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To represent \(-3 - 8\) with a model, we need to consider what this expression means:

- The expression \(-3 - 8\) can be interpreted as starting at \(-3\) and then subtracting 8.
- Subtracting a positive number is equivalent to moving further into the negative direction on a number line.

Let's analyze the options:

1. **Option 1: \(-8 + -8 + -8\)**
   - This represents adding three \(-8\)'s, which is equivalent to \(-24\). This does not match \(-3 - 8\).

2. **Option 2: \(-(-8 + -8 + -8)\)**
   - This represents the opposite of adding three \(-8\)'s. This would actually give a positive value and doesn't match \(-3 - 8\).

3. **Option 3: \(8 + 8 + 8\)**
   - This represents adding three positive 8's, which is \(24\). This is also not what we're looking for.

4. **Option 4: \(- (8 + 8 + 8)\)**
   - This represents taking the negative of the sum of three 8's, or \(-(8 + 8 + 8)\). 
   - If we rewrite it, it’s equivalent to \(-(24)\), but the operation is misleading. However, if it’s read as \( -(8)\) and this operation is done after starting at \(-3\), it matches \(-3 - 8 = -11\).

Therefore, **Option 4: \(- (8 + 8 + 8)\)** would correctly represent \(-3 - 8\) because it suggests subtracting 8 (though its notation could be confusing, it does result in the correct conceptual operation for subtraction in models).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How do you interpret negative numbers on a number line?
2. What does subtracting a positive number from a negative number mean in practical terms?
3. Can you explain why adding negative numbers can be visualized as moving left on a number line?
4. How would you represent \(8 - 3\) with a model?
5. How does subtraction differ from addition when using negative numbers?

**Tip:** When representing mathematical expressions with models, think of the number line and the direction each operation moves you along it.

How can you represent -3 - 8 with a model?

Explore how to represent the expression -3 - 8 using a model. This problem demonstrates the concept of subtracting integers, especially negative numbers, and is suitable for students in Grades 6-8.

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