# Learner copy · two fresh independent checks

**Use on Days 15 and 20.** These prompts are fresh relative to the lessons, but the public library also exposes their teacher key, so they are not secure exams. A teacher should adapt the invented case if learners may have seen answers. Both cases are entirely invented. Units are arbitrary sensor units; no actual material or room was tested. Calculator, large print, read-aloud, tactile number cards, AAC and exact-word scribe are access choices. Work alone on the first response. State the source for a claim and keep prediction separate from record.

## Check A · Day 15 · folded card notice

An invented Folded Card team wrote: “Each added card always halves the sensor value. The improvement proved reliable viewing.” Its one invented tabletop table starts at **96** and lists: zero cards **96**, one **48**, two **27**, three **18**. The team gives no calibration, repeated readings or background-light note. Let `P(n)=96×2^-n` be the **conditional** exact-half model.

1. Find `P(3)` using a negative exponent and show why the exponent does **not** mean a negative sensor value.
2. Compare `P(3)` to the listed three-card value with a signed `record − prediction` gap. Identify which source statement this comparison tests.
3. Explain how “the improvement” hides an actor, an action or a particular comparison. Rewrite the final sentence so the team, invented record and a limit are visible. Do not claim reliable viewing in a real place.
4. Give one precise additional measurement or method detail you would request before a stronger claim.

## Check B · Day 20 · theatre backdrop paper

An invented theatre group suggests that every extra sheet halves a sensor reading from a baseline of **120**. They list three fictional rounds:

| Sheets | Round 1 | Round 2 | Round 3 |
| ---: | ---: | ---: | ---: |
| 0 | 120 | 119 | 121 |
| 1 | 61 | 60 | 62 |
| 2 | 35 | 34 | 36 |
| 3 | 23 | 21 | 22 |

The note says “same desk,” but gives no sensor calibration, paper specification, background light or independent observer. No real stage use has happened.

1. For `P(n)=120×2^-n`, calculate `P(3)` and compare it to the middle of the three-sheet round values. Show the numerical gap.
2. Explain what is consistent within the three-sheet rounds and what the table cannot show about independent reproducibility or other conditions.
3. Write an investigable question and **two operational controls** for a supervised retest. State whether your written plan itself proves the retest occurred.
4. Write a short recommendation for the fictional group: decision, source-bound numerical reason, method limit and a next check. Do not approve public use or state a real safety result.