Identity property for addition | TPT - Free Printable

Problem Analysis:

The task involves identifying and classifying number sentences based on two properties of addition:
1. Commutative Property of Addition: This property states that the order of adding numbers does not affect the sum. Mathematically, it is expressed as:
\[
a + b = b + a
\]
2. Identity Property of Addition: This property states that adding zero to any number leaves the number unchanged. Mathematically, it is expressed as:
\[
a + 0 = a
\]

The goal is to analyze each given number sentence and determine whether it demonstrates the Commutative Property, the Identity Property, or neither.

---

Solution Approach:

We will evaluate each number sentence step by step:

#### 1. 8 + 0 = 8
- This sentence shows that adding zero to 8 results in 8.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

#### 2. 1 + 3 = 4
- This sentence is a simple addition statement but does not demonstrate either the Commutative Property or the Identity Property.
- Classification: Neither

#### 3. 9 + 0 = 9
- This sentence shows that adding zero to 9 results in 9.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

#### 4. 2 + 7 = 7 + 2
- This sentence shows that the order of adding 2 and 7 does not change the sum.
- It satisfies the Commutative Property of Addition.
- Classification: Commutative Property

#### 5. 6 + 7 = 7 + 6
- This sentence shows that the order of adding 6 and 7 does not change the sum.
- It satisfies the Commutative Property of Addition.
- Classification: Commutative Property

#### 6. 1 + 5 = 5 + 1
- This sentence shows that the order of adding 1 and 5 does not change the sum.
- It satisfies the Commutative Property of Addition.
- Classification: Commutative Property

#### 7. 7 + 0 = 7
- This sentence shows that adding zero to 7 results in 7.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

#### 8. 8 + 3 = 9 + 3
- This sentence does not show the Commutative Property (order is not being swapped) or the Identity Property (zero is not involved).
- Classification: Neither

#### 9. 7 + 0 = 7
- This sentence shows that adding zero to 7 results in 7.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

#### 10. 8 + 5 = 8 + 5
- This sentence is simply restating the same expression and does not demonstrate either property.
- Classification: Neither

#### 11. 9 + 0 = 9
- This sentence shows that adding zero to 9 results in 9.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

#### 12. 8 + 5 = 8 + 5
- This sentence is simply restating the same expression and does not demonstrate either property.
- Classification: Neither

#### 13. 7 + 5 = 7 + 5
- This sentence is simply restating the same expression and does not demonstrate either property.
- Classification: Neither

#### 14. 8 + 2 = 2 + 8
- This sentence shows that the order of adding 8 and 2 does not change the sum.
- It satisfies the Commutative Property of Addition.
- Classification: Commutative Property

#### 15. 8 + 1 = 8
- This sentence does not satisfy either property. Adding 1 to 8 does not result in 8.
- Classification: Neither

#### 16. 4 + 0 = 4
- This sentence shows that adding zero to 4 results in 4.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

#### 17. 1 + 3 = 3 + 1
- This sentence shows that the order of adding 1 and 3 does not change the sum.
- It satisfies the Commutative Property of Addition.
- Classification: Commutative Property

#### 18. 9 + 6 = 9 + 6
- This sentence is simply restating the same expression and does not demonstrate either property.
- Classification: Neither

#### 19. 7 + 8 = 7 + 8
- This sentence is simply restating the same expression and does not demonstrate either property.
- Classification: Neither

#### 20. 8 + 1 = 9
- This sentence is a simple addition statement but does not demonstrate either property.
- Classification: Neither

#### 21. 7 + 0 = 7
- This sentence shows that adding zero to 7 results in 7.
- It satisfies the Identity Property of Addition.
- Classification: Identity Property

---

Final Classification:

- Commutative Property: Sentences 4, 5, 6, 14, 17
- Identity Property: Sentences 1, 3, 7, 9, 11, 16, 21
- Neither: Sentences 2, 8, 10, 12, 13, 15, 18, 19, 20

---

Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Commutative Property:} & 4, 5, 6, 14, 17 \\
\text{Identity Property:} & 1, 3, 7, 9, 11, 16, 21 \\
\text{Neither:} & 2, 8, 10, 12, 13, 15, 18, 19, 20
\end{array}
}
\]