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.
 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 selfcorrect.
 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 5point questions) and any variable expressions (e.g., 5f is the number of points available for the 5point 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 5point questions and 5f is the number of points available for the 5point 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 8point 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?
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. 