Populations, samples and fair sampling
Distinguish a population from a sample drawn from it; explain why a convenient or biased sample (choosing whoever is easiest to reach, volunteers, or a group linked to the answer) can misrepresent the population; explain that random selection gives every member of the population an equal chance of being chosen, which tends to produce representative samples — while recognising that any single random sample can still, by chance, be unrepresentative
Lesson
Set out your lesson
“Populations, samples and fair sampling 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
- Tally sheet or simple bar sketch
- A short set of category counts
Extra for the adult
Worked example. Cats 4, dogs 2 — cats have more. The tally and comparison are the proof.
Optional challenge. For Populations, samples and fair sampling, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Populations, samples and fair sampling, not mastery.
Share and support
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Practice this concept
Start practicePopulations, samples and fair sampling practice
Practice key ideas from Populations, samples and fair sampling.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Making S'Mores
Before you open · source notes
Making S'Mores supports populations, samples and fair sampling. Not every worksheet pack.
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Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Making S'Mores.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- In a described survey (e.g. a school asks 40 of its 800 pupils about the lunch menu), identify the population and the sample, and explain why a sample is used instead of asking everyone
- Identify the selection bias in a sampling method (e.g. asking people leaving a gym how often they exercise, or surveying only the lunch queue on pizza day), explain the direction in which it would likely distort the result, and propose a better method using random selection from the whole population (e.g. drawing names from the full school register)
- Explain the difference between random selection and simply choosing whoever is easiest to reach, and explain — with an example such as a random sample of 10 pupils that happens to contain mostly Year 7s — why random sampling makes a representative sample likely but does not guarantee it
“If a school wanted to know what all its pupils think of the lunch menu but only asked children in the lunch queue on pizza day, could your child explain why that might give a misleading answer — and suggest a fairer way to choose who to ask, like picking names at random from the whole school list?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Data & Statistics
- Age range
- Ages 10–13
Standards