Generalising with repeated reasoning
Recognise and use repeated reasoning to generalise: describe algebraic rules for nth terms, use properties of operations to simplify, and verify generalisations with specific cases
Lesson
Set out your lesson
“Generalising with repeated reasoning means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Balance or equation cards with a box for the unknown
- Pencil
Extra for the adult
Worked example. □ + 3 = 10 → □ = 7 because 7 + 3 = 10.
Optional challenge. For Generalising with repeated reasoning, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Generalising with repeated reasoning, not mastery.
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1 approach
Generalising with repeated reasoning means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Balance or equation cards with a box for the unknown; Pencil. Adult solves one simple unknown (□ + 3 = 10) and checks by substituting. Child solves three unknowns and checks each by putting the number back in. Done: three checked solutions. Stop after the fresh check; keep optional challenge for another day.
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Start practiceGeneralising with repeated reasoning practice
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Learning resources
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NRICH · Practice link — not the full lesson
Primary
Before you open · source notes
Primary supports Generalising with repeated reasoning. An adult previews and guides; this is a learning page, not a scored quiz.
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Before you openAsk the learner one fact they learned and one question they still have.
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Source, access and review notes
Public NRICH page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
NRICH. “Primary.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Explain that the interior angle sum of an n-sided polygon is (n−2) × 180° based on the pattern for triangles, quadrilaterals, pentagons
- Predict the 20th term of a linear sequence by identifying and applying the general rule
- Generalise that dividing by n always gives a denominator of n in the fraction, for any whole numbers
“When your child finds the rule for a number sequence — like "add 7 each time" or "multiply the position number by 3" — can they use that rule to find any term without having to list all the ones before it?”
Curriculum record
- Type
- Meta
- Subject
- Mathematics
- Domain
- Mathematical Thinking
- Age range
- Ages 10–11
Standards