Reasoning with Equivalences
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
Lesson
Set out your lesson
“Reasoning with Equivalences 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
- Paper strips or a folded circle
- Pencil and labels (1/2, 1/4)
Extra for the adult
Worked example. Fold a strip in half: each piece is 1/2 of the whole.
Optional challenge. For Reasoning with Equivalences, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Reasoning with Equivalences, not mastery.
Share and support
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceReasoning with Equivalences practice
Practice key ideas from Reasoning with Equivalences.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
NRICH · Practice link — not the full lesson
Primary
Before you open · source notes
Primary supports Reasoning with Equivalences. An adult previews and guides; this is a learning page, not a scored quiz.
Free educational page, no sign-in required for the tested path.
Before you openAsk the learner one fact they learned and one question they still have.
Opening this link does not save learning or assess mastery.
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.
Unknown — link only
Check understanding
- 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
“When your child 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?”
Curriculum record
- Type
- Meta
- Subject
- Mathematics
- Domain
- Mathematical Thinking
- Age range
- Ages 9–10
Standards