| Definition | Identify the value, relationship, comparison, or decision the problem actually asks you to determine. | List known quantities separately from statements that connect them, constrain them, or compare them. | Select an equation, inequality, graph, table, or linear system according to the kind of relationship and answer needed. | Build the representation in small pieces and attach each term, coefficient, sign, and boundary to its meaning. | Apply operations that keep the solution set unchanged, documenting restrictions or branches when they matter. | Return candidate results to the original relationship and the original situation before accepting them. |
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| Primary decision question | What must the final statement say, and what symbol could represent that unknown? | Which facts are fixed values, and which phrases describe how values depend on one another? | Is the situation asking for exact equality, an allowed range, visual behavior, organized values, or simultaneous conditions? | What does each symbol represent, and which phrase supports each mathematical relationship? | Why is this transformation valid, and did it act on every required part of the relationship? | Does the result satisfy the mathematics, respect the context, and answer the requested quantity? |
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| Purpose | Prevents an accurate calculation from answering a different question than the one posed. | Turns dense prose into a compact inventory without prematurely choosing operations. | Matches the mathematical tool to the reasoning task instead of defaulting to a familiar formula. | Makes reversal errors, missing units, and unsupported operations visible before they spread. | Treats algebra as controlled reasoning rather than a sequence of symbol-moving shortcuts. | Catches arithmetic errors, introduced candidates, missing branches, unsuitable units, and incomplete conclusions. |
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| Time horizon | Before selecting an equation, graph, table, inequality, or system. | After identifying the target and before translating relationship language. | Before symbolic manipulation begins. | During model construction, before solving. | From the original representation to candidate result or solution set. | After solving and before the learner submits their own response. |
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| Typical information | The learner can state the requested quantity with a label, meaning, and relevant unit when one exists. | A short learner-written list of variables, known values, units, boundaries, and dependencies. | A one-sentence justification that names what the representation preserves or reveals. | A symbol-to-meaning note and a plain-language reading of the completed representation. | Each line can be connected to a property, inverse operation, distribution step, or justified case decision. | Substitution, graph or table consistency, boundary testing, unit review, and a concluding sentence tied to the question. |
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| Common confusion | Treating every number in the prompt as something that must be used immediately. | Converting a phrase into an operation before deciding which quantities the phrase connects. | Using an equation when boundary language calls for an inequality, or one equation when two independent conditions must hold together. | Reading subtraction or comparison phrases in surface word order without checking the underlying relationship. | Changing a sign because a term crossed the equals sign instead of explaining the same operation on both sides. | Checking only the last simplified line, which may preserve an earlier mistake consistently. |
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| What does not belong | Do not reproduce a current graded prompt; summarize the mathematical relationship in your own words. | Do not invent missing values or silently assume a relationship the problem never states. | This is a Domyclass reasoning step, not an official AMU sequence or required classroom method. | Do not force a generic template onto a situation whose quantities or conditions do not match it. | A helper may diagnose a learner-owned step, but the learner performs and owns the final solution. | Verification supports learning; it is not a guarantee of a grade or a replacement for classroom instructions. |
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