Introduction to Multi-Step Equations

Overview

In this first lesson of the five-part unit “Mastering Multi-Step Equations,” students build on prior work with inverse operations and one-step equations. They learn how to use the order of operations in reverse to simplify expressions, isolate a variable, and justify each algebraic step.

Learning intentions

Students will be able to:

• Identify the operations in a multi-step equation.
• Use the reverse order of operations to solve for a variable.
• Explain why each step preserves equality.
• Check a solution by substituting it into the original equation.

Success criteria

• I can identify which operation should be undone first.
• I can solve a multi-step equation and show every step.
• I can explain how each step follows from the previous equation.
• I can check whether my solution makes the original equation true.

Curriculum links

• Reasoning with equations: explain each step in solving an equation using the equality of numbers asserted at the previous step.
• Reasoning with equations: solve linear equations in one variable, including equations with numerical coefficients.
• Creating equations: create and use a one-variable equation to represent and solve a situation.
• Creating equations: represent relationships between quantities using equations in two or more variables.

Lesson structure (45 minutes)

1. 0–5 min · Hook and retrieval. Display the prompt in the opening hook and retrieval slides: “If (3x+5=20), which operation should be undone first, and why?” Students solve a related one-step equation independently, then compare their reasoning with a partner. Invite two students to explain why subtracting 5 comes before dividing by 3.

2. 5–12 min · Introduce the process. Use the multi-step equation teaching slides to connect solving an equation with reversing a sequence of operations. Model (3x+5=20): subtract 5 from both sides to obtain (3x=15), then divide both sides by 3 to obtain (x=5). Emphasize that the same operation is performed on both sides and that each line is an equivalent equation.

3. 12–20 min · Teacher think-aloud. Continue with (2(x+4)-3=15), using the worked-example slides. First simplify or distribute as appropriate, then undo addition or subtraction, and finally undo multiplication or division. Pause after each line and ask, “What changed?” and “Why is this allowed?” Students record the steps and annotate the operation undone at each stage.

4. 20–30 min · Guided practice. Distribute the guided multi-step equations worksheet. Students complete the first four problems with a partner, showing one equality-preserving step per line. Include equations such as (4x-7=21), (5+2x=17), and (3(x+2)=24). Circulate, checking that students do not combine unlike terms or perform an operation on only one side. Pause for a whole-class check after the second problem.

5. 30–38 min · Independent practice and justification. Students complete the next three worksheet problems independently, including one short context problem: “A phone plan charges a $12 fee plus $8 per month. The total bill is $44. Write and solve an equation to find the number of months.” Students must write a sentence explaining one step and check one answer by substitution. Use the practice-check slides to display solutions one at a time for self-correction.

6. 38–45 min · Discussion and exit assessment. Display the final prompts in the discussion and exit slides. Students respond to: “Why must an operation be performed on both sides of an equation?” Then complete an exit response: solve (4x+6=30), explain why the first step is valid, and check the solution. Collect responses as students leave.

Resources

• the complete introduction and practice slide deck
• the guided multi-step equations worksheet
• Whiteboard or document camera
• Student notebooks or lined paper
• Pencils and colored pens for marking operations
• Exit ticket slips or scrap paper
• Calculators for designated students who require them

Assessment

• During modeling, listen for explanations that connect each operation to maintaining equality.
• Check worksheet work for correct inverse-operation order, operations performed on both sides, and clearly shown steps.
• Use the exit response to identify students who can solve, justify, and verify a multi-step equation before the next lesson.

Differentiation

• Support students with a color-coded equation model: circle the variable term, underline constant terms, and label the operation to undo. Provide the sentence frame, “I ______ both sides because ______.”
• Confer with students who need additional support using simpler equations before returning to parentheses or context problems. Allow graph paper, extra processing time, and a calculator for computation checks where appropriate.
• For English learners, preview and display the terms variable, coefficient, constant, inverse operation, equivalent, and solution; pair each term with a student-friendly definition.
• Extend ready students by asking them to create a multi-step equation with solution (x=6), solve it, and explain how they know each line remains equivalent.