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Let's break down the problems one by one.

### 1. **Expression for the sum of 13 and 12, which is then multiplied by 2:**
   - First, calculate the sum of 13 and 12: $ 13 + 12 $
   - Then, multiply this sum by 2: $ (13 + 12) \times 2 $

   The expression is:
   \[
   (13 + 12) \times 2
   \]

### 2. **Expression for dividing 16 by 4 and adding the sum of 3 and 8 to the quotient:**
   - First, divide 16 by 4: $ 16 \div 4 $
   - Then, add the sum of 3 and 8 to the quotient: $ (16 \div 4) + (3 + 8) $

   The expression is:
   \[
   (16 \div 4) + (3 + 8)
   \]

### 3. **Expression for multiplying 12 and 6 and then dividing the product by q:**
   - First, multiply 12 and 6: $ 12 \times 6 $
   - Then, divide the product by $ q $: $ (12 \times 6) \div q $

   The expression is:
   \[
   (12 \times 6) \div q
   \]

### 4. **Without calculating, circle the expression with the greater value:**
   Expressions to compare:
   - $ 3 \times (126 + 12) $
   - $ 6 \times (126 + 12) $
   - $ \frac{18 - 8}{2} $
   - $ \frac{18 - 8}{5} $

   The greater expression here is $ 6 \times (126 + 12) $ because multiplying by 6 will yield a greater value than multiplying by 3 for the same addition operation.

### 5. **Explain how you knew which expression had the greater value:**
   - The expression $ 6 \times (126 + 12) $ is greater because multiplying by a larger number (6 instead of 3) produces a larger result for the same sum.

### 6. **Expression for Ivan's video game score:**
   - Ivan starts with 1,300 points, earns 120 more, then loses 12 points. Finally, his score doubles.
   - First, calculate his new score: $ 1300 + 120 - 12 $
   - Then, double the result: $ 2 \times (1300 + 120 - 12) $

   The expression is:
   \[
   2 \times (1300 + 120 - 12)
   \]

### 7. **Write a situation modeled by the expression $ 6 \times (24 - 5) $:**
   One possible situation is:
   - "A group of 6 friends goes shopping. Each friend buys $ (24 - 5) $ items, where 24 represents the original number of items they wanted, but they removed 5 items. The total number of items bought by the group is $ 6 \times (24 - 5) $."

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Let me know if you'd like further explanations or help with any step. 

Here are 5 related questions you can try:
1. How would you model the expression $ 4 \times (10 + 7) $?
2. Can you create an expression where a number is first divided by 3 and then multiplied by 5?
3. If an item costs $15 and you buy 3, then get a $10 discount, how can you express this?
4. How would you compare two expressions like $ 4 \times 50 $ and $ 6 \times 35 $?
5. What would happen if Ivan's score tripled instead of doubling?

**Tip**: Always work through the operations in the correct order (PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)).

Write an expression that models the calculation described in words. The sum of 13 and 12, which is then multiplied by 2. Divide 16 by 4 and add the sum of 3 and 8 to the quotient. Multiply 12 and 6 and divide the product by q.

Learn how to model expressions based on word problems involving sums, products, and quotients. This exercise covers key algebraic concepts suitable for students in Grades 5-6.

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