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 $6 \times (24 - 5)$."

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)).