Grade: Grade 6 Subject: SAT/ACT Skills Unit: Algebra Readiness SAT: Algebra ACT: Math

Review Mistakes

Learn

Every mistake is a learning opportunity. Top test-takers don't just check if they got a problem right or wrong. They analyze WHY they made each error and create a plan to avoid it next time.

The Three Types of Errors

1. Careless Errors

You knew how to solve it but made a small slip.

  • Copying a number wrong
  • Simple arithmetic mistake (like 7 + 5 = 11)
  • Forgetting a negative sign
  • Answering a different question than asked

Fix: Slow down, double-check arithmetic, re-read the question before answering.

2. Concept Errors

You didn't fully understand the math concept.

  • Using addition when you should subtract
  • Not knowing what "decreased by" means
  • Confusing the order of operations

Fix: Go back to the lesson, study examples, practice similar problems.

3. Strategy Errors

You understood the concept but used an inefficient approach.

  • Taking too long on one problem
  • Not recognizing the question type
  • Making the problem harder than needed

Fix: Learn question patterns, practice identifying shortcuts.

The Error Log Method

Keep a notebook where you record each mistake using this format:

Column What to Write
Problem Copy the original problem
My Answer What you wrote
Correct Answer The right answer
Error Type Careless, Concept, or Strategy
Why I Missed It Specific explanation
How to Avoid It Your action plan

Examples: Error Analysis

Example 1: Careless Error

Problem: If x = 4, what is 3x + 2?

Student wrote: 3(4) + 2 = 14 (This is correct!)

But circled: Answer choice B: 10

Analysis: Careless error. Calculated correctly but marked the wrong answer.

Fix: Always double-check that your circled answer matches your work.

Example 2: Concept Error

Problem: Solve: n - 8 = 15

Student wrote: n = 15 - 8 = 7

Correct: n = 15 + 8 = 23

Analysis: Concept error. Subtracted instead of adding to undo the subtraction.

Fix: Remember: to undo subtraction, add to both sides. Review inverse operations.

Example 3: Strategy Error

Problem: "A number increased by 7 equals 20." Find the number.

Student approach: Tried random numbers until one worked. Took 2 minutes.

Better approach: Write equation n + 7 = 20, then solve n = 13. Takes 20 seconds.

Analysis: Strategy error. Guessing wastes time.

Fix: Always write an equation first, then solve algebraically.

Practice: Identify the Error Type

For each situation, identify whether it's a Careless, Concept, or Strategy error.

1. Jamie solved 5 + 3x when x = 2 and got 16. (Correct answer: 11)

Jamie's work: 5 + 3(2) = 5 + 6 = 16

Error type: _____________

2. Sam was asked to simplify 4a + 3a and wrote 7a^2.

Error type: _____________

3. Taylor spent 4 minutes on one easy problem and ran out of time for harder ones.

Error type: _____________

4. Alex solved m + 12 = 20 correctly (m = 8) but wrote "8" as "6" on the answer sheet.

Error type: _____________

5. Morgan translated "5 less than n" as 5 - n instead of n - 5.

Error type: _____________

6. Jordan didn't notice a "solve" problem had two steps and only did one.

Error type: _____________

7. Casey calculated 8 - 3 = 6 when simplifying.

Error type: _____________

8. Riley didn't know that "quotient" means division and skipped the problem.

Error type: _____________

Answer Key

  1. Careless (5 + 6 = 11, not 16)
  2. Concept (like terms add coefficients, not exponents)
  3. Strategy (poor time management)
  4. Careless (transcription error)
  5. Concept (order matters in subtraction phrases)
  6. Careless/Strategy (didn't read carefully or check)
  7. Careless (arithmetic mistake)
  8. Concept (vocabulary gap)

Check Your Understanding

1. Look at your recent math work. Find one mistake you made. What type of error was it?

2. Which error type do you think you make most often?

3. What is one specific action you can take to reduce that type of error?

4. Why is it important to analyze errors rather than just count how many you got wrong?

Your Error Log Template

Use this format to track your mistakes:

Problem My Answer Correct Type Fix
     
     
     

Next Steps

  • Start an error log in a notebook or spreadsheet
  • Review your error log before each practice session
  • Look for patterns (do you make the same type of error repeatedly?)
  • Move on to Mixed Set to practice all skills together