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Literal Equations: Rearranging Formulas

Ninth graders learn to rearrange literal equations — formulas with several variables — to solve for any one variable, a skill used constantly in science, geometry, and real-world formulas.

Grade 9Equations55 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 a formula for a given variable.
  • ✓Use inverse operations.
  • ✓Rearrange real formulas.
  • ✓Treat letters like numbers.
Essential Question

The formula A = l × w finds area. But what if you know the area and length and need the width? You rearrange the formula to solve for w. How?

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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

Solve for the Variable

Project each item and have students rearrange the formula. The tool explains isolating a variable with inverse operations.

🔤 Rearrange each formulaTry it
Solve each formula for the requested variable.
The Lesson · Gradual Release (I Do · We Do · You Do)

55 minutes, five moves

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

1

Launch — Formula in Reverse

5 min

A = l × w finds area — but how do you find w?

👩‍🏫 Teacher Moves

  • Show a formula.
  • Ask to solve for a different variable.
  • Set the goal: literal equations.

🎒 Student Actions

  • See the formula.
  • Want another variable.
  • Predict the idea.
2

I Do — Isolate the Variable

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Pick the target variable.
  • Use inverse operations.
  • Treat other letters as numbers.

🎒 Student Actions

  • Pick the variable.
  • Undo operations.
  • Isolate it.
3

We Do — Solve Together

13 min

Class uses Solve for the Variable.

👩‍🏫 Teacher Moves

  • Rearrange each formula.
  • Explain each step.
  • Check the result.

🎒 Student Actions

  • Rearrange it.
  • Explain steps.
  • Check it.
4

You Do — On Your Own

12 min

Students rearrange.

👩‍🏫 Teacher Moves

  • Solve formulas for a variable.
  • Use inverse operations.
  • Apply to real formulas.

🎒 Student Actions

  • Solve them.
  • Use inverses.
  • Apply them.
5

Close — Close

5 min

One formula.

👩‍🏫 Teacher Moves

  • Give a formula to rearrange.
  • Solve for a variable.
  • Hand out the exit ticket.

🎒 Student Actions

  • Rearrange it.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (High School Algebra).

CCSS
A-CED.4

Rearrange formulas to highlight a quantity of interest.

CCSS
A-REI.1

Explain each step in solving an equation.

CCSS
A-CED.1

Create equations that describe relationships.

CCSS
A-REI.3

Solve equations in one variable.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Same steps, with letters.
  • Sentence frame: “To isolate ___, I ___.”
  • Compare to a numeric equation.

Support & Access

IEP / 504
  • Start with one-step formulas.
  • Solve a numeric version first.
  • Isolate step by step.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Rearrange multi-step formulas.
  • Solve science formulas.
  • Rearrange, then evaluate.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Calculators
  • 💻Solve for the Variable
  • 📄Formula charts
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

literal equationa formula with several variablesformulaa rule relating quantitiesvariablea letter for a quantityisolateto get a variable aloneinverse operationthe opposite operationrearrangeto solve for a different variablecoefficientthe number in front of a variableconstanta fixed value
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 for h: A = ½ b h (area of a triangle).
h = 2A / b.
QUESTION 2
Solve for t: d = r t (distance = rate × time).
t = d / r.
QUESTION 3
How is solving a literal equation like solving a regular equation?
You use the same inverse operations to isolate the variable — you just work with letters instead of numbers.

Going deeper? Rearrange, then use it.

Have students rearrange a science formula (like solving F = ma for a) and then plug in numbers to find the answer. A printable literal-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.

🃏 Literal 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.

📝 Literal 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.

🖨️ Literal EquationsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: coefficient, constant, formula, inverse operation, isolate, literal equation, rearrange, variable
  1. to solve for a different variable
  2. a letter for a quantity
  3. the opposite operation
  4. a formula with several variables
  5. the number in front of a variable
  6. to get a variable alone
  7. a rule relating quantities
  8. a fixed value

Part B · Show what you learned

  1. Solve for h: A = ½ b h (area of a triangle).
  2. Solve for t: d = r t (distance = rate × time).
  3. How is solving a literal equation like solving a regular equation?
Answer key — Part A: 1) rearrange · 2) variable · 3) inverse operation · 4) literal equation · 5) coefficient · 6) isolate · 7) formula · 8) constant
Part B: 1) h = 2A / b. 2) t = d / r. 3) You use the same inverse operations to isolate the variable — you just work with letters instead of numbers.