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The problem is asking how to represent the expression \( -2 \cdot 9 \) with a model. 

The expression \( -2 \cdot 9 \) can be interpreted as "negative two groups of nine." When we think about multiplication with negative numbers, particularly in terms of models, we typically use models like the number line or groups.

Here’s a breakdown of the options:

1. **\(-2 + 2\):** This represents the sum of a negative two and a positive two, not multiplication.
2. **\(9 + 9\):** This represents two groups of nine, but both are positive, so it’s \(2 \times 9\).
3. **\(- (9 + 9)\):** This is the correct choice, as it represents the sum of two nines with the entire expression negated, which effectively models \( -2 \times 9 \).
4. **\(-9 + (-9)\):** This also represents the sum of two nines, both negative, and thus models \( -2 \times 9 \) as well.

Therefore, **both** options 3 and 4 correctly represent \( -2 \cdot 9 \) using a model.

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What would the model look like for \( -3 \cdot 4 \)?
2. How can you represent \( -2 \cdot (-5) \) using a model?
3. What is the significance of the negative sign in multiplication?
4. How does the commutative property apply to multiplication involving negative numbers?
5. What happens when you multiply three negative numbers together?

**Tip:** When dealing with multiplication involving negative numbers, think about how many groups you have and whether those groups are positive or negative to help visualize the problem.

How can you represent -2 * 9 with a model?

Learn how to represent the multiplication of -2 and 9 using a model. This guide explains the mathematical concept of multiplying negative numbers and helps students visualize the operation with detailed examples, suitable for Grades 6-8.

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