📚 Part 1: Identifying Properties

1. Which property is shown in the equation 4 + x + 7 = x + 4 + 7?

Commutative Property

Associative Property

Distributive Property

2. Which property allows you to rewrite (3 + y) + 5 as 3 + (y + 5)?

Commutative Property

Associative Property

Distributive Property

3. Check all expressions that are equivalent to 2(x + 6):

2x + 12

2x + 6

2 · x + 2 · 6

x + 6 + 2

✏️ Part 2: Applying Properties to Simplify

4. Simplify the expression: 8 + n + 3

Show your work using properties:

Final answer: ___________

5. Simplify the expression: (x + 4) + 9

Show your work using properties:

Final answer: ___________

6. Use the distributive property to simplify: 5(2 + m)

Show your work:

Final answer: ___________

7. Real-World Problem: Maria is buying school supplies. She buys 3 packs of pencils for $2 each and 3 erasers for $1 each. Write and simplify an expression for her total cost.

Expression: ___________

Simplified using distributive property: ___________

Total cost: $ ___________

🎯 Part 3: Problem Solving & Explanation

8. Shopping Scenario: Jake is buying fruit. He gets 4 apples, some bananas (b), and 6 oranges. His friend Emma gets the same bananas (b), 6 oranges, and 4 apples. Write expressions for both and explain why they're equivalent.

Jake's expression: ___________

Emma's expression: ___________

9. A recipe calls for 2 cups of flour and 2 cups of sugar for each batch. If you want to make 3 batches, write two equivalent expressions for the total amount of ingredients needed.

Expression 1: ___________

Expression 2: ___________

Which property did you use? ___________

10. Reflection: Choose one property (Commutative, Associative, or Distributive) and explain in your own words how it helps you simplify expressions. Give an example.

Property chosen: ___________

✅ Answer Key

1. Commutative Property

2. Associative Property

3. 2x + 12, 2 · x + 2 · 6

4. Final answer: n + 11

5. Final answer: x + 13

6. Final answer: 10 + 5m

7. Expression: 3(2) + 3(1); Simplified: 6 + 3; Total cost: $9

8. Jake's expression: 4 + b + 6; Emma's expression: b + 6 + 4; They are equivalent because addition is commutative.

9. Expression 1: 2 * 3 + 2 * 3; Expression 2: 6 + 6; Property used: Distributive Property

10. Property chosen: (example will vary by student)

Properties in Expressions

Properties in Expressions

📚 Part 1: Identifying Properties

✏️ Part 2: Applying Properties to Simplify

🎯 Part 3: Problem Solving & Explanation

✅ Answer Key

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