Properties of Addition worksheet for third-grade students to practice identifying identity and commutative properties.

Problem-Solving Practice: Properties of Addition

The task involves solving addition problems and identifying whether each problem demonstrates the Identity Property or the Commutative Property of addition. Let's solve each problem step by step and explain the solution.

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#### 1. \( 6 + 5 = \_\_\_ + 6 \)
- Solution: The equation is \( 6 + 5 = 5 + 6 \).
- Explanation: This shows that the order of the numbers being added does not change the sum. This is the Commutative Property of addition.
- Answer: \( 5 \), property: Commutative

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#### 2. \( 0 + 7 = \_\_\_ \)
- Solution: The equation is \( 0 + 7 = 7 \).
- Explanation: Adding zero to any number leaves the number unchanged. This is the Identity Property of addition.
- Answer: \( 7 \), property: Identity

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#### 3. \( 7 + 3 = \_\_\_ + 7 \)
- Solution: The equation is \( 7 + 3 = 3 + 7 \).
- Explanation: Again, this shows that the order of the numbers being added does not change the sum. This is the Commutative Property of addition.
- Answer: \( 3 \), property: Commutative

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#### 4. \( 3 + \_\_\_ = 3 \)
- Solution: The equation is \( 3 + 0 = 3 \).
- Explanation: Adding zero to any number leaves the number unchanged. This is the Identity Property of addition.
- Answer: \( 0 \), property: Identity

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#### 5. \( 5 + 5 = 5 + \_\_\_ \)
- Solution: The equation is \( 5 + 5 = 5 + 5 \).
- Explanation: This shows that the order of the numbers being added does not change the sum. This is the Commutative Property of addition.
- Answer: \( 5 \), property: Commutative

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#### 6. \( 52 + 0 = \_\_\_ \)
- Solution: The equation is \( 52 + 0 = 52 \).
- Explanation: Adding zero to any number leaves the number unchanged. This is the Identity Property of addition.
- Answer: \( 52 \), property: Identity

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#### 7. \( 8 + 6 = 6 + \_\_\_ \)
- Solution: The equation is \( 8 + 6 = 6 + 8 \).
- Explanation: This shows that the order of the numbers being added does not change the sum. This is the Commutative Property of addition.
- Answer: \( 8 \), property: Commutative

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#### 8. \( \_\_\_ + 3 = 3 + 2 \)
- Solution: The equation is \( 2 + 3 = 3 + 2 \).
- Explanation: This shows that the order of the numbers being added does not change the sum. This is the Commutative Property of addition.
- Answer: \( 2 \), property: Commutative

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#### 9. \( 0 + 1,500 = \_\_\_ \)
- Solution: The equation is \( 0 + 1,500 = 1,500 \).
- Explanation: Adding zero to any number leaves the number unchanged. This is the Identity Property of addition.
- Answer: \( 1,500 \), property: Identity

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#### 10. \( 13 + \_\_\_ = 13 \)
- Solution: The equation is \( 13 + 0 = 13 \).
- Explanation: Adding zero to any number leaves the number unchanged. This is the Identity Property of addition.
- Answer: \( 0 \), property: Identity

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Final Answers:

1. \( 5 \), property: Commutative
2. \( 7 \), property: Identity
3. \( 3 \), property: Commutative
4. \( 0 \), property: Identity
5. \( 5 \), property: Commutative
6. \( 52 \), property: Identity
7. \( 8 \), property: Commutative
8. \( 2 \), property: Commutative
9. \( 1,500 \), property: Identity
10. \( 0 \), property: Identity

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & 5, \text{ Commutative} \\
2. & 7, \text{ Identity} \\
3. & 3, \text{ Commutative} \\
4. & 0, \text{ Identity} \\
5. & 5, \text{ Commutative} \\
6. & 52, \text{ Identity} \\
7. & 8, \text{ Commutative} \\
8. & 2, \text{ Commutative} \\
9. & 1,500, \text{ Identity} \\
10. & 0, \text{ Identity} \\
\end{array}
}
\]