Home›Lesson Plans›Mathematics›Expressions & Equations · Grade 7

Two-Step Equations

Seventh graders learn to solve two-step equations like 3x + 5 = 17 — undoing operations in reverse order to isolate the variable — a foundational skill for all of algebra.

Grade 7Equations50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Solve two-step equations.
  • ✓Undo operations in reverse.
  • ✓Keep the equation balanced.
  • ✓Check the solution.
Essential Question

In “3x + 5 = 17,” there are two things happening to x. How do you undo them both to find what x equals?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Equation Solver

Project this and change the equation. Watch the two steps unfold — undo the addition, then undo the multiplication — to solve for x!

⚖️ Solve a two-step equation, step by stepTry it
a: 3
x (answer): 4
b: 5
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Two Things to Undo

5 min

In 3x + 5 = 17, two things happen to x — how do we undo both?

👩‍🏫 Teacher Moves

  • Show a two-step equation.
  • Ask how to isolate x.
  • Set the goal: two-step equations.

🎒 Student Actions

  • See the equation.
  • Wonder how.
  • Predict the steps.
2

I Do — Undo in Reverse

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Undo addition/subtraction first.
  • Then undo multiplication/division.
  • Keep it balanced.

🎒 Student Actions

  • Undo the +.
  • Undo the ×.
  • Stay balanced.
3

We Do — Solve Together

13 min

Class uses the Equation Solver.

👩‍🏫 Teacher Moves

  • Follow the two steps.
  • Isolate x.
  • Check the solution.

🎒 Student Actions

  • Follow steps.
  • Isolate x.
  • Check it.
4

You Do — On Your Own

12 min

Students solve.

👩‍🏫 Teacher Moves

  • Solve two-step equations.
  • Show both steps.
  • Check solutions.

🎒 Student Actions

  • Solve them.
  • Show steps.
  • Check them.
5

Close — Close

5 min

One equation.

👩‍🏫 Teacher Moves

  • Give a two-step equation.
  • Solve it.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve it.
  • Check it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
7.EE.4a

Solve two-step equations of the form px + q = r.

CCSS
7.EE.4

Use variables to solve real-world problems.

CCSS
7.EE.3

Solve multi-step problems with rational numbers.

SMP
MP.1

Make sense of problems and persevere.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Balance-scale model.
  • Sentence frame: “First undo ___, then undo ___.”
  • Show both sides.

Support & Access

IEP / 504
  • Start with one-step equations.
  • Use a balance model.
  • Do one step at a time.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Solve equations with variables on both sides.
  • Solve two-step inequalities.
  • Write and solve from a word problem.
Materials

What to gather

  • 📽️Projector / board
  • ⚖️A balance model
  • 💻The Equation Solver
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

equationa math sentence with an =variablea letter for an unknownsolveto find the variable’s valueisolateto get the variable aloneinverse operationthe opposite operationbalancekeep both sides equalcoefficientthe number in front of a variablesolutionthe value that makes it true
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Solve: 2x + 3 = 11.
x = 4.
QUESTION 2
In a two-step equation, which do you undo first — addition or multiplication?
Addition/subtraction first, then multiplication/division.
QUESTION 3
Why do you do the same thing to both sides?
To keep the equation balanced (equal).

Going deeper? Variables on both sides.

Have students solve equations with the variable on both sides, like 3x + 2 = x + 10. A printable equations sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Two-Step EquationsFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Two-Step EquationsQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Two-Step EquationsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: balance, coefficient, equation, inverse operation, isolate, solution, solve, variable
  1. a math sentence with an =
  2. the number in front of a variable
  3. the opposite operation
  4. a letter for an unknown
  5. to find the variable’s value
  6. the value that makes it true
  7. to get the variable alone
  8. keep both sides equal

Part B · Show what you learned

  1. Solve: 2x + 3 = 11.
  2. In a two-step equation, which do you undo first — addition or multiplication?
  3. Why do you do the same thing to both sides?
Answer key — Part A: 1) equation · 2) coefficient · 3) inverse operation · 4) variable · 5) solve · 6) solution · 7) isolate · 8) balance
Part B: 1) x = 4. 2) Addition/subtraction first, then multiplication/division. 3) To keep the equation balanced (equal).