# Optional five-minute practice and no-purchase home ideas

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](TEACHER-KEY.md#optional-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. |

**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.