Getting Started 
Misconception/Error The student does not demonstrate an understanding of what it means for a number to be a solution of an equation. 
Examples of Student Work at this Level The student:
 Adds two constants in the equation and presents their sum as a solution.
 Substitutes a value for x into an equation and then adds all quantities in the equation.

Questions Eliciting Thinking What does an equation mean? How is it different than an expression? What does the variable represent in the equation?
What does the equal sign between the two expressions mean? What must be true of the expressions on each side of the equal sign?
What does it mean for a number to be a solution of an equation? How could you check to see which numbers are solutions? 
Instructional Implications Review what it means for a value to be a solution of an equation. Given an equation, provide examples of values that are solutions as well as values that are not solutions. Demonstrate how to use substitution to test values to determine whether or not they are solutions. Provide additional equations and sets of values and ask the student to determine if any are solutions. Assist the student in using the order of operations to evaluate expressions within the equation. Guide the student to carefully and systematically check each value and to write the appropriate corresponding work on the paper.
If necessary, clarify the meaning of expressions such as 8x. Be sure the student understands that 8x means 8 times x. Also distinguish between and . Rewrite each as an equivalent division problem.
Consider using MFAS task Solutions of Equations (6.EE.2.5) to allow the student the opportunity to explain what it means for a number to be a solution of an equation. 
Moving Forward 
Misconception/Error The student makes errors when calculating with rational numbers or variable expressions. 
Examples of Student Work at this Level The student does not correctly calculate with decimal numbers by:
 Misplacing the decimal point, e.g., getting the value 2.13 for 8.5 + 12.8, rather than 21.3.
 Rightjustifying the digits of the numbers without consideration of place value, e.g., getting the value 8.7 when adding 14 and 7.3.
 Misinterprets as , giving an answer of three (or 3 and 48).
 Misinterprets the variable as one digit in a number (e.g., after substituting one for x in 8x, the student writes “81” rather than “eight times one”).

Questions Eliciting Thinking What is the value of the digits 7, 3, 1, and 4? Does place value matter when you add? How can you set up the problem so you add the digits that have the same place value?
Can you estimate what the sum of 14 and 7.3 will be? Is your answer close to your estimate?
Does equal ? What is different between these quotients? Which one is greater than one? Can you check the other numbers that were given to see if any of them will make the equation true?
What does the expression 8x mean? What does the x represent? What operation is implied in this expression? 
Instructional Implications Review with the student the meaning and use of place value when adding and subtracting decimal numbers. Guide the student to estimate an answer before making the calculation and to compare the calculated answer to the estimate.
Guide the student to understand the order of division implied in simple division statements and in fractions. Give the student a general statement to follow such as “. That means how many times q divides into p.” Also address rewriting fractions as long division problems, since that is the method the student will likely use to evaluate fractions or convert them to decimals. Ask the student to redo the problems on the Finding Solutions of Equations worksheet. Provide feedback as needed.
Note: The Finding Solutions of Equations worksheet is editable and can be rewritten with new equations and number sets to give the student further practice. 
Almost There 
Misconception/Error The student does not find all the solutions for the identity equation. 
Examples of Student Work at this Level The student only chooses one (or two) of the values as a solution for the third equation, without checking to see if the other numbers may also be solutions.

Questions Eliciting Thinking Why did you choose this as your answer? Did you check any of the other numbers? Is it possible for an equation to have more than one answer? 
Instructional Implications Provide the student with additional experience with equations that contain more than one solution such as identities, quadratic, and absolute value equations. Provide examples of equations of these types along with sets of values and ask the student to determine if any of the values are solutions. Be sure to include equations with one solution and no solutions so the student understands that equations may have any number of 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 solves each equation or checks each of the given values to determine the solutions of the equations. The student finds the following solutions:
 x = 8.5
 x = 48
 x = 1, 20, 300, 4000 or “x can equal any number.”

Questions Eliciting Thinking Why do some equations have many solutions and other equations have only one solution? Is it possible for an equation to have no solutions?
Can you write a new equation for the given ones that would result in one of the other listed numbers being a solution?
If the answer choices were not given to you, can you think of a way you might find the solution to one of these equations? 
Instructional Implications Provide examples of linear inequalities along with sets of values and ask the student to determine if any of the values are solutions of the inequalities. Challenge the student with compound inequalities such as x + 5 < 12 and 3x > 9 and ask the student to find several examples of values that are solutions and several examples of values that are not solutions. 