Home›Lesson Plans›Mathematics›Operations & Algebraic Thinking · Grade 3

The Commutative Property: Order Doesn’t Matter

Third graders discover a powerful multiplication shortcut — the commutative property — which says you can multiply numbers in any order and get the same answer, so 3 × 4 equals 4 × 3.

Grade 3Properties50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Assign or share this lesson
Share to Google Classroom Share to Microsoft Teams

Copy link works with Canvas, Schoology, Moodle and any other LMS — paste it in as a resource or assignment.

Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Explain the commutative property.
  • ✓Show 3 × 4 = 4 × 3.
  • ✓Use it to learn facts faster.
  • ✓Flip an array.
Essential Question

Is 3 × 4 the same as 4 × 3? If you already know one, do you get the other for free? Let’s find out with arrays!

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

Flip the Array

Project this and flip the array. Watch the rows and columns swap — but the total stays exactly the same!

🔄 Flip the array — same total either way!Try it
First number: 3
Second number: 4

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 — Same Answer?

5 min

Is 3 × 4 the same as 4 × 3? How can we be sure?

👩‍🏫 Teacher Moves

  • Show 3 × 4 and 4 × 3.
  • Ask if they’re equal.
  • Set the goal: commutative property.

🎒 Student Actions

  • Compare them.
  • Predict equal or not.
  • Guess the rule.
2

I Do — Flip the Array

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Build a 3 × 4 array.
  • Flip it to 4 × 3.
  • Show the total is the same.

🎒 Student Actions

  • Build it.
  • Flip it.
  • See the total.
3

We Do — Explore Together

13 min

Class uses Flip the Array.

👩‍🏫 Teacher Moves

  • Flip arrays.
  • Read both equations.
  • See the same total.

🎒 Student Actions

  • Flip arrays.
  • Read both.
  • Note the match.
4

You Do — On Your Own

12 min

Students use the property.

👩‍🏫 Teacher Moves

  • Write both orders of a fact.
  • Use a known fact to find another.
  • Explain why it works.

🎒 Student Actions

  • Write both.
  • Use a fact.
  • Explain it.
5

Close — Close

5 min

One fact.

👩‍🏫 Teacher Moves

  • Give a fact like 6 × 2.
  • Write it the other way.
  • Hand out the exit ticket.

🎒 Student Actions

  • Flip the fact.
  • Explain it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
3.OA.5

Apply properties of operations as strategies to multiply (commutative property).

CCSS
3.OA.1

Interpret products of whole numbers.

CCSS
3.OA.7

Fluently multiply and divide within 100.

SMP
MP.7

Look for and make use of structure.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Show both arrays side by side.
  • Sentence frame: “___ × ___ equals ___ × ___.”
  • Flip real objects.

Support & Access

IEP / 504
  • Use small factors.
  • Build both arrays with counters.
  • Count both totals.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Use the property with three factors.
  • Explain the associative property.
  • Use it to learn tough facts.
Materials

What to gather

  • 📽️Projector / board
  • 🔵Counters
  • 💻Flip the Array
  • 📐Grid paper
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

commutative propertyorder doesn’t change the productmultiplyto add equal groupsproductthe answer to multiplicationfactora number being multipliedarrayobjects in rows and columnsorderthe sequence of the numbersequalthe samepropertya rule that always works
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
If 7 × 3 = 21, what is 3 × 7?
21 (the commutative property — order doesn’t change the answer).
QUESTION 2
What does the commutative property say about multiplication?
You can multiply the numbers in any order and get the same product.
QUESTION 3
How can the commutative property help you learn facts faster?
If you know one fact, you automatically know it the other way too — so you learn two facts at once.

Going deeper? Three factors.

Have students explore multiplying three numbers in different orders (like 2 × 3 × 4) and discover they still get the same product. A printable properties 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.

🃏 The Commutative PropertyFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

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

📝 The Commutative PropertyQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

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.

🖨️ The Commutative PropertyPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: array, commutative property, equal, factor, multiply, order, product, property
  1. a rule that always works
  2. order doesn’t change the product
  3. objects in rows and columns
  4. to add equal groups
  5. a number being multiplied
  6. the answer to multiplication
  7. the sequence of the numbers
  8. the same

Part B · Show what you learned

  1. If 7 × 3 = 21, what is 3 × 7?
  2. What does the commutative property say about multiplication?
  3. How can the commutative property help you learn facts faster?
Answer key — Part A: 1) property · 2) commutative property · 3) array · 4) multiply · 5) factor · 6) product · 7) order · 8) equal
Part B: 1) 21 (the commutative property — order doesn’t change the answer). 2) You can multiply the numbers in any order and get the same product. 3) If you know one fact, you automatically know it the other way too — so you learn two facts at once.