Free 3rd grade math worksheet templates to customize - Free Printable

Problem Overview:

The task involves solving each equation and identifying which property of operations was used to solve it. Based on the property, you will color the corresponding "scoop" using the provided key.

Key Properties:

1. Blue (Associative Property): The grouping of numbers does not affect the result.
- Example: \( (a + b) + c = a + (b + c) \) or \( (a \times b) \times c = a \times (b \times c) \).

2. Pink (Commutative Property): The order of numbers does not affect the result.
- Example: \( a + b = b + a \) or \( a \times b = b \times a \).

3. Green (Identity Property): Adding 0 or multiplying by 1 does not change the number.
- Example: \( a + 0 = a \) or \( a \times 1 = a \).

4. Purple (Zero Property): Any number multiplied by 0 equals 0.
- Example: \( a \times 0 = 0 \).

5. Orange (Distributive Property): Distributing multiplication over addition or subtraction.
- Example: \( a \times (b + c) = a \times b + a \times c \).

Equations to Solve:

We will solve each equation and determine the property used.

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#### Left Scoop:
1. \( 6 \times 7 = \)
- Solution: \( 6 \times 7 = 42 \).
- Property: No specific property is directly applied here. This is a straightforward multiplication.
- Color: None (or leave as is if no specific rule applies).

2. \( 3 \times 2 \times 5 = \)
- Solution: \( (3 \times 2) \times 5 = 6 \times 5 = 30 \) or \( 3 \times (2 \times 5) = 3 \times 10 = 30 \).
- Property: Associative Property (grouping does not matter).
- Color: Blue.

3. \( 18 \times 4 = \)
- Solution: \( 18 \times 4 = 72 \).
- Property: No specific property is directly applied here. This is a straightforward multiplication.
- Color: None (or leave as is).

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#### Middle Scoop:
1. \( 3 \times 0 = \)
- Solution: \( 3 \times 0 = 0 \).
- Property: Zero Property (any number multiplied by 0 is 0).
- Color: Purple.

2. \( 1 \times 8 = \)
- Solution: \( 1 \times 8 = 8 \).
- Property: Identity Property (multiplying by 1 does not change the number).
- Color: Green.

3. \( 0 \div 5 = \)
- Solution: \( 0 \div 5 = 0 \).
- Property: Division involving 0. No specific property from the list applies directly.
- Color: None (or leave as is).

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#### Right Scoop:
1. \( 7 \div 1 = \)
- Solution: \( 7 \div 1 = 7 \).
- Property: Identity Property (dividing by 1 does not change the number).
- Color: Green.

2. \( 6 \times 2 \times 4 = \)
- Solution: \( (6 \times 2) \times 4 = 12 \times 4 = 48 \) or \( 6 \times (2 \times 4) = 6 \times 8 = 48 \).
- Property: Associative Property (grouping does not matter).
- Color: Blue.

3. \( 5 \times 3 = \)
- Solution: \( 5 \times 3 = 15 \).
- Property: No specific property is directly applied here. This is a straightforward multiplication.
- Color: None (or leave as is).

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Final Coloring Guide:

- Blue (Associative Property): \( 3 \times 2 \times 5 \), \( 6 \times 2 \times 4 \).
- Pink (Commutative Property): None.
- Green (Identity Property): \( 1 \times 8 \), \( 7 \div 1 \).
- Purple (Zero Property): \( 3 \times 0 \).
- Orange (Distributive Property): None.

Final Answer:

\[
\boxed{
\text{Blue: } 3 \times 2 \times 5, 6 \times 2 \times 4; \text{ Green: } 1 \times 8, 7 \div 1; \text{ Purple: } 3 \times 0
}
\]