Guide

Find the cause of a wrong answer without guessing

Find a likely reason for a wrong answer, check it against the worked solution and plan one retry. The practice case is fictional.

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Step 1 of 6

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1

Start with the question and the written steps

Use this fictional fraction example to practise helping a learner. For a real question, keep the exact wording and written steps, but remove names, school details and other personal information. You can work through this worksheet yourself; one approved assistant is optional. A wrong number is a clue, not a full explanation. The answer has not come with a tiny detective attached.

Read all steps
  1. Start with the question and the written steps

    Use this fictional fraction example to practise helping a learner. For a real question, keep the exact wording and written steps, but remove names, school details and other personal information. You can work through this worksheet yourself; one approved assistant is optional. A wrong number is a clue, not a full explanation. The answer has not come with a tiny detective attached.

  2. Keep the facts separate from the guesses

    Fictional teaching example. [W1] Question: calculate 3/4 + 2/3. [W2] Written final answer: 5/7. No intermediate steps have been supplied. [W3] We do not know whether this was a rule mistake, a copying mistake or something else. There is no information about the learner’s wider ability. [W4] First ask for the working and give one small hint. Let the learner attempt the question before showing a full solution. Keep W1–W4 when editing. Do not invent the missing working to make the story neater.

  3. Ask for a useful first response

    Use only the supplied question, learner answer and visible working. State what is known, identify missing working and ask the learner to show the step needed to understand the answer. Give one hint tied to the actual skill without revealing the final answer. For fictional W1–W4, ask how the numerator and denominator were obtained and hint about equal-sized parts; do not impose fraction reasoning on a different problem. Keep possible causes as questions, not diagnoses. Do not label the learner careless, weak at maths or having a learning difficulty. Keep the first response separate from any later worked solution. If more working is supplied, locate the exact line needing correction, check the calculation and explain the applicable rule. If no error is established, say so. Source:

  4. Compare the hint, then the worked correction

    Example first response: “I see 5/7 [W2]. Can you show how you got the 5 and the 7? Before adding, think about whether quarters and thirds describe equal-sized parts. Can you rewrite both fractions using parts of the same size?” This asks for evidence without naming an unproved cause [W3] or giving the answer [W4]. Later fictional reply, supplied only for this worked example: “I added 3 + 2 and 4 + 3.” Now there is evidence for the specific error: adding denominators as though the pieces were the same size. Do not treat this later reply as part of the original W1–W4 source. Worked correction after the learner has tried: 1. Use twelfths: 3/4 = 9/12 and 2/3 = 8/12. Multiply the numerator and denominator of each fraction by the same number. 2. Add equal-sized pieces: 9/12 + 8/12 = 17/12. The denominator stays 12 because each piece is still one twelfth. 3. If a mixed number is requested, 17/12 = 1 5/12. 4. Check the size: 2/3 is larger than 1/4, so 3/4 + 2/3 must exceed 1. The original 5/7 is below 1, which rules it out. This check detects a wrong result; it does not prove how the error happened. Example log entry: question 3/4 + 2/3; original answer 5/7; observed step, added both numerators and denominators; correction, use equal-sized twelfths; check, result exceeds 1; next attempt, explain why the denominator stays unchanged. Retry outcome: not yet observed. Wrong: “You are careless with fractions.” Better: “In the working you just showed, the denominators were added. Let’s change both fractions to twelfths first.”

  5. Check the explanation, not the learner’s label

    Before using your response, check five things. Does the first reply ask for missing working instead of treating a possible cause as fact? Does its hint leave the final answer for the learner to find? Is any later error explanation tied to an actual written step? Are 9/12, 8/12 and 17/12 correct, with the unchanged denominator explained? Does the log leave retry success unknown until a new attempt exists? If the first reply says “you added the denominators” from W2 alone, replace it with “show how you got the 7”. If a drawing or question cannot be read, ask for a clearer copy rather than filling in the blanks. Rewrite your draft before ticking the checks below.

  6. Keep one record and try again

    Copy your reviewed response and error log before leaving; edited worksheet text is not saved. Ask the learner to retry the original question and explain why the denominator stays the same. Record what they actually write, including any point that is still unclear. Use the similar-practice Task below only after the original method is understood; check the new question and answer before giving it to the learner. A completed worksheet means you prepared a response and a record, not that the learner has mastered fractions. If the explanation is still unclear, ask a teacher to look at the written steps.

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