All cards are constructed learning data. Use paper, counters, spreadsheet without an account, a tactile graph or plain text. Keep the qualifier fictional when a table is shown away from its lesson.
Week 1: repair counts and model totals
n is the number of repairs, restricted to non-negative whole numbers. Plan A: A(n)=18+7n. Plan B: B(n)=10n. Amounts are invented Australian-dollar teaching values and exclude all other possible costs.
| n repairs | A: 18+7n | B: 10n | Lower model total |
|---|---|---|---|
| 0 | $18 | $0 | B |
| 2 | $32 | $20 | B |
| 4 | $46 | $40 | B |
| 6 | $60 | $60 | equal |
| 8 | $74 | $80 | A |
Difference A(n)-B(n)=18-3n. Equal when 18-3n=0, so n=6, verified by 18+7×6=60=10×6. For whole n<6 B is lower; for whole n>6 A is lower. If a student draws continuous lines to see the algebra, mark only integer points as possible repair counts. Joining the dots helps show trend but half a repair is outside this model.
Fresh Day 5 check: imaginary art studio option C has $12 entry plus $5 per visit, C(v)=12+5v; D costs $8 per visit, D(v)=8v. C and D meet at v=4, both $32. At 3 visits C=$27, D=$24; at 6 visits C=$42, D=$48. v is a non-negative whole number; real service conditions are not supplied.
Week 2: invented travel population and samples
Categories are neutral labels, not a hierarchy: walk/roll | bus | bicycle | other. “Walk/roll” can include mobility aids; do not infer individual ability. Imagined population of 100: 40 | 30 | 20 | 10. Simulated simple random sample A of 20: 8 | 7 | 3 | 2; simulated simple random sample B of 20: 10 | 5 | 4 | 1. Constructed convenience sample C, 20 beside bicycle racks: 1 | 1 | 16 | 2. All people and counts are fictional; the two random simulations are reproducible below and are not real surveys.
| Source | Walk/roll | Bus | Bicycle | Other | Total | Bicycle share |
|---|---|---|---|---|---|---|
| Model population | 40 | 30 | 20 | 10 | 100 | 20% |
| Random model A | 8 | 7 | 3 | 2 | 20 | 15% |
| Random model B | 10 | 5 | 4 | 1 | 20 | 20% |
| Rack convenience C | 1 | 1 | 16 | 2 | 20 | 80% |
Two same-size random model samples need not have identical proportions; here A and B differ by five percentage points for bicycle. The rack sample is selected from a location linked to cycling, so it should not be used to estimate the whole school. The constructed population is known only so students can inspect error; in real investigations it is usually unknown.
Optional sample-size simulation for Day 9: Using the same fictional 100 IDs and the selection method below, run seeds 0–999 for sample sizes 10 and 40. For each simulated sample, calculate how many percentage points its bicycle share is from the known model 20%, then average those 1000 distances. The averages are 8.95 percentage points for size 10 and 3.92 percentage points for size 40. This particular repeated simulation illustrates that larger fair samples often vary less; it does not mean every size-40 draw is closer than every size-10 draw, or that a real population is known. Learners can compare this reported summary without programming.
Fresh Day 10 check, different domain: imaginary school arts club has a model population of 100 students, 60 interested in a new music room session and 40 not interested. Two seeded pseudorandom simulations of 20 report 11 interested/9 not and 14 interested/6 not (55% and 70%). A constructed convenience sample of 20 taken at a music-club meeting reports 18 interested/2 not (90%). The samples differ; the meeting sample is selected where interested people are likely overrepresented. No real student interests are being recorded.
How the simulated random samples were made
Assign fictional travel IDs 0–39 to walk/roll, 40–69 bus, 70–89 bicycle and 90–99 other. Python's random.Random(seed).sample(range(100), 20) selects 20 distinct model IDs. Seed 1 gives travel A's counts 8, 7, 3, 2; seed 67 gives travel B's 10, 5, 4, 1. For the fictional arts population, IDs 0–59 mean interested and 60–99 not interested. Seeds 5 and 4 give 11/9 and 14/6. These are reproducible pseudorandom simulations, not claims about students. The rack/meeting convenience examples are deliberately constructed contrasts, not outcomes of this mechanism.
Rights: Original fictional values and cards © NeuroForgeIO Pty Ltd 2026, SubjectNest, CC BY 4.0; credit, source and changes required.