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#245

Finding original values in percentage calculations

Number · Grade 4–6

Strand: Number Substrand: Percentage change Sparx code: U286 Sparx levels: 1, 2, 3, 4, 5

Key steps (method)

  • Convert the percentage to a multiplier (e.g. +12% → ×1.12, −15% → ×0.85).
  • For percentage of an amount, multiply the amount by the percentage as a decimal.
  • For reverse percentages, divide by the multiplier to get the original amount.
  • Keep money calculations to 2 d.p. at the end.
  • Check: does increase/decrease direction match the question?

Common mistakes

  • Using ×0.12 instead of ×1.12 for an increase (or similar).
  • Mixing up reverse percentage (dividing by the percentage instead of the multiplier).
  • Rounding too early in multi-step percentage problems.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Finding original values in percentage calculations (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes