Worked examples · Eqora guide
How to learn from worked math examples without copying the steps
Turn a finished solution into predictions, explanations, changed examples, and a problem you can solve alone.
A worked example can make a difficult method look obvious because every decision has already been made. That feeling of fluency is useful, but it is not yet proof that you can choose and carry out the method when the model disappears.
The goal is to treat the solution as a temporary guide. Read the problem, predict each important move, explain why it is valid, remove support gradually, and finish with a new question you solve from a blank page.
Read the decisions, not only the calculations
Take 4(2x − 1) = 3x + 17. A worked solution may expand to 8x − 4 = 3x + 17, collect terms as 5x = 21, and conclude x = 21/5. Before copying, name the decisions: distribute across the bracket, put variable terms on one side, put constants on the other, then divide by the remaining coefficient.
Check the result in the original equation, not only the final line. With x = 21/5, the left side is 4(42/5 − 1) = 148/5 and the right side is 63/5 + 17 = 148/5. The check shows what the answer must satisfy and protects against a copied sign error.
For every important line, ask: what changed, why is it allowed, and how could I check it?
Cover the next line and predict it
Reveal only the problem and the first line. Write the next operation before looking, then compare your choice with the model. A prediction can be different and still valid: subtracting 3x before expanding is awkward here, while expanding first is clearer, but two correct routes may eventually meet.
When your prediction differs, do not replace it automatically. Ask whether both transformations preserve equality, which route keeps the arithmetic simpler, and whether the example uses a convention required by your course. This turns reading into a sequence of mathematical decisions instead of transcription.
Fade the help one step at a time
Use a three-example sequence. Keep the first solution complete. In the second, hide the middle algebra but leave the method cue and answer. In the third, keep only the question. For instance, move from 4(2x − 1) = 3x + 17 to 3(x + 2) = 2x + 11, then to 5(2x − 3) = 4x + 9.
The second equation gives x = 5 and the third gives x = 4. Do not use those answers as prompts; use them only after finishing as checks. If one missing line stops you, restore just that line, explain it, cover it again, and restart from the previous step.
- Complete model with reasons beside the steps
- Partly completed example with one decision left to make
- Bare problem solved without the model in view
- Final substitution into the original equation
Explain the cue and the reason
A useful self-explanation links a visible cue to a method: ‘The variable appears on both sides, so I will collect variable terms before isolating x.’ Saying only ‘move 3x’ hides the fact that you subtract the same quantity from both sides and preserve equality.
Also explain what would make the move inappropriate. Cancelling factors is valid in a product or fraction under the right conditions, but not across addition. Naming the boundary of a rule makes it easier to recognize both correct uses and tempting imitations.
Change one feature and compare
After studying x² − 7x + 12 = 0, which factors as (x − 3)(x − 4) = 0, change only the constant to get x² − 7x + 10 = 0. Now the factor pair is 2 and 5. Compare which information stayed fixed, which clue changed, and why the roots changed.
Useful variations change a sign, move the unknown, introduce a fraction, rotate a diagram, or ask for a different quantity. Change one feature at first so you can identify its effect. Later, combine changes to test whether you recognize the structure rather than the page layout.
Study wrong steps as carefully as right ones
For (x + 3)/2 = 5, a common wrong line is x + 3 = 5, which forgets to multiply the right side by 2. The correct transformation is x + 3 = 10, so x = 7. Substitution makes the contrast decisive: (7 + 3)/2 = 5, while the mistaken answer x = 2 gives 5/2, not 5.
Label the cause precisely: operation applied to only one side, distribution error, sign error, wrong formula condition, or unchecked answer. Then repair the earliest wrong line and continue from there. Recopying the correct finish without locating the first invalid step teaches very little.
Finish with a blank-page problem
Close the example and solve a nearby problem without headings, hints, or an answer in sight. Before calculating, write the problem type, the clue that identified it, and a short plan. Afterward, check the original conditions and explain one step aloud or in a margin note.
If you cannot start, return to the model only long enough to recover the missing cue. If you can start but fail later, isolate that step and practise it. Success means reconstructing the method after support is removed, not remembering the visual position of each line.
Use Eqora to question the example, then close it
You can scan a worked example into Eqora and ask why one transformation is valid, whether your alternative route works, or for a similar problem with one changed feature. State the exact line you are questioning so the conversation stays focused on reasoning rather than producing another full answer.
Confirm that the symbols and signs were read correctly, because an AI tutor can misread notation or make a calculation error. Then put the explanation away and solve the new problem independently. Your own derivation and check remain the evidence that the method transferred.
Put it into practice now
Choose one problem from your current homework or review set. Attempt it before opening Eqora, then use the app only at the point where your own reasoning stops.
- State what the problem is asking before you solve it
- Identify the first step you cannot justify
- Ask Eqora one focused follow-up about that step
- Finish with a similar problem and no solution in view
The session is complete when the method is clearer, not simply when the worksheet has one more answer.