The permanent collection

Find the guide for your next decision.

Start with what your assignment needs: a clearer question, a valid method, a stronger paragraph or a focused review. These practical guides are ready to use now.

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Find your exact sticking point

What are you
working on?

Start with a topic such as brackets, molarity or paragraph evidence. Each link opens the relevant explanation, with worked examples and practice in the same guide.

34 topic routes. Choose an explanation below.

Math

Equations with x on both sides

Collect the variable terms, preserve equality and substitute to check.

Math

Brackets and negative signs

Distribute to every term or divide first when the structure allows it.

Math

Equations with fractions

Clear denominators while changing every term on both sides.

Math

Straight-line graphs

Connect slope, intercept and a simple system of equations.

Math

Right triangles and Pythagoras

Identify the hypotenuse before finding a missing side.

Math

Angles in triangles

Use marked facts and the appropriate angle relationship.

Math

Similarity and scale factors

Match corresponding sides and distinguish length from area scaling.

Math

Area versus perimeter

Choose the requested quantity and the correct dimensional unit.

Math

Fixed costs and hourly rates

Define the unknown and separate a one-off charge from a rate.

Math

Percentages and discounts

Identify the amount the percentage uses before calculating.

Math

Rate, time and unit conversions

Make time units agree with the rate, then interpret the result.

Science

Speed versus velocity

Distinguish total path length from displacement in a journey.

Science

Reading a motion graph

Use axis labels and changes over the requested interval.

Science

Net force and acceleration

Combine forces with direction before applying Newton’s second law.

Science

Work and energy

Use the force direction and the conditions of the energy model.

Science

Moles from mass

Distinguish mass, amount of substance and molar mass.

Science

Molarity and final solution volume

Convert volume to liters before finding amount per volume.

Science

Balancing chemical equations

Change coefficients while preserving each chemical formula.

Science

Limiting reactants

Use the balanced mole relationship to find which reactant runs out.

Science

Osmosis and water movement

State the membrane and solution conditions before choosing direction.

Science

Diffusion versus active transport

Compare what moves, the gradient and the energy requirement.

Science

Biology graphs and percentage change

Separate the observed pattern from its proposed cause.

English

Claims supported by a passage

Build an interpretation that the supplied words can justify.

English

Short quotations and analysis

Explain the role of the evidence instead of leaving the quote alone.

English

Literary devices and their effects

Explain what a device contributes to this particular passage.

Study tools

Prepare a homework photo

Keep the question, symbols, diagram and instruction readable.

Study tools

Ask for a hint or follow-up

Show your attempt and name the exact missing connection.

Study tools

Inspect a step-by-step solution

Locate the earliest transition you cannot justify.

Study tools

Improve an essay draft

Inspect the argument, evidence and limits before polishing the draft.

Study tools

Make flashcards and quizzes

Write focused recall tasks and verify the answers before practice.

Study tools

Plan tonight’s homework

Fit assignments, checks and a buffer inside the available time.

Study tools

Choose exam revision

Separate a concept gap, a wrong setup and an execution mistake.

Study tools

Rebuild a concept with a lesson

Connect an explanation, a visual relationship and a new attempt.

Study tools

Keep a useful error log

Record the first error, a correction and a fresh test.

Six ways into the work

Choose the difficulty.
Find a useful route.

You do not have to read the whole collection in order. Choose the action closest to your current difficulty. Each route connects two guides so you can move from understanding the task to doing something with it.

These are permanent learning resources with prepared examples, checks and prompts you can adapt in Lirno. The study journal will hold future articles separately.

01

Read the question before solving it

A worksheet can include a calculation, a diagram and a written explanation in the same exercise. Begin with the command word and the thing you must produce. A photo should include the supporting material, not just the line that contains numbers.

Use the scanner guide to prepare the input, then the subject guide to identify the reasoning. If several questions depend on the same diagram, keep that diagram available while focusing on one part. Before requesting a solution, check that the task being discussed matches the original.

02

Find the connection between two steps

When a solution stops making sense, locate the exact transition. Name what changed: an operation on both sides, a substituted quantity, an assumption about a model or an interpretation of evidence. That gives your tutoring question a clear target.

Use the step-by-step guide for the reasoning, then the AI tutor guide for a focused follow-up. Ask for a smaller example if a prerequisite is missing. Predict the next move before opening the response, and use the explanation to inspect that prediction.

03

Build a model from a story or a diagram

An equation needs to represent the situation it answers. Define the unknown, identify fixed and changing quantities, and choose consistent units. For science, state the system or sample before selecting the relationship. A familiar formula is useful only if it fits the conditions.

Use word problems for translating a story into a model, or science help for connecting measurements with a mechanism. Try changing one condition and predict the effect. Then check whether the model still describes the new question before repeating the calculation.

04

Choose the writing guide for the actual task

A reading response and an argument essay have different jobs. For a supplied passage, inspect which interpretation its words can support. For a proposal or evaluation, inspect the claim, the evidence and the conditions under which the recommendation works.

Use English for literary analysis: a short quotation needs an explanation of its effect. Use Writing Lab for outlining and revising an argument: a survey preference cannot by itself prove better grades. Both routes work from actual evidence, but they address different writing decisions.

05

Practice the idea after the explanation

Choose practice that asks you to produce the skill. Definitions can become focused recall cards. A process can become a blank sequence to explain. A calculation needs a new case with different values. The format should fit what you want to be able to do independently.

Use Lesson Studio when the topic needs a fuller explanation, then use flashcards or quizzes to test the central connection. Check generated materials against your notes before practicing. Hide the answer, make an attempt and use the result to decide which part needs another pass.

06

Review what failed and plan the next attempt

A missed question gives you a decision to investigate. Was the concept unclear, the model wrong or the execution inaccurate? Keep the first error and a short correction. Choose a fresh question that tests the same idea, rather than only rereading the finished answer.

Use Mistake Book for the correction, and Exam Coach when you need to diagnose a set of topics before a test. Put the next action into a realistic homework block. Review the result of that block and update the plan with the progress you actually made.

Use a guide with your homework

Read one example.
Make one attempt.

Read the worked example and pause before the next step. Predict the operation, interpretation or check you would use. Then compare your reasoning with the explanation. This gives the example a job beyond showing you a completed answer.

For example, the step-by-step page repairs an invalid division operation; the tutor page shows how to question a membrane-transport classification; Lesson Studio connects fractions, decimals and percentages. Choose the example whose decision resembles yours. The shared layout helps navigation, while the teaching task changes from page to page.

Finish with a small independent attempt. Use new values, a new passage or one changed condition. Check both the result and the reason for the key decision. Keep the useful clue for your next session.

Give that next attempt a place in your plan →

Start with a concrete example

Three subjects.
Three kinds of reasoning.

Choose an equation, a science process or a paragraph. The method changes with the task, while the habit of explaining and checking stays useful.

FAQs

Choose one route, then try it.

Are these blog articles?

These are permanent subject and app-workflow guides. The journal overview is separate, and the first journal articles are still being prepared.

What if I do not know the missing concept?

Start with your attempt and the step that feels unclear. Use the AI tutor guide to ask a focused question, or the Lesson Studio guide to rebuild the topic with more context.

Can I follow a route across subjects?

Yes. A science calculation may need both a scientific model and an algebraic method. Use each guide for the part of the reasoning it addresses.

Try the method on your homework.

Bring your question and attempt to Lirno for a focused tutoring conversation.

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