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Properties of Multiplication

Third graders learn the rules that make multiplication flexible, from switching the order of factors to breaking a hard fact into easier ones, and how each property helps them compute.

Grade 3Properties of Multiplication50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Name the properties.
  • ✓See how each one works.
  • ✓Use them to multiply.
  • ✓Explain why they help.
Essential Question

You know 6 x 2 is 12, and 2 x 6 is also 12. Why does the order not matter, and what other rules make multiplying easier?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Explore the Properties · Interactive

Explore the Properties

Project this and open each card to explore a property of multiplication and how it makes multiplying easier.

✖️ Explore the properties of multiplicationTry it

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

Hook — Same Answer, Easier Way

5 min

You know that 6 x 2 is 12. So what is 2 x 6? The order changed, but the answer did not. Why does that happen, and how can rules like this make multiplying easier?

👩‍🏫 Teacher Moves

  • Show 6 x 2 and 2 x 6.
  • Ask what you notice.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Explore the Properties

12 min

Students explore each property of multiplication.

👩‍🏫 Teacher Moves

  • Send students to Explore the Properties.
  • Open each card.
  • Name the property.

🎒 Student Actions

  • Explore.
  • Read.
  • Say it.
3

Modify — Try It Out

13 min

Students apply a property to a fact.

👩‍🏫 Teacher Moves

  • Pick a multiplication fact.
  • Use a property to make it easier.
  • Show both ways match.

🎒 Student Actions

  • Pick.
  • Use.
  • Show.
4

Create — My Property Poster

15 min

Students illustrate a property.

👩‍🏫 Teacher Moves

  • Choose one property.
  • Write an example of it.
  • Draw why it works.

🎒 Student Actions

  • Choose.
  • Write.
  • Draw.
5

Reflect — Rules That Help

5 min

Students reflect on the properties.

👩‍🏫 Teacher Moves

  • What does the commutative property say?
  • How does breaking apart a factor help?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say 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.B.5

Apply properties of operations as strategies to multiply and divide.

CCSS
3.OA.A.1

Interpret products of whole numbers, such as 5 x 7 as the total in 5 groups of 7.

CCSS
3.OA.C.7

Fluently multiply and divide within 100 using strategies and properties.

CCSS
MP.7

Look for and make use of structure.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Property example cards.
  • Sentence frame: “___ x ___ = ___ x ___ .”
  • Explore one property at a time.

Support & Access

IEP / 504
  • Start with commutative and identity.
  • Show one property with counters.
  • Learn one property before the next.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Prove the distributive property with an array.
  • Combine two properties in one problem.
  • Explain why order and grouping keep the product.
Materials

What to gather

  • 📽️Projector / board
  • 🔢Counters or tiles
  • 💻Explore the Properties
  • 🃏Array cards
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

productthe answer when you multiply two or more numbersfactora number being multiplied in a problemcommutative propertyorder of the factors does not change the productassociative propertygrouping of the factors does not change the productdistributive propertybreak a factor into parts, multiply, then addidentity propertyany number times one equals that same numberzero propertyany number times zero equals zeroregroupto group numbers a different way to make them easier
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
What does the commutative property of multiplication say?
The order of the factors does not change the product, so 4 x 7 equals 7 x 4.
QUESTION 2
How can the distributive property make 8 x 6 easier?
Break 6 into 5 and 1: (8 x 5) + (8 x 1) = 40 + 8 = 48.
QUESTION 3
What is any number times zero?
Zero. Zero groups of anything is nothing.

Create: my property poster.

Have students choose one property, write an example, and draw why it works, so each rule becomes something they can show. A printable properties-of-multiplication worksheet is in the Mathematics 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.

🃏 Properties of MultiplicationFlip
Card 1
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.

📝 Properties of MultiplicationQuiz
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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.

🖨️ Properties of MultiplicationPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: associative property, commutative property, distributive property, factor, identity property, product, regroup, zero property
  1. grouping of the factors does not change the product
  2. break a factor into parts, multiply, then add
  3. any number times zero equals zero
  4. to group numbers a different way to make them easier
  5. order of the factors does not change the product
  6. any number times one equals that same number
  7. the answer when you multiply two or more numbers
  8. a number being multiplied in a problem

Part B · Show what you learned

  1. What does the commutative property of multiplication say?
  2. How can the distributive property make 8 x 6 easier?
  3. What is any number times zero?
Answer key — Part A: 1) associative property · 2) distributive property · 3) zero property · 4) regroup · 5) commutative property · 6) identity property · 7) product · 8) factor
Part B: 1) The order of the factors does not change the product, so 4 x 7 equals 7 x 4. 2) Break 6 into 5 and 1: (8 x 5) + (8 x 1) = 40 + 8 = 48. 3) Zero. Zero groups of anything is nothing.