# Integrated Week 2 — A poll result is not a population

Five **35-minute** sessions using only a fictional 100-person population and constructed 20-person samples. The mathematical idea is selection and sample variation; the English idea is how a post uses a number to push a decision. This route addresses parts of `AC9M8ST01`, `AC9M8ST02`, `AC9M8ST03`, `AC9M8ST04`, `AC9E8LY02`, `AC9E8LY03`, `AC9E8LY06`, `AC9E8LY07`. Source review notes are [here](../../../SOURCES-AND-REVIEW.md).

**Safeguard:** do not survey actual classmates about travel, address, family resources or disability. Do not invite personal disclosures to make the task “real”. Use [Text B](../english/MATERIALS.md), the constructed [sample table](../mathematics/MATERIALS.md), [100-cell print grid](../print/sample-grid.pdf) and its [plain-text route](../print/TEXT-ALTERNATIVES.md). If a future real data study is authorised, it needs school consent, purpose, minimisation and safe storage first.

## Day 1 — Define whose question it is

1. **Question · 3 min.** Read the fictional post's 80% claim. Ask: “80% of whom?”
2. **Model groups · 5 min.** Write `population: 100 invented students`; `sample C: 20 at bicycle racks`; `respondents reporting bicycle: 16`. Name who is missing from the sample frame.
3. **Guided scope · 7 min.** Learners sort `16/20 reported bicycle`, `80% of all students`, `remove shelter` as calculation, inference and action. The last two need further justification.
4. **Independent inquiry card · 12 min.** Each learner writes the population question, one fair selection idea, one possible harm from acting on biased data, and one privacy safeguard. No actual data collected.
5. **Peer review · 5 min.** Partner checks whether the inquiry asks about a whole group while selecting only one location.
6. **Exit · 3 min.** Key: C gives 80% **of its 20 rack respondents**, not of all 100 fictional people.

## Day 2 — Give everyone a chance to be selected

1. **Recall · 3 min.** Ask why asking only by racks can distort the answer.
2. **Model mechanism · 5 min.** With ten numbered scrap cards, shuffle face down and select two without replacement. Each card had a chance; selection did not depend on travel mode. This mini-demo is **not** the 100-person result.
3. **Scale plan · 7 min.** Learners explain how the same method could use 100 numbered fictional cards and select 20. Teacher can use prepared cards if time allows; no real people are selected.
4. **Compare model results · 12 min.** Use supplied constructed random A and B. For bicycle, A `3/20=15%`, B `4/20=20%`. Record both without declaring one wrong.
5. **Method audit · 5 min.** Ask what would break the fair-chance plan: leaving some cards out, replacing only some or selecting after seeing mode labels.
6. **Exit · 3 min.** Key: a fair mechanism can still produce two different samples; equality of results is not a requirement.

## Day 3 — Read a chart before using its headline

1. **Spot · 3 min.** Display A, B and C bicycle shares `15%, 20%, 80%`. Ask which sample came from the racks.
2. **Model · 5 min.** Teacher fills a 20-cell grid for A: three selected bicycle cells, seventeen other; writes `3/20`, not `3/100`.
3. **Guided display · 7 min.** Groups make B and C 20-cell strips; then label C “convenience at racks” on the display itself.
4. **Independent caption · 12 min.** Learners write an accessible text caption or speak it: exact percentage, selected group, source and limit. “80% of those 20 respondents…” is valid; “80% of school…” is not.
5. **Counter-reading · 5 min.** Partner reads only the image, then only the caption. If the caption omits sample method, add it; graphics do not carry meaning alone.
6. **Exit · 3 min.** Key: 5 percentage points between A and B bicycle shares equals **one** person out of 20, not five people.

## Day 4 — What does the known model population teach?

1. **Reveal · 3 min.** Show the artificial population shares: 40% walk/roll, 30% bus, 20% bicycle, 10% other. Say real investigators usually do not know the exact population beforehand.
2. **Model error · 5 min.** A bicycle estimate is 15%, five percentage points from known model 20%; B matches 20%; C is 60 points above. One match does not prove that a method always matches.
3. **Guided claim audit · 7 min.** Test “Random samples are perfect” and “A larger sample is always exact.” Both are false. A [repeated fictional simulation](../mathematics/MATERIALS.md#week-2-invented-travel-population-and-samples) gives a smaller average error for size 40 than size 10, but any individual sample may still miss the model proportion.
4. **Independent report · 12 min.** Learners write a three-sentence report: two contrasting sample results, why selection matters, one question before changing a shelter. They may use a table/tactile grid plus dictated caption.
5. **Ethical check · 5 min.** Ask whose access to transport might be overlooked by a shelter change, without asking peers how they personally travel.
6. **Exit · 3 min.** Key: the rack sample's 80% is much higher than the **known fictional model** 20%; selection method is the concern.

## Day 5 — A usable, bounded correction

1. **Audience · 3 min.** Address a fictional school newsletter editor, not a real student group.
2. **Plan · 5 min.** Put full quotation, sample method, valid fraction, uncertainty and next action in order.
3. **Rehearse · 7 min.** Partner paraphrases the correction and asks one question. A quiet one-to-one or AAC route is equal for reasoning.
4. **Create · 12 min.** Make a corrected post, accessible audio script, poster with text alternative or memo. State that all figures are fictional. Do not present the 100-person constructed distribution as a real school fact.
5. **Check · 5 min.** Teacher marks `fraction correct / denominator named / method explained / action bounded`; select one next teaching move per learner.
6. **Exit · 3 min.** “What should a reader do before believing a whole-school percentage?” Key: ask who was in the population, how the sample was selected and what uncertainty remains.

**Teacher next moves:** If a student computes 80% correctly but generalises it, teach denominator labels, not division. If they critique bias but cannot compute percentages, use a 20-cell strip where one cell equals 5%. If they want to use real data, direct them to the school's approval process; the pack works without it.

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