App tools

Make a mistake useful for the next attempt.

Turn a wrong answer into a useful error note. Keep the first incorrect decision, explain the correction and test a cue on a fresh problem before closing the loop.

iPhone & iPad · Free to download

Record the first incorrect decision, a useful correction and a new task that tests it.

A blue pencil, white eraser and fresh blank notes

See the idea in action

A correction worth keeping.

Track the first incorrect product, check the repair and keep a reminder you can apply before the same mistake happens again.

App tools · WORKED EXAMPLE

Why is −2(x − 3) = −2x − 6 an incorrect expansion?

ANSWERThe second product is positive

Prepared example for learning.

  1. 1

    Locate the first mismatch

    The first product, −2 × x, is −2x. The error is in the product of the two negative numbers.

  2. 2

    Repair the operation

    −2 × −3 = +6, so the correct expansion is −2x + 6.

  3. 3

    Check with a value

    At x = 4, the original expression is −2. The corrected expression is also −2; the incorrect one gives −14.

  4. 4

    Keep a useful clue

    Multiply every term inside the bracket, including its sign. Try −3(y − 2) without looking at the correction.

Try it in Lirno

Keep the clue that changes your next attempt.

Use Lirno’s Mistake Book to record what went wrong and why. Return with a fresh question that tests the same decision.

Start here

Find the first error. Keep the reason. Retest.

  1. 01

    Name the error

    Identify the operation, assumption or missing connection that changed the answer.

  2. 02

    Keep the correction

    Write the valid move and a short reason you can explain.

  3. 03

    Test a new question

    Choose a fresh case that needs the same decision, then attempt it before opening the note.

Record the cause rather than the whole page

A long copied solution can hide the important part of a mistake. Keep the original question or enough context to understand the error, then identify the first decision that needs repair. “Wrong answer” is an outcome; “treated area as a length” names something you can change.

Use a specific description that remains useful tomorrow. Include the operation, condition or relationship that failed. If you cannot identify the cause, share the attempt with Lirno and ask about the earliest mismatch rather than requesting a replacement solution.

Connect the correction with a reason

Write the corrected move beside the error and explain why it is valid. For distribution, include every term and sign. For physics, state which quantity belongs in the relationship. For writing, connect the claim with evidence that actually supports it.

Check the correction against your course material and the original task. A correction should do more than give a different answer. It should identify the condition or reasoning that lets you choose the valid move on another question.

Choose a clue that comes before the mistake

A useful clue tells you what to notice at the decision point. “Check my answer” comes late. “Circle the negative before expanding” comes before the sign error. “Name the requested quantity before selecting the formula” comes before a model mismatch.

Keep the clue short and observable. Use it while setting up the next problem, then gradually try the same type of task without the note. The goal is to recognize the pattern yourself, with the correction available when you need to inspect it.

Separate a concept gap from a slip

A repeated error may reveal a missing concept; a single arithmetic slip may need a different response. Explain the step in your own words. If you cannot say why it applies, revisit the idea. If the reason is clear but the execution failed, use a targeted check and a few fresh attempts.

Avoid assigning a fixed label to yourself from one result. Record what happened in this task and choose practice that addresses it. The next attempt gives you more evidence about whether the change helped.

Use an error log with a fresh test

A useful entry for −2(x − 3) = −2x − 6 records the first error as multiplying two negative numbers incorrectly. The correction is −2x + 6. The reason is (−2) × (−3) = +6, and the early clue is “multiply each term with its sign.” Keep these beside enough of the original task to recognize the issue.

Retest with −3(y − 2), whose expansion is −3y + 6. Then vary the sign structure: −3(y + 2) becomes −3y − 6. Explaining the difference tests the decision more directly than copying the old correction. Recent subject activity can help choose a review area, but the new attempted work gives evidence about this particular error.

Retest the correction after a gap

Use a different question with the same underlying decision. Change the numbers, wording or representation while keeping the skill in view. Attempt it before opening the mistake note. Then compare both the result and your reason for the key step.

If the error returns, refine the clue or revisit the missing prerequisite. If the attempt succeeds, keep the note available and move to a nearby challenge. Review works best as a conversation with new evidence about what you can do, rather than repeated reading of an old answer.

Decide when a note still needs attention

Keep the error note until a new attempt tests its cue. One correct result after reading the correction tells you less than a fresh problem attempted with the note closed. If a negative-distribution error returns, record whether you missed the second product or computed its sign incorrectly; those are different points to repair.

A note can become more compact once the cue is usable. Retain the original error, the reason for the correction and a changed test. A log full of copied pages is harder to act on than a short set of recurring decisions. Use the new attempts to decide which notes deserve another review.

Your next small win

Keep a clue you can use next time.

A correction becomes useful when you can recognize the risky decision before repeating it. Keep the first error, its reason and a small cue. Then choose a new question that tests that exact part of the method.

Prepared mini exercise

A previous error was −2(x − 3) = −2x − 6. Try expanding −3(y − 2), and name the clue that prevents the same mistake.

Give me a hint

Multiply each term inside the bracket by −3. Inspect the product involving the second negative sign separately before joining the terms.

Show the reasoning

The expansion is −3y + 6 because (−3) × (−2) = +6. A useful clue is “multiply every term, including its sign.” Checking with y = 4 gives −3(4 − 2) = −6 and −3 × 4 + 6 = −6.

Make it yours

Carry the idea into your own homework.

Write a note with the incorrect decision, a corrected example and one early clue. Try a changed expression before looking back at the note. If the error returns, identify which part of the clue you did not use.

Adapt a question for Lirno →

Catch it before it trips you up

Three small details.
A stronger attempt.

Inspect the part of the method that this exercise actually tests. These are the three errors to check first.

01

Saving only the final answer

The useful note identifies the decision that caused the mistake. Include a short reason and an early check, so you can act on it when another question looks different.

02

Changing several skills at once

Start with a nearby exercise that tests the same issue. A much harder task can add new gaps and make it unclear whether the original misconception was repaired.

03

Reviewing by recognition alone

Try the fresh question before reading the correction. Then explain why your new line is valid. That gives the stored note a role in checking and repairing an actual attempt.

Try a different case

Same idea.
A new decision.

Make an attempt before opening the explanation. These original tasks test a different part of the method, so a familiar answer alone will not be enough.

01

Keep the first error and a fresh test

Your error log says 4(x − 2) = 4x − 2. Write the correction, an early clue and a different test.

Compare your reasoning

Correction: 4(x − 2) = 4x − 8. Clue: multiply every term inside the bracket by 4, including its sign.

Fresh test: expand −2(y + 5) before viewing the correction. The answer is −2y − 10. This changes the signs and coefficient while testing the same distribution decision.

Keep this clue: Saving only x’s final value would lose the mistake the note needs to catch.

02

A unit error needs a unit clue

You used 15 instead of 0.25 when finding distance at 40 km/h for a 15-minute trip. What belongs in the error log?

Compare your reasoning

Record the mismatch: time was in minutes but the rate was per hour. Correction: 15/60 = 0.25 h, so distance = 40 × 0.25 = 10 km.

Fresh test: 60 km/h for 10 minutes gives 60 × (10/60) = 10 km. The useful clue is “make the time unit match the rate before substituting.”

Keep this clue: The same numerical answer in a new task still needs its own unit reasoning.

Ask a better question

A prompt you
can make your own.

Paste this into Lirno with your assignment. Add your attempt and say where you need help.

Here is my attempt and the corrected solution. Help me identify the first error, the idea behind the correction and one clue to notice next time. Give me a different practice question that tests the same decision, without revealing the answer first.

Quick quality check

Is the mistake note useful for a new question?

  • The note identifies a specific cause
  • The correction includes a valid reason
  • The clue points to something you can notice early
  • A fresh attempt tests the same decision without the answer

FAQs

Questions about Mistake Book & review

What should I put in a mistake note?

Keep enough of the task to understand it, the first error, the corrected reasoning and a short clue for the next attempt.

Is every error a concept gap?

No. Distinguish an unclear idea from an execution slip by explaining the step and trying a fresh case. Choose practice around the evidence.

What does a knowledge map tell me?

Use it to understand subject activity and choose a next review area. Combine that signal with independent attempts instead of treating activity as proof of mastery.

How do I know a correction has stuck?

Try a new question after a gap without opening the answer. Check whether you chose the right method and can explain the important step.

Check the foundations

Sources & further reading

The examples on this page are original teaching exercises. These resources explain the underlying concepts.

Published by Rocket Digital Limited for HomeworkPath. How these guides are prepared →

Keep going

More help for
the next assignment.

Keep the clue. Try again.

Record the correction in Lirno’s Mistake Book and test it with a fresh question.

Get Lirno for iOS

iPhone & iPad · Free to download