Getting Started 
Misconception/Error The student makes significant algebraic errors when attempting to solve a multistep equation. 
Examples of Student Work at this Level The student:
 Attempts to combine unlike terms.
 Multiplies both sides of the equation by the wrong value.
 Uses a different operation (in the same step) on each side of the equation.

Questions Eliciting Thinking How are these terms alike and different? What does it mean to â€ścombine like terms?â€ť How do you decide which terms are alike?
Why did you choose to do this operation in this step? Did you do the same operation on both sides of your equation? 
Instructional Implications Review the order of operations conventions, the Distributive Property, and combining like terms. Be sure to include terms in which the coefficient of the variable is 1 and 1. Also include expressions in which 1 can be distributed, such as â€“(3x â€“ 2) or 7 â€“ (2x + 1).
Be sure the student understands what it means to solve an equation. If needed, provide instruction on solving equations using the Addition, Subtraction, Multiplication, and Division Properties of Equality. Model for the student the order the properties should be used to solve equations.
Consider using the MFAS tasks 7.EE.1.1 and 7.EE.1.2 for further assessment of work with equivalent expressions.
Provide additional opportunities to solve equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. 
Moving Forward 
Misconception/Error The student makes errors using the Distributive Property. 
Examples of Student Work at this Level The student does not distribute to both terms in the parentheses.

Questions Eliciting Thinking Can you show me how you distributed in this step of work? What exactly do you need to multiply in each step of the process? 
Instructional Implications Review the Distributive Property and provide opportunities to use this property to expand expressions with integer coefficients and constants. Guide the student to carefully write out pairs of factors to be multiplied before finding their products. For example, rewrite 3(2x â€“ 5) as 3[2x + (5)] and then as [(3)(2x) + (3)(5)] before evaluating the products. Caution the student to be mindful of the signs of the factors, particularly when subtraction is involved. Eventually reintroduce expressions with rational coefficients and constants.
Show the student that equations of the form p(x + q) = r can also be solved by first dividing both sides of the equation by p. Discuss with the student when this might be a more advantageous approach.
Provide additional opportunities to solve equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. 
Almost There 
Misconception/Error The student makes errors with operations on rational numbers. 
Examples of Student Work at this Level The student makes errors with rational numbers. For example, the student:
 Converts a fraction to a decimal incorrectly.
 Only multiplies numerators when multiplying two fractions (e.g., Â Ă— Â = ).
 Calculates Â Ă— Â by multiplying Â by .
 Calculates 20 Ă· Â by dividing 20 by 4.
 Errs in performing operations with positive and negative numbers.

Questions Eliciting Thinking Can you explain how you converted this fraction (e.g., )Â to a decimal (e.g., 0.6)?
Can you explain how you multiplied (or divided) these fractions?
How did you add the negative and positive numbers? How can you check your work to see if your answer makes sense?
What is the sign of the product of two negative numbers? 
Instructional Implications Review converting fractions to decimals. Discuss with the student when it might be more advantageous to work with fractions rather than convert to decimals.
Review operations with rational numbers focusing on computations with positive and negative fractions and mixed numbers.
Provide additional opportunities to solve equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
Note: The Solve Equations worksheet is editable and can be rewritten with new coefficients and operations for later assessment. 
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 correctly getting xÂ = 77 for the first equation and xÂ = 80Â or 80.75 for the second equation.
Â Â Â

Questions Eliciting Thinking Do you notice any similarities and differences in these equations or your methods of solution?
Is it possible to solve either equation in a different way?
Is it always possible to solve an equation with fractions using their decimal equivalents? 
Instructional Implications Challenge the student with more complex equations to solve by including both fractions and decimals in the same equation, more terms, or variables on both sides of the equation. 