Find the first maths mistake and coach the next step
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Guide

Find the first maths mistake and coach the next step

Compare the question with each line of working. Find the first step that does not follow, give one hint and let the learner try again.

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1

Start with the written line, not a label

Use this fictional algebra example to practise finding the first unsupported step and asking one useful question. For real work, keep the exact question and numbered working, but remove names, school details and personal images. Work it out yourself or use one approved assistant; this worksheet does not inspect uploaded homework or assess ability. “Careless” is not a mathematical explanation. It is just a label wearing a calculator hat.

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  1. Start with the written line, not a label

    Use this fictional algebra example to practise finding the first unsupported step and asking one useful question. For real work, keep the exact question and numbered working, but remove names, school details and personal images. Work it out yourself or use one approved assistant; this worksheet does not inspect uploaded homework or assess ability. “Careless” is not a mathematical explanation. It is just a label wearing a calculator hat.

  2. Keep the question, working and unknowns together

    Fictional teaching case. [M1] Question: solve 3(x + 2) = 18. [M2] Learner working: L1: 3x + 2 = 18 L2: 3x = 16 L3: x = 16/3 [M3] The original question and these three lines are the only observed work. We do not know what the learner intended, which method was taught or whether this is a repeated error. [M4] Goal: identify the first line that does not follow, ask one hint-first question, then let the learner rewrite that line. Keep the full solution in a separate adult/teacher reference until after the retry. [M5] If the distribution step is understood after retry, prepare one new equation with the same structure and positive whole-number solution. No brackets inside brackets, negatives, fractions or extra operations. Keep M1–M5 and L1–L3 when editing. Do not invent spoken reasoning to make the cause look certain.

  3. Ask for the first break and a hint ladder

    Use only the supplied maths question, learner working and permitted topic or method. Preserve their labels. Find the earliest line that does not follow from the previous one and explain the rule to check. If working or required context is missing, ask for it instead of inventing an error. Do not infer ability, carelessness or a repeated misconception. Give a three-level hint ladder: a question, a more specific cue, then the corrected first line; do not reveal later lines or the final answer in these hints. Put the complete solution and an independent check under Adult/teacher reference — keep separate. Then give one same-skill practice question and a separate key within the supplied scope. For fictional M1–M5/L1–L3, preserve M5’s restrictions; do not impose that example’s equation on another question. Say what a learner retry could demonstrate without treating it as proof of general mastery. Source:

  4. Compare with a complete correction and retry plan

    First unsupported line: L1. From M1, the factor 3 multiplies the entire bracket, so it must multiply both x and 2. L1 changes 3(x + 2) to 3x + 2 and leaves the second term undistributed. This identifies the written error. It does not prove why the learner made it or whether it happens elsewhere [M3]. Hint ladder — give one level at a time: 1. Question: “In 3(x + 2), which terms inside the bracket are multiplied by 3?” 2. More specific cue: “Write 3 × x and 3 × 2 before simplifying.” 3. Corrected first line, only if needed after another attempt: “3x + 6 = 18.” Stop after the first hint that helps. Do not read all three like a tiny lecture staircase. Adult/teacher reference — keep separate until after the retry: 3(x + 2) = 18 3x + 6 = 18 3x = 12 x = 4 Substitute into the original question: 3(4 + 2) = 3 × 6 = 18. The equality holds. A second route divides both sides by 3 first: x + 2 = 6, then x = 4. Both routes agree. Feedback after seeing L1 only: “In L1, the 3 was applied to x but not to 2. Try writing both products before simplifying.” Avoid: “You always forget brackets.” M3 contains no repeated history. Same-skill practice, after the learner has corrected and explained L1: Question for learner: solve 4(x + 3) = 28. Optional first hint: “Which two terms does 4 multiply?” Separate key: 4x + 12 = 28; 4x = 16; x = 4. Check: 4(4 + 3) = 4 × 7 = 28. Same structure: one number multiplies a two-term bracket, followed by isolating x; positive whole-number solution and no extra operation [M5]. Evidence from the retry: Record whether the learner independently writes 3x + 6, explains that 3 multiplies both terms and checks x = 4 in the original equation. One corrected line supports “this distribution step was corrected in this attempt”. It does not establish mastery across other questions. If the corrected line was copied after hint 3, record that support was needed. Wrong diagnosis: “The learner is weak at algebra.” Repair: “In this attempt, L1 did not multiply 2 by 3. Ask the learner to expand both products and retry [M2–M4].”

  5. Check the algebra and the level of help

    Independently expand 3(x + 2), solve the equation and substitute the answer into M1. Check the practice item the same way. Does the feedback point to L1 rather than treating later lines as separate causes? Are the three hints ordered from least to most revealing, with the answer kept outside them? Is the practice question within every M5 limit? Record which hint was used. Do not label a copied correction as independent success. Remove claims about ability, attention or repeated behaviour absent from M3. If the original symbols or learner working are unclear, ask for a clearer copy; do not reconstruct a missing line. Revise before ticking the checks below. These checks verify the prepared explanation, not the learner’s understanding.

  6. Let the retry decide the next move

    Copy the checked explanation, hint ladder and separate keys before leaving; edited worksheet text is not saved. Give only the first needed hint, wait for a written retry and record the exact new line. If the learner explains the distribution step, use the similar-practice Task below to prepare one more checked item; it includes a route for keeping this same skill. If the step remains unclear, pause and ask a teacher with the original question and working. Completion here means the coaching material is ready, not that the learner has retried or mastered algebra.

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