Mathematics: keyed formative… | Year 7 Maths · T1 W1–2 · Assessment

These tasks sample the opening fortnight, not the Year 7 achievement standard. Keep four fields per learner: exact representation/calculation; explanation; access and prompts; next teaching move. Use a rotating focus roster; an unseen or partner-copied answer is not yet observed for independent reasoning. Accept a different correct strategy with a coherent unit and check.

Day	Keyed exit	Next move for a common misconception
1	`1/4 = 0.25 = 25%` of the same whole	If 0.4, partition the whole into four equal parts, then hundredths.
2	`0.25 < 3/8 (=0.375) < 0.5`	If 3/8 is read as 3.8, use eighths on a 0–1 strip and write 0.375.
3	`7/10 = 0.7 = 70%`	If 7%, contrast 7 of 10 with 7 of 100 cells.
4	`12.684` to a tenth = 12.7	If 12.6, check hundredths digit 8 and proximity to 12.7.
5A	`2/5 = 0.4 = 40%`; lies between 0.25 and 0.5	Rebuild as 4/10, then 40/100; do not teach a memorised conversion only.
5B	`0.65 < 3/4 (=0.75)`; `12.684 → 12.7` to tenths	If 0.65 > 3/4, use hundredths on equal-length bars.
6	`3/4 − 1/8 = 5/8`	If numerator and denominator are subtracted separately, express 3/4 as 6/8 first.
7	`$25.00 − $21.35 = $3.65`; inverse totals $25	If $4.35, align cents and use a 100-cent exchange.
8	30% of 50 = 15	If 30, name 50 as whole and use 10% of 50 = 5.
9	$120 − $38.40 − $46.75 = $34.85	If $35.15, add costs to $85.15, then subtract and add back.
10	`3/5=0.6=60%`; `7.486→7.49` hundredths; remaining $37.45	Diagnose equivalence, rounding and money model separately.

Day 5 check A — equivalent forms, order and precision

Prompts: (1) Show 2/5 as decimal and percentage, and place it between 0.25 and 0.5. (2) Compare 0.65 with 3/4 using a numeric reason. (3) Round 12.684 to one decimal place. Key: 2/5 = 4/10 = 0.4 = 40%; 0.65 < 0.75; 12.7.

Worked response decisions: “Two fifths equals 0.25 because it has a 2 and 5” signals digit matching, so represent five equal segments and shade two, then ask for a new 3/5. “0.65 is less than 3/4 because 65 hundredths < 75 hundredths” is convincing. “12.68” is accurate rounding to hundredths, but the requested place was tenths; repeat the instruction and point to the tenths digit before a new number such as 8.247 → 8.2. Record whether a cue was necessary.

Day 10 check B — representation, rounding and model

Prompt 1: Rename 3/5 in decimal/percent and locate it on a 0–1 line. Key: 0.6, 60%, to the right of 1/2. Prompt 2: round 7.486 to hundredths. Key: 7.49; the thousandths digit 6 makes hundredths 8 round to 9. Prompt 3: $100 minus $26.80 and $35.75, with a model and inverse check. Key: costs $62.55; remainder $37.45; $62.55 + $37.45 = $100.00.

Example next moves:

Student writes 3/5 = 0.35: use 3 of 5 equal parts, then 6 of 10; ask whether 0.35 being below one half is plausible for 3/5.
Student rounds to 7.48: compare 7.486 to 7.48 and 7.49 on a hundredth line, then round an unseen 4.273 to hundredths.
Student obtains $37.45 but no model: ask for an equation or bar showing total and two costs; do not call the strategy independently known yet.
Student writes $162.55 after adding costs to the starting budget: identify whether $100 is a whole or an extra part; return to a simple $10 whole with two small costs.
Student uses a calculator under an access plan after showing a coherent model: record the model and tool, then check interpretation; do not silently reclassify the solution as unaided calculation.

The next lesson should use a different but structurally similar example. Feedback names what happened today and what to try next, not a fixed ability tier. A correct calculation with no unit in a money story needs the unit added; it does not erase the arithmetic evidence.