📚 Part 1: Understanding the Properties

1. Match each property with its correct definition:

1. Commutative Property

2. Associative Property

3. Distributive Property

A. Changing the grouping of numbers does not change the result

B. Changing the order of numbers does not change the result

C. Multiplying a sum is the same as multiplying each part and then adding

2. Which of these statements is true about the commutative property?

It only works with addition

It works with both addition and multiplication

It only works with multiplication

It works with subtraction and division

🔢 Part 2: Commutative Property

3. Complete these equations using the commutative property:

a) 7 × 5 = _____ × _____

b) 12 + 8 = _____ + _____

c) 9 × 4 = _____ × _____

d) 15 + 6 = _____ + _____

4. Show your working to prove that 6 × 8 = 8 × 6:

5. Explain in your own words why the commutative property works:

🎯 Part 3: Associative Property

6. Fill in the missing numbers to show the associative property:

a) (3 + 4) + 5 = 3 + (_____ + _____)

b) (2 × 6) × 3 = _____ × (6 × _____)

c) (8 + 7) + 2 = _____ + (7 + _____)

d) (5 × 4) × 2 = 5 × (_____ × _____)

7. Calculate both sides to prove they are equal:

(4 + 3) + 6 = 4 + (3 + 6)

8. Draw a diagram or use objects to show why (2 × 3) × 4 = 2 × (3 × 4):

🌟 Part 4: Distributive Property

9. Complete these distributive property equations:

a) 3 × (4 + 5) = (3 × _____) + (3 × _____)

b) 6 × (2 + 7) = (_____ × 2) + (_____ × 7)

c) 4 × (8 + 3) = (4 × _____) + (_____ × 3)

d) 5 × (6 + 4) = (_____ × _____) + (_____ × _____)

10. Use the distributive property to solve 7 × (10 + 3). Show all your working:

11. Which expressions are equivalent to 8 × (5 + 2)? Check all that apply:

(8 × 5) + (8 × 2)

8 × 7

(8 + 5) × (8 + 2)

40 + 16

56

🧠 Part 5: Mixed Practice

12. Identify which property is being used in each example:

a) 9 + 7 = 7 + 9 → _________________ property

b) (5 × 2) × 3 = 5 × (2 × 3) → _________________ property

c) 4 × (6 + 1) = (4 × 6) + (4 × 1) → _________________ property

d) 12 × 8 = 8 × 12 → _________________ property

13. Use properties to make these calculations easier. Show your method:

a) 25 × 4 × 7

b) 6 × 19 (Hint: think of 19 as 20 - 1)

14. Create your own example for each property:

Commutative: _________________________________

Associative: __________________________________

Distributive: __________________________________

💭 Part 6: Real-Life Applications

15. Sarah is buying school supplies. She needs 4 packs of pens at $3 each and 4 packs of pencils at $2 each. Use the distributive property to find the total cost:

16. Explain how understanding these properties helps you in mathematics:

17. Give a real-life example where you might use the commutative property:

Properties of Operations

Properties of Operations

📚 Part 1: Understanding the Properties

🔢 Part 2: Commutative Property

🎯 Part 3: Associative Property

🌟 Part 4: Distributive Property

🧠 Part 5: Mixed Practice

💭 Part 6: Real-Life Applications

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