Optional five-minute… | Year 9 Maths · T1 W3–4 · Extras And Home

The two five-minute extras in each row are alternatives, not extra mandatory lesson time. Home routes are optional and can be done with scrap paper or an oral/AAC explanation. No device, purchase, journey, personal money/technology data, family interview or adult marking is needed. All domains and figures are fictional. Give Day 15/20 extras after collecting the held-out checks. Teacher quick key is separate.

Day	Extra A · five minutes	Extra B · five minutes	No-purchase home/low-material route
11	Recipe-card paths: `4^2×4^1`: explain why 4³ counts ordered choices if each stage has four options.	Game buttons: compare `2^2×2^5` with `2^2+2^5` and give both values.	Make up two independent small choice stages on paper and explain why the counts multiply. No real game data.
12	Paper stack: `7^4/7^2=7^2`; expand enough factors to check.	Equal packs: explain `9^3/9^3=9^0` without using `0^0`.	Use identical counters to show six items grouped by three; then narrate how powers group in a larger invented model.
13	Mini-scale: `10^−1=1/10` of a drawn 1 m line is 0.1 m. Label metres.	Correct “`3^−2=−9`” using a fraction and the non-zero-base condition.	Draw a paper strip and split it into ten equal parts; label one tenth without measuring a real object.
14	Cue pairs: `(4^2)^2=4^4`; verify with 16×16.	Explain why `(5^1)^3=5^3` differs from `5^1×5^3=5^4`.	Invent two paper choice lists and write a bracketed expression for ordered pairs.
15	After check: revisit Card A and explain why 8+16 is not 128 pairs.	Reopen Card B and rewrite one same-base quotient as expanded factors.	Use an earlier model only to say where the rule is valid; do not rehearse today's new source.
16	Music-loop sketch: `y^2×y^4=y^6` for y independent options; test y1.	Compare `z^4/z^2` at z2 and z0, naming the denominator restriction.	Draw six equal-choice abstract slots labelled y and explain what y0 would mean; no real music file is needed.
17	Signed ratio: `w^1/w^4=w^−3`; evaluate w−1 and state w≠0.	Refute “a negative exponent always means a fraction less than 1” with base `1/2`: `(1/2)^−1=2`.	Create a two-row table for an invented non-zero scale factor, with one positive and one negative input.
18	Branching story: `3^t×3^(t+1)=3^(2t+1)`; check t1.	Contrast `2^(k+1)×2^(k+1)` with `2^(k+2)` at k1.	Place k plus k+1 labelled paper cards in two groups and count how many exponent slots combine.
19	Tile grid: `(4^j)^2=4^(2j)`; at j1, 16 paper tiles.	A two-column design has `2×3^s`, not `(3^s)^2`; explain at s1.	Sketch two different paper arrays with the same label but different row counts; match each to its expression.
20	After check: revisit Card F and identify why u0 invalidates the quotient.	Revise Card H's 64-icon caption to name a missing print/reader check.	Choose an earlier practice card and explain its domain to a hypothetical reader; do not use today's held-out values.