What does each variable expression represent?
Instructional Implications
Ask the student to describe the specific meaning of any variables used to represent unknowns and the meaning of any variable expressions used in an equation, (e.g., f is
the number of 5-point questions and 5f is the number of points available for the 5-point questions). Explain that the meaning of the variables should be explicitly stated so
that the reader can interpret and understand the equations. Provide additional opportunities to write systems of equations from problem contexts and ask the student to
clearly define any variables used.
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 defines the variables and writes a correct system of equations for each problem. For the first problem, the student indicates that f represents the number of 5point questions and e represents the number of 8-point questions. The student writes the system as f + e = 24 and 5f + 8e = 150. For the second problem, the student
indicates that p is the cost of a package of pens and h is the cost of a package of highlighters. The student writes the system as 5p + 2h = 8.23 and 4p + 3h = 7.83.
Note: The student may initially neglect to explicitly define the variables but upon questioning is able to do so readily and with ease.
Questions Eliciting Thinking
What method(s) could you use to solve each system of equations?
How can you check to see if a solution you find is a solution of the system?
page 3 of 4 Suppose there were three unknowns in this problem. How many independent equations are needed when there are three unknowns?
Instructional Implications
Expose the student to a wide variety of contexts and structures for writing systems of equations, such as mixture problems, rate problems, investment comparisons, work
ratios, and geometry contexts. Ask the student to both write and solve systems of equations.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Writing System Equations 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.8.EE.3.8:
Description
Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection
of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the
equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because
3x + 2y cannot simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given
coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line
through the second pair.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students work toward meeting this standard, they build on what they know about two-variable linear
equations, and they enlarge the varieties of real-world and mathematical problems they can solve.
page 4 of 4