# General Mathematics teacher key and next moves

**Keep separate from learner copies.** This is a formative key, not a QCAA instrument or marking guide. Save first attempts before feedback. Record technology and access supports; a supplied *r* can demonstrate interpretation, not independent calculation with technology.

## Daily exact checks

| Day | Keyed evidence | Next move when missing |
| ---: | --- | --- |
| 1 | Variables: session (morning/afternoon) and room choice (quiet/group); observational unit: **visit**. | Make paired category cards; ask what each one card represents. |
| 2 | Row totals 20, 20; column totals quiet 18, group 22; grand total 40 both ways. | Colour or tactile-trace rows versus columns; recompute only one line. |
| 3 | Morning quiet 12/20 = 60%; group 8/20 = 40%. Afternoon quiet 6/20 = 30%; group 14/20 = 70%. | Ask “of which group?” before dividing. |
| 4 | Quiet is 30 **percentage points** higher in morning visits than afternoon visits in this invented table. Time-of-day causation is unsupported. | Compare 60 and 30 on a 0–100 bar, then label the denominator. |
| 5 | See fresh Check 1 key below. | Reteach the first missing step: totals, denominator, comparison or causal limit. |
| 6 | x = later-opening hours, y = visits **during those hours**. Points (1,8), (2,10), (3,9), (4,14), (5,13), (6,16). | Locate a single pair in the table and on the axes; keep units visible. |
| 7 | Positive, roughly linear, strong association; not perfect because some adjacent points dip. | Give three separate prompts: direction / form / strength. |
| 8 | `CORREL` on six paired rows returns +0.9189132409545…; report +0.9189 or +0.919. | Check ranges and headers, then distinguish sign from strength. |
| 9 | *R*² = 0.8444015444… ≈ 0.8444, or 84.4% of observed y variation around its mean accounted for by a straight-line fit to x in this toy dataset. It is not “84.4% caused”. | Square unrounded *r*; separate model description from cause. |
| 10 | See fresh Check 2 key below. | Form a group by the first missing dimension, then provide a new six-pair task. |

## Check 1 exact result

Rows: 15 direct-message invitations, 15 poster invitations. Columns: 13 attended, 17 did not; grand total 30. Attended shares: **9/15 = 60%** within direct message; **4/15 = 26⅔% ≈ 26.7%** within printed poster. Difference **33⅓ percentage points ≈ 33.3 percentage points**. A defensible statement: “In these 30 invented invitations, attendance was more common among direct-message invitees (60%) than poster invitees (about 26.7%).” Do not accept “33.3% more”: the comparison is percentage **points**. Channel assignment could differ by prior interest, access to devices, timing or other factors; no assignment process is given. These are possible confounders, not observed facts.

## Check 2 exact result

Card C x = 1,2,3,4,5,6 hours; y = 5,7,10,9,13,12 visits during those hours. The cloud is positive, roughly linear and strong, with local decreases from x=3 to 4 and x=5 to 6. Pearson's **r = +0.9230930832457… ≈ +0.923**; **R² = 0.8521008403361… ≈ 0.852**, or about 85.2%. A careful explanation: “A straight-line relation with trial hours accounts for about 85.2% of the observed variation in visits about their mean across these six invented pairs.” This is descriptive of the fitted linear relationship, not a causal share. Technology should calculate *r* from paired x/y ranges; a negative result suggests mismatched rows or data entry. Do not infer an actual service's attendance, optimum hours, unique users or reasons for visits.

**Recalculation receipt:** Card B has centred sums Σ(x−x̄)² = 17.5, Σ(y−ȳ)² = 49⅓, Σ(x−x̄)(y−ȳ) = 27, so *r* = 27/√(17.5 × 49⅓) = 0.918913… . Card C has 17.5, 45⅓ and 26 respectively, so *r* = 26/√(17.5 × 45⅓) = 0.923093… . The student task requires approved technology, but these independent sums guard the answer key.

## Four formative dimensions

Use **ready / developing / revisit** per dimension; no QCAA grade or threshold is implied.

| Dimension | Ready evidence | Next move if developing/revisit |
| --- | --- | --- |
| Table or plot construction | Correct observational unit, complete totals or six correctly paired points, with axis/category labels. | Rebuild one record at a time with row/column or x/y markers. |
| Calculation | Correct within-row denominator or correctly paired technology ranges and sensible rounding. | Ask the question's “of whom?” or audit range endpoints. |
| Interpretation | Names a contextual association and explains *r* or *R*² within its linear/sample scope. | Use a sentence mat and ask what the number is a number **of**. |
| Boundary | Separates observed association from causal or population claim and identifies plausible missing information. | Compare a valid report sentence and one overclaim; ask what evidence would distinguish them. |

**Access note:** Large print, text table, screen-reader-compatible coordinates, tactile grid, calculator/spreadsheet, speech, AAC and supported transcription can preserve the intended statistical reasoning. Record which was used. If a screen reader cannot access graphing software, offer the coordinate list and assess graph interpretation separately; arrange technology access for the required calculation later.

**Rights:** Original key © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).