Expression:
Evaluate 3 × (x + 4) when x = 5

Student Work:
3 × (x + 4) → 3 × (x) + 4 → 3 × 5 + 4 = 19

Why It's Wrong:
The student split the expression incorrectly, applying multiplication only to x, not to the whole parenthetical expression.

Discussion Prompt:

• “Why can’t we break the parentheses apart like this?”

• “What operation should be done first?”

🔸 Error 2: Ignoring Parentheses

Student Work:
3 × (x + 4) → 3 × x + 4 → 3 × 5 + 4 = 19

Why It's Wrong:
The student ignored the parentheses, treating it as 3x + 4 instead of distributing 3 to both x and 4.

Discussion Prompt:

• “How do parentheses change the meaning of the expression?”

• “Would 3x + 4 be the same as 3(x + 4)? Why or why not?”

🔸 Error 3: Adding Before Substituting

Student Work:
3 × (x + 4) → 3 × (x) + (4) → 3 × x = 15, then 15 + 4 = 19

Why It's Wrong:
The student mixed substitution and evaluation in the wrong order.

Discussion Prompt:

• “What should we do first: substitute or evaluate?”

• “Does x + 4 mean you wait to add until you know x?”

🔸 Error 4: Misapplying the Order of Operations

Student Work:
3 × (x + 4) = 3 × x + 4 = 3 × 5 + 4 = 19
(Doesn’t follow PEMDAS strictly)

Why It's Wrong:
This shows a lack of understanding of the precedence of parentheses.

Discussion Prompt:

• “What does PEMDAS say about expressions inside parentheses?”

• “Can you evaluate the expression in a different order?”

🔸 Error 5: Incorrect Arithmetic

Student Work:
3 × (x + 4) → 3 × (5 + 4) = 3 × 8 = 24

Why It's Wrong:
Simple arithmetic mistake (5 + 4 = 9, not 8).

Discussion Prompt:

• “Let’s recheck our addition. What’s 5 + 4?”

• “Even if your process was right, what went wrong here?”