Students can use this worksheet to practice identifying the commutative and associative properties of addition through various equation problems.

Problem Analysis:

The worksheet focuses on addition properties, specifically the commutative property and the associative property. Let's solve each part step by step.

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Left Column: Answer the questions and write which operation property is being shown.

#### 1)
- 5 + 9 = _______
- Calculation: \( 5 + 9 = 14 \)
- 9 + 5 = _______
- Calculation: \( 9 + 5 = 14 \)
- Property:
- The order of the numbers does not change the sum. This demonstrates the Commutative Property of Addition.

#### 2)
- 7 + (4 + 2) = _______
- First, calculate inside the parentheses: \( 4 + 2 = 6 \)
- Then, add: \( 7 + 6 = 13 \)
- (7 + 4) + 2 = _______
- First, calculate inside the parentheses: \( 7 + 4 = 11 \)
- Then, add: \( 11 + 2 = 13 \)
- Property:
- The way the numbers are grouped does not change the sum. This demonstrates the Associative Property of Addition.

#### 3)
- 3 + (12 + 6) = _______
- First, calculate inside the parentheses: \( 12 + 6 = 18 \)
- Then, add: \( 3 + 18 = 21 \)
- (12 + 6) + 3 = _______
- First, calculate inside the parentheses: \( 12 + 6 = 18 \)
- Then, add: \( 18 + 3 = 21 \)
- Property:
- The way the numbers are grouped does not change the sum. This demonstrates the Associative Property of Addition.

#### 4)
- 8 + 10 + 11 = _______
- Add sequentially: \( 8 + 10 = 18 \), then \( 18 + 11 = 29 \)
- 10 + 11 + 8 = _______
- Add sequentially: \( 10 + 11 = 21 \), then \( 21 + 8 = 29 \)
- Property:
- The order of the numbers does not change the sum. This demonstrates the Commutative Property of Addition.

#### 5)
- 40 + (26 + 29) = _______
- First, calculate inside the parentheses: \( 26 + 29 = 55 \)
- Then, add: \( 40 + 55 = 95 \)
- (40 + 26) + 29 = _______
- First, calculate inside the parentheses: \( 40 + 26 = 66 \)
- Then, add: \( 66 + 29 = 95 \)
- Property:
- The way the numbers are grouped does not change the sum. This demonstrates the Associative Property of Addition.

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Right Column: Complete the number sentences and identify the property used.

#### 10)
- 4 + _______ = 7
- To find the missing number, subtract: \( 7 - 4 = 3 \)
- So, \( 4 + 3 = 7 \)
- ______ + 3 = 7
- To find the missing number, subtract: \( 7 - 3 = 4 \)
- So, \( 4 + 3 = 7 \)
- Property:
- The order of the numbers does not change the sum. This demonstrates the Commutative Property of Addition.

#### 11)
- 44 + _______ = 72
- To find the missing number, subtract: \( 72 - 44 = 28 \)
- So, \( 44 + 28 = 72 \)
- ______ + 28 = 72
- To find the missing number, subtract: \( 72 - 28 = 44 \)
- So, \( 44 + 28 = 72 \)
- Property:
- The order of the numbers does not change the sum. This demonstrates the Commutative Property of Addition.

#### 12)
- 33 + (______ + 37) = 93
- First, let the missing number be \( x \). The equation becomes: \( 33 + (x + 37) = 93 \)
- Simplify inside the parentheses: \( x + 37 \)
- Then, \( 33 + (x + 37) = 93 \) simplifies to \( 33 + x + 37 = 93 \)
- Combine like terms: \( 70 + x = 93 \)
- Solve for \( x \): \( x = 93 - 70 = 23 \)
- So, \( 33 + (23 + 37) = 93 \)
- (33 + _______) + 37 = 93
- Let the missing number be \( y \). The equation becomes: \( (33 + y) + 37 = 93 \)
- Simplify: \( 33 + y + 37 = 93 \)
- Combine like terms: \( 70 + y = 93 \)
- Solve for \( y \): \( y = 93 - 70 = 23 \)
- So, \( (33 + 23) + 37 = 93 \)
- Property:
- The way the numbers are grouped does not change the sum. This demonstrates the Associative Property of Addition.

#### 13)
- 12 + _______ + 8 = 62
- Let the missing number be \( x \). The equation becomes: \( 12 + x + 8 = 62 \)
- Combine like terms: \( 20 + x = 62 \)
- Solve for \( x \): \( x = 62 - 20 = 42 \)
- So, \( 12 + 42 + 8 = 62 \)
- ______ + 8 + 12 = 62
- Let the missing number be \( y \). The equation becomes: \( y + 8 + 12 = 62 \)
- Combine like terms: \( y + 20 = 62 \)
- Solve for \( y \): \( y = 62 - 20 = 42 \)
- So, \( 42 + 8 + 12 = 62 \)
- Property:
- The order of the numbers does not change the sum. This demonstrates the Commutative Property of Addition.

#### 14)
- 31 + (______ + 43) = 119
- Let the missing number be \( x \). The equation becomes: \( 31 + (x + 43) = 119 \)
- Simplify inside the parentheses: \( x + 43 \)
- Then, \( 31 + (x + 43) = 119 \) simplifies to \( 31 + x + 43 = 119 \)
- Combine like terms: \( 74 + x = 119 \)
- Solve for \( x \): \( x = 119 - 74 = 45 \)
- So, \( 31 + (45 + 43) = 119 \)
- (45 + _______) + 31 = 119
- Let the missing number be \( y \). The equation becomes: \( (45 + y) + 31 = 119 \)
- Simplify: \( 45 + y + 31 = 119 \)
- Combine like terms: \( 76 + y = 119 \)
- Solve for \( y \): \( y = 119 - 76 = 43 \)
- So, \( (45 + 43) + 31 = 119 \)
- Property:
- The way the numbers are grouped does not change the sum. This demonstrates the Associative Property of Addition.

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Final Answers:

#### Left Column:
1. \( 5 + 9 = 14 \), \( 9 + 5 = 14 \), Commutative Property
2. \( 7 + (4 + 2) = 13 \), \( (7 + 4) + 2 = 13 \), Associative Property
3. \( 3 + (12 + 6) = 21 \), \( (12 + 6) + 3 = 21 \), Associative Property
4. \( 8 + 10 + 11 = 29 \), \( 10 + 11 + 8 = 29 \), Commutative Property
5. \( 40 + (26 + 29) = 95 \), \( (40 + 26) + 29 = 95 \), Associative Property

#### Right Column:
10. \( 4 + 3 = 7 \), \( 3 + 4 = 7 \), Commutative Property
11. \( 44 + 28 = 72 \), \( 28 + 44 = 72 \), Commutative Property
12. \( 33 + (23 + 37) = 93 \), \( (33 + 23) + 37 = 93 \), Associative Property
13. \( 12 + 42 + 8 = 62 \), \( 42 + 8 + 12 = 62 \), Commutative Property
14. \( 31 + (45 + 43) = 119 \), \( (45 + 43) + 31 = 119 \), Associative Property

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Left Column:} & \text{Right Column:} \\
1. & 14, 14, \text{Commutative Property} \\
2. & 13, 13, \text{Associative Property} \\
3. & 21, 21, \text{Associative Property} \\
4. & 29, 29, \text{Commutative Property} \\
5. & 95, 95, \text{Associative Property} \\
10. & 3, 4, \text{Commutative Property} \\
11. & 28, 44, \text{Commutative Property} \\
12. & 23, 23, \text{Associative Property} \\
13. & 42, 42, \text{Commutative Property} \\
14. & 45, 43, \text{Associative Property} \\
\end{array}
}
\]