# Two-week mathematics formative assessment — unseen transfer

**Teacher use:** Keep this sheet from learners until Day 10. Administer as a 12–18-minute separate check/conference, starting one or two items in Day 10's six-minute transfer block. Provide labelled equal-unit axes, square-root/calculator support, large-print/tactile/digital route, AAC or scribe at learner direction. Record the mathematical cue separately. No speed score. Each item scores **0** = not yet with access, **1** = correct after a mathematical prompt/model, **2** = independently correct with a valid explanation. Total /16 is a next-teaching signal, not a Year 9 attainment claim.

## Learner prompts — print this part

1. On an equal-unit grid, A(-2,1), B(4,4). Find the gradient. Show Δx and Δy.
2. Give the gradient of C(-5,2) to D(1,2) and of E(3,-1) to F(3,5). Explain the difference.
3. Find the midpoint of G(-4,2) and H(2,8).
4. Find the straight-line distance in grid units from P(1,1) to Q(7,-7). Show a right triangle or formula.
5. **Fresh invented model:** A fictional workshop's Plan L passes through (0,10) and (4,30), where input h is whole booked hours and output is model dollars. Write L(h); explain both numbers.
6. Plan M in the **same fictional workshop** is M(h)=22+3h. For which h do L and M cost the same, and what is that cost?
7. Within whole hours h=0–8, which plan has the lower stated price at h=4 and at h=8? Show both comparisons.
8. A made-up post says “M is the best choice for every booking.” Evaluate that claim using one number, the domain and one important missing condition.

**Response record:** item scores ___/___/___/___/___/___/___/___; total ___/16; axes/tool ___; read-aloud/scribe/AAC ___; mathematical prompts ___; next teaching ___; fresh recheck date ___. Keep records under school policy.

## Worked teacher key and decision route

| Item | Worked answer and acceptable explanation | If not yet, teach then recheck |
| --- | --- | --- |
| 1 | Δx=4−(-2)=6; Δy=4−1=3; m=3/6=**1/2**. | Mark horizontal/vertical changes separately; new pair, not same answer. |
| 2 | C→D has Δy=0, Δx=6 ⇒ **0** (horizontal). E→F has Δx=0, Δy=6 ⇒ **undefined** (vertical; dividing by 0 is not allowed). | Place perpendicular strips; compare numerator 0 versus denominator 0. |
| 3 | ((-4+2)/2,(2+8)/2)=**(-1,5)**. | Pair x with x and y with y; check equal displacements. |
| 4 | Δx=6, Δy=-8; d=√(6²+(-8)²)=√100=**10 grid units**. | Distinguish 14-unit two-leg path from 10-unit straight segment. |
| 5 | Gradient (30−10)/(4−0)=20/4=**5 dollars/hour**; intercept **$10**; **L(h)=10+5h** for stated whole-hour domain. | Identify rate from two points, then fixed amount at h=0. |
| 6 | 10+5h=22+3h ⇒ 2h=12 ⇒ **h=6**; L(6)=M(6)=**$40**. | Solve equality, substitute back into **both** rules. |
| 7 | h=4: L=10+20=**$30**, M=22+12=**$34** ⇒ L lower. h=8: L=10+40=**$50**, M=22+24=**$46** ⇒ M lower. | Two-column table; do not use only intercept. |
| 8 | Universal claim **unsupported**: at h=4, L $30 < M $34. Domain is whole h=0–8; model does not establish quality, availability, taxes or added fees. One relevant missing condition is enough. | Make a precise counterexample and ask what real quote term must be checked. |

**Next teaching:** If Items 1–2 are fragile, revisit signed changes and horizontal/vertical before formulas. If 3–4 are fragile, contrast midpoint (point) and distance (quantity). If 5–7 are fragile, use a table and graph before algebraic intersection. If 8 is fragile but calculation secure, practise interpreting domains and missing assumptions with a fresh invented quote. A high total with mathematical cues is not independent mastery; retain access adjustments while fading only the cue.

**Fresh recheck, never preteach as an answer:** R(−1,−2), S(5,6): Δx=6, Δy=8, m=4/3, midpoint (2,2), distance 10. New fictional plans N(h)=9+4h and P(h)=21+2h for whole h=0–8: equal h=6 at $33; at h=3, N $21 < P $27; at h=8, P $37 < N $41. Require a limit of the model.

**Rights:** Original prompts and key © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). ACARA source/terms in [README](README.md). Educator review pending.