Using each of these numbers exactly once 5, 8, 12, and 6, create 13 mathematical expressions. Each expression should evaluate to the numbers 1 through 13.

Let's create mathematical expressions using the numbers 5, 8, 12, and 6 exactly once in each expression. The goal is to obtain the numbers 1 through 13 as the results of these expressions.

1. \( 12 - 8 - 5 + 2 = 1 \)
2. \( 6 \div (12 - 8) + 5 - 6 = 2 \)
3. \( 12 - 8 + 6 \div 6 = 3 \)
4. \( 5 - 8 + 12 \div 6 = 4 \)
5. \( 12 - 8 + 6 - 5 = 5 \)
6. \( (12 - 8) \times 6 \div 12 = 6 \)
7. \( 8 - 12 + 5 \times 2 = 7 \)
8. \( 8 + 5 - 12 + 7 = 8 \)
9. \( 8 + 5 - (12 \div 6) = 9 \)
10. \( 12 - 5 - 8 + 10 = 10 \)
11. \( 12 - 5 + 4 = 11 \)
12. \( (12 \times 6) \div 12 + 5 = 12 \)
13. \( (12 - 8) + (5 \times 2) = 13 \)

Would you like more details or explanations on how these expressions were formed? Here are 5 related questions for further practice:

1. Can you create a different set of expressions that evaluates to the numbers 1 through 13 using the same four numbers?
2. How would these expressions change if we added a fifth number to use in each expression?
3. Can you find another set of four numbers that can produce all the values from 1 to 13?
4. What happens if you restrict the operations allowed to only addition and subtraction?
5. Could you form the numbers 14 through 20 with the same set of numbers?

**Tip:** Breaking down each target number into possible operations can simplify the process of creating these expressions.

Explore how to create mathematical expressions using the numbers 5, 8, 12, and 6 to evaluate numbers from 1 to 13. Discover various arithmetic operations and strategies used in forming these expressions. Suitable for students in Grades 6-8.

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