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A prerequisite knowledge graph of 1590 learning concepts across 8subjects. Track what you've mastered and see exactly what you're ready to learn next — the topics whose prerequisites you've already met. Built on the Marble Open Skill Taxonomy.

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Reasoning with Equivalences

Mathematics · Mathematical Thinking · meta

Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms

What mastery looks like

  • Notice that multiplying any number by 25 can be done by multiplying by 100 then dividing by 4, and explain why
  • Describe the general rule for a sequence and predict the 20th term
  • Generalise: to find 10% divide by 10, to find 5% halve 10%, and use this to find 35% of any number

Check your understanding

When Reasoning with Equivalences sees a sequence of equivalent fractions — like 1/2, 2/4, 3/6… — can they describe the rule and use it to find the next few terms, or to quickly convert between fractions and percentages?