Lesson 2.12

Error Analysis

To truly master algebra, you must become a math detective. Finding mistakes in someone else's work strengthens your own ability to avoid them.

Introduction

Everyone makes mistakes! The best mathematicians spot them quickly. In this lesson, we won't just solve problems; we will critique "incorrect" student work to explain what went wrong.

Past Knowledge

You need to know the correct D.C.M.M.D steps to spot when they are broken.

Today's Goal

Identify distribution errors, sign errors, and arithmetic mistakes.

Future Success

This builds the "Internal Spellcheck" you need for higher-level math exams.

Key Concepts

The "Spot the Error" Checklist

  • Did they Distribute correctly?

    Check if the second number was multiplied. ()

  • Did signs flip correctly?

    Subtracting a negative becomes positive. Multiplying by a negative flips signs.

  • Did they do the same thing to BOTH sides?

    If they subtracted 5 from the left, did they subtract 5 from the right?

Worked Examples - Find the Error

Case 1: The "Lazy Distribute"

Error Found

Problem:

// Student Work

Step 1: ← ERROR HERE

Step 2:

Step 3:

Correction:

The student forgot to multiply the 5 by 2. It should be .

Correct Answer:

Case 2: The "Magic Minus"

Error Found

Problem:

// Student Work

Step 1: Divide by 3

Step 2: ← ERROR HERE

Correction:

The student dropped the negative sign. A positive divided by a negative is negative.

Correct Answer:

Case 3: Inverse Operations Mix-up

Error Found

Problem:

// Student Work

Step 1: Subtract 4 from both sides ← ERROR HERE

Step 2:

Correction:

The inverse of subtraction is addition. The student should have ADDED 4.

Correct Answer:

Common Pitfalls

The Plug-In Method

Take your answer (e.g., 5) and plug it back into the original equation. Does ? Yes (). If it doesn't match, you made a mistake.

Rushing

90% of structural errors come from doing two steps in your head at once. Write every step down vertically!

Practice Quiz

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