# Formative fresh checks · Days 15 and 20

These two original sources are **different from** teaching examples, learner routes, print aids and extras. The prompts and worked key are publicly accessible, so they are formative rather than secure tests; change a case locally if prior access matters. They sample selected integer-exponent reasoning, not a Year 9 achievement-standard judgement, diagnosis, speed test or prediction about actual technology. Give a blank law aid, calculator, read-aloud, AAC or a directed scribe as needed, and record the mathematical prompt separately from access. Capture the first response before an edit. If no response can be observed, write *not yet observed* and revisit with a different fresh source. Give the learner a clean prompt before using the [teacher worked key](TEACHER-KEY.md). Do not upload identifiable pupil work.

## Check A Day 15 fresh number source

**New fictional archive card, shown only today:**

> An imaginary paper archive has `4^3` first-part label strings and `4^2` second-part label strings. Each first part can pair with every second part. A separate box holds `5^4` equal paper cells, packed into equal groups of `5^2` cells. A tiny drawing uses a scale factor `10^−3` of one model unit. An editor writes: “The two label lists make 80 combined labels because 64+16=80; dividing powers should add exponents; the tiny scale is negative.” No real archive, labels or measured object exists.

**Learner tasks:**

1. Find the number of **paired** label strings using a same-base product rule and one arithmetic check. Explain why 64+16 answers a different question.
2. Find the number of groups of paper cells using a same-base quotient rule and give the unit of the answer.
3. Rewrite the scale factor as a positive fraction and decimal. Explain why its negative exponent does not mean a negative scale.
4. Write, direct or give a quiet oral/AAC two- or three-sentence correction for the fictional editor, identifying one false rule and the conditions for using the right rule.

**Timing within Day 15:** 2-minute frame, 5-minute exact reading, 6-minute first marks, 6-minute response, 4-minute self-audit, 2-minute collection. No question from this card is rehearsed earlier.

## Check B Day 20 fresh variable source

**New fictional branching-card note, shown only today:**

> A made-up story-card maker has `p` possible symbols for each independent slot, where `p` is a **positive whole number**. In one stage there are `p^(m+1)` choice strings; in a second independent stage there are `p^(2m)`, with `m` a **non-negative whole number**. Every first string can pair with every second string. For the sample `p=2, m=2`, the maker wants a total count. A separate, unitless comparison uses `q^2/q^5`, where `q` may be any **non-zero real number**. An advertising sentence says: “The laws also work at q=0, and the number of possible pairs proves that every reader will use the game.” No game or readers have been observed.

**Learner tasks:**

1. Simplify the combined `p` expression, keeping the whole `m+1` and `2m` exponents grouped, and explain why the rule applies.
2. Check the combined count at `p=2, m=2` using both source expressions and the simplified one. Give the unit **model string pairs**.
3. Rewrite `q^2/q^5` without a negative exponent, test `q=2`, and explain what fails at `q=0` in the **original** quotient.
4. Correct the advertising sentence so it states a mathematical domain and a model-versus-reader limit without claiming an observed outcome.

**Timing within Day 20:** 2-minute frame, 5-minute exact reading, 6-minute first marks, 6-minute response, 4-minute self-audit, 2-minute collection. Do not display the public key until after collection.

## Private evidence strip

`Date | local learner code | A/B | exact first working | revision | access tool/route | mathematical hint given | criterion next move | recheck date`. Store only in school-approved private storage. A calculator check is not an explanation of the law; an adult's equation is not independent learner reasoning.

**Original resource rights:** © NeuroForgeIO Pty Ltd 2026, SubjectNest, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). Credit author, source, licence and changes.