Substitution and Order Operations

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Date:

📚 Part 1: Order of Operations Review

Remember GEMA: Grouped (brackets), Exponents (powers), Multiplicative (× and ÷), Additive (+ and −)

Step-by-Step Instructions: Follow the GEMA order when solving expressions. Always start with operations inside brackets, then calculate exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.

Example: For the expression 3 + 2² × 4, first calculate the exponent: 2² = 4. Then, perform the multiplication: 4 × 4 = 16. Finally, add: 3 + 16 = 19.

1. Which operation should be done FIRST in the expression: 3 + 2² × 4?

Addition (3 + 2)

Exponent (2²)

Multiplication (2 × 4)

2. Explain why the order of operations is important when solving expressions:

3. Identify the correct order of operations for the expression: (5 + 3) × 2 - 4 ÷ 2. List the steps in order:

✏️ Part 2: Substitution Practice

Instructions: Replace the variable with the given value, then calculate using GEMA order of operations. Show all steps!

Step-by-Step Instructions: When substituting, replace the variable with its value and then follow the GEMA order of operations to solve the expression. Write out each step clearly.

Example: If x = 3, for the expression 2x + 5, substitute to get 2(3) + 5. Then calculate: 2 × 3 = 6, and finally 6 + 5 = 11.

4. If x = 3, calculate: 2x + 5

Answer: _________

5. If a = 4, calculate: 3a² − 7

Answer: _________

🎯 Part 3: Challenge Problems

Step-by-Step Instructions: For each challenge problem, substitute the values into the expression and follow the GEMA order of operations. Be sure to show all your work!

6. If m = 3 and n = 2, calculate: 2m² + 3n − 5

Answer: _________

7. If x = 4, calculate: 3(x − 1)² + 2x

Answer: _________

8. Check your answer to question 7 by estimation. Explain your reasoning:

9. Explain in your own words why the order of operations is important when substituting values into algebraic expressions: