Properties of Operations

Grade 5 · Mathematics

Semester 1 | Period 1 | Week 1

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Subject: Mathematics

Semester: 1

Period: 1

Week: 1

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 1
Lesson Duration: 45 minutes
Week & Period: Week 1, Period 1
Topic: Properties of Operations
Sub-topic: Commutative, Associative, Distributive, Zero, and Identity Properties

Learning Objectives
By the end of the lesson, students should be able to:

  1. Define and explain the properties of operations in mathematics.
  2. Apply commutative, associative, distributive, zero, and identity properties correctly.
  3. Solve numerical problems using these properties.

Previous Knowledge
Students already know basic addition, subtraction, multiplication, and division from Grade 5.

Instructional Materials
Mathematics textbook for Grade 5, counters, graph paper, charts, markers

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
The teacher asks quick questions such as:
• What is 3 + 5? What about 5 + 3?
• What is 2 × 7? What about 7 × 2?
Learners discuss whether the answers change if the order of numbers is switched.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

🧠 Definitions and Explanations

Understanding the Properties of Operations is essential for simplifying and solving mathematical problems, especially in arithmetic and algebra. These properties describe how numbers behave under addition and multiplication.

  1. Commutative Property
  • Definition: The order in which you add or multiply numbers does not change the result.
  • Applies to: Addition and Multiplication only (❌ Not subtraction or division)

Formulas:

  • Addition:                  a + b = b + a
  • Multiplication:               a × b = b × a

Examples:

  • 4 + 6 = 10 and 6 + 4 = 10
  • 7 × 3 = 21 and 3 × 7 = 21
  • 9 + 2 = 11 and 2 + 9 = 11

 

  1. Associative Property
  • Definition: The grouping of numbers (using parentheses) in addition or multiplication does not affect the result.
  • Applies to: Addition and Multiplication (❌ Not subtraction or division)

Formulas:

  • Addition:                  (a + b) + c = a + (b + c)
  • Multiplication:              (a × b) × c = a × (b × c)

Examples:

  • (3 + 4) + 5 = 7 + 5 = 12 and 3 + (4 + 5) = 3 + 9 = 12
  • (2 × 3) × 4 = 6 × 4 = 24 and 2 × (3 × 4) = 2 × 12 = 24

 

  1. Distributive Property
  • Definition: Multiplying a number by a group of numbers added together is the same as multiplying each number individually and then adding the results.

Formula:

  • a × (b + c) = (a × b) + (a × c)

Examples:

  • 5 × (2 + 3) = 5 × 5 = 25
       and (5 × 2) + (5 × 3) = 10 + 15 = 25
  • 4 × (6 + 1) = 4 × 7 = 28
       and (4 × 6) + (4 × 1) = 24 + 4 = 28

 

  1. Zero Property of Multiplication
  • Definition: Any number multiplied by zero gives a result of zero.

Formula:

  • a × 0 = 0 or 0 × a = 0

Examples:

  • 8 × 0 = 0
  • 0 × 256 = 0
  • 13 × 0 = 0
  1. Identity Property of Multiplication
  • Definition: Any number multiplied by 1 remains unchanged.

Formula:

  • a × 1 = a or 1 × a = a

Examples:

  • 9 × 1 = 9
  • 1 × 45 = 45
  • 73 × 1 = 73

 

🧩 Learners' Activities (Expanded)

Use these engaging activities to build hands-on understanding:

 

🔹 1. Counters and Dominoes (Commutative & Associative)

  • Learners use colored counters or dominoes to show:
    • 2 + 3 = 5 and 3 + 2 = 5
    • (1 + 2) + 3 = 6 and 1 + (2 + 3) = 6
  • Have learners arrange counters in different orders and groupings to verify properties.

🔹 2. Paper Folding and Group Work (Associative)

  • Learners write 3 numbers on colored paper.
  • Fold paper or arrange numbers to form different groupings.
  • Solve both groupings to prove the result is the same.

🔹 3. Graph Paper (Distributive Property)

  • On graph paper, students shade:
    • 3 rows of (2 + 4) blocks = total 18 blocks.
    • Then 3 × 2 and 3 × 4 blocks separately to show 6 + 12 = 18.

 

🔹 4. Game: "True or False Property?"

  • Teacher reads out equations like:
    • 7 × 1 = 7 (True - Identity)
    • 0 × 5 = 5 (False - Zero)
    • (2 + 4) + 5 = 2 + (4 + 5) (True - Associative)
  • Learners say which property it shows, and if it’s true or false.

 

🔹 5. Real-Life Examples

  • Commutative: Choosing 2 shirts and 3 trousers = 3 trousers and 2 shirts → same total outfits.
  • Distributive: 4 boxes with 3 red and 2 blue toys = 4 × (3 + 2) = (4 × 3) + (4 × 2)

 

✅ Assessment Checks (Formative Assessment Prompts)

During or after the lesson, ask students:

  1. Identify the Property:
    • What property is used in this equation:
      (7 + 3) + 2 = 7 + (3 + 2)?
    • Answer: Associative Property of Addition
  2. Complete the Statement:
    • Fill in the blank:
      6 × (2 + 4) = (6 × __) + (6 × __)
    • Answer: (6 × 2) + (6 × 4)
  3. True or False:
    • 10 × 0 = 10
    • Answer: False (Zero property → should be 0)
  4. Multiple Choice:
    Which property is shown below?
    3 × (4 + 5) = (3 × 4) + (3 × 5)
    Commutative
    B. Associative
    C. Distributive
    D. Zero
    • Correct answer: C. Distributive

 

📒 Notes (Expanded & Detailed)

  • Emphasize that properties make math easier — you don’t always have to calculate everything if you understand how numbers behave.
  • Teach names + meaning + use:
    • What is the property?
    • What does it tell us?
    • How can we use it to check or simplify math?
  • Help learners understand where properties apply:
    • Associative & Commutative → only for addition and multiplication
    • Distributive → connects multiplication with addition
    • Zero & Identity → help with shortcuts and mental math

 

✍️ Additional Practice Questions

  1. Fill in the blank using the correct property:
    • 4 + ___ = ___ + 4 → Name the property used.
  2. Apply Distributive Property:
    • Use distributive property to solve:
      6 × (2 + 7)
  3. Short-answer:
    • Explain why a + 0 = a is not listed as one of the multiplication properties.
  4. Draw it:
    • Draw a rectangle made of 3 rows of 4 + 2 blocks to show how
      3 × (4 + 2) is the same as 3 × 4 + 3 × 2.
  5. Challenge:
    • Is subtraction commutative? Try 5 – 3 and 3 – 5 — what happens?

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews each property with examples.

Evaluation Method (Expanded):
Exit slip/quiz: Learners solve 5 quick questions such as:

  1. 7 × (4 + 2) = ?
  2. (6 + 5) + 9 = ?
  3. 12 × 0 = ?
  4. 8 × 1 = ?
  5. Identify the property used in 2 + 9 = 9 + 2

Teacher will collect slips and provide oral feedback.

Assignment (Expanded):
Complete exercises on page ___ of the textbook on properties of operations.

Follow-up Activity:
Students create flashcards of properties with definitions and examples.

Differentiation / Inclusive Strategies
Provide counters for weaker learners and ask advanced learners to solve word problems involving properties.

Teacher’s Reflection (After Class)
• What worked well? ___________________________________________
• What needs improvement? ____________________________________
• Students’ engagement level: ☑ High ☑ Medium ☑ Low