Home›Lesson Plans›Mathematics›Operations & Algebraic Thinking · Grade 5

Order of Operations: Which Step Comes First?

Students learn that math has rules of order — parentheses first, then multiply and divide, then add and subtract — so that everyone solving the same expression gets the same answer.

Grade 5Expressions45 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…

  • ✓Explain why math needs an order of operations.
  • ✓Do operations inside parentheses first.
  • ✓Do multiply/divide before add/subtract.
  • ✓Evaluate expressions correctly.
Essential Question

Does 6 + 2 × 3 equal 24 or 12? Two people can get different answers — unless everyone follows the same order. What are the rules?

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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

Which Step First?

Project each expression and have students choose the correct answer. The tool explains which operation to do first and why.

🔢 Read the expression — what’s the answer?Try it
Follow the order of operations. What is the answer?
The Lesson · Gradual Release (I Do · We Do · You Do)

45 minutes, five moves

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

1

Launch — Two Answers?!

5 min

6 + 2 × 3 — is it 24 or 12?

👩‍🏫 Teacher Moves

  • Have students solve 6 + 2 × 3 freely.
  • Show two different answers appear.
  • Set the goal: a shared order.

🎒 Student Actions

  • Solve it their own way.
  • See answers differ.
  • Predict a rule.
2

I Do — The Rules of Order

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Parentheses first.
  • Then multiply and divide.
  • Then add and subtract.

🎒 Student Actions

  • Learn the order.
  • See each step.
  • Solve one together.
3

We Do — Order Together

12 min

Class drives Which Step First?

👩‍🏫 Teacher Moves

  • Work through the expressions.
  • Name the first step before solving.
  • Compare to the wrong (left-to-right) answer.

🎒 Student Actions

  • Name the first step.
  • Choose the answer.
  • Explain the order.
4

You Do — On Your Own

13 min

Students evaluate expressions.

👩‍🏫 Teacher Moves

  • Assign expressions with ×÷ and parentheses.
  • Have them show each step.
  • Include one with brackets.

🎒 Student Actions

  • Evaluate expressions.
  • Show each step.
  • Follow the order.
5

Close — Close

5 min

Solve the opener.

👩‍🏫 Teacher Moves

  • Return to 6 + 2 × 3.
  • Have students explain why it’s 12.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve 6 + 2 × 3 = 12.
  • Explain the order.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
5.OA.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

CCSS
5.OA.2

Write simple expressions that record calculations with numbers, and interpret them.

CCSS
3.OA.D.8

Solve problems using the order of operations.

SMP
MP.6

Attend to precision by following the order of operations exactly.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • A visual order-of-operations poster.
  • Sentence frame: “First I do ___, then ___.”
  • Underline the first step in color.

Support & Access

IEP / 504
  • Start with expressions of only two operations.
  • Provide a step-by-step order chart.
  • Offer two answer choices.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Evaluate expressions with brackets and braces.
  • Write an expression for a word problem.
  • Add parentheses to change the answer.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻Which Step First?
  • 📋An order-of-operations poster
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

expressiona math phrase with numbers and operationsoperationadd, subtract, multiply, or divideorder of operationsthe rules for which step to do firstparenthesessymbols ( ) that group a stepevaluateto find the value of an expressionbracketssymbols [ ] used to groupgrouping symbol( ), [ ], or { }valuethe answer to an expression
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
In 6 + 2 × 3, which operation do you do first, and what is the answer?
Multiplication first: 2 × 3 = 6, then 6 + 6 = 12.
QUESTION 2
What do you always do first in an expression with parentheses?
Solve what is inside the parentheses first.
QUESTION 3
Evaluate: (10 − 4) × 2.
12 — parentheses first (10 − 4 = 6), then 6 × 2 = 12.

Going deeper? Move the parentheses.

Give students an expression and challenge them to add parentheses in different places to make different answers. A printable expression-puzzle 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.

🃏 Order of OperationsFlip
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Term
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Meaning
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Practice · Quiz

Check your understanding

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

📝 Order of OperationsQuiz
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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.

🖨️ Order of OperationsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: brackets, evaluate, expression, grouping symbol, operation, order of operations, parentheses, value
  1. a math phrase with numbers and operations
  2. symbols [ ] used to group
  3. the answer to an expression
  4. symbols ( ) that group a step
  5. to find the value of an expression
  6. add, subtract, multiply, or divide
  7. the rules for which step to do first
  8. ( ), [ ], or { }

Part B · Show what you learned

  1. In 6 + 2 × 3, which operation do you do first, and what is the answer?
  2. What do you always do first in an expression with parentheses?
  3. Evaluate: (10 − 4) × 2.
Answer key — Part A: 1) expression · 2) brackets · 3) value · 4) parentheses · 5) evaluate · 6) operation · 7) order of operations · 8) grouping symbol
Part B: 1) Multiplication first: 2 × 3 = 6, then 6 + 6 = 12. 2) Solve what is inside the parentheses first. 3) 12 — parentheses first (10 − 4 = 6), then 6 × 2 = 12.