# Change-base lab · complete paper/tactile equivalent

The [offline interactive](change-base-lab.html) calculates invented examples. This page contains the same method, source numbers, worked examples, error test and limits. No device, account, sound, live price or purchase is needed.

**Paper method:** (1) State the **original amount** and unit. (2) Find the first dollar gap as `original × first percent ÷ 100`; add for a rise or subtract for a fall. (3) Name the **new amount**. (4) To return, divide the **same dollar gap by the new amount**, then multiply by 100 for the reverse percentage. (5) Test the mistaken repeated-first-percentage shortcut against the new amount. (6) Say that a word or image crop may hide one base; the values are fictional.

| Original | First step | New base | Correct return | Repeating first % instead |
| ---: | --- | ---: | --- | --- |
| `$96` | 25% rise is `$24` | `$120` | `$24÷$120×100=20%` fall; `$120−$24=$96` | 25% of `$120` is `$30`; fall gives `$90` |
| `$60` | 20% fall is `$12` | `$48` | `$12÷$48×100=25%` rise; `$48+$12=$60` | 20% of `$48` is `$9.60`; rise gives `$57.60` |

**Tactile route:** Arrange three numbered raised-edge cards ORIGINAL, CHANGED and RETURN. Place a labelled dollar-gap token between each pair, and place a FIRST PERCENT and RETURN PERCENT token beside their **own starting amount**. Use Braille/large-text labels or speech for every token; texture alone is insufficient. Move the same gap amount, then calculate its percentage of the new base. The learner may direct a supporter to move pieces and state the conclusion.

**Public sentence prompt:** “In this invented model, the amount changed from [original] to [new] by [first percent] of [original]. Returning to [original] needs [reverse percent] of [new]. A same-number percentage in the opposite direction does not generally reverse it.” No real price trend, accessibility impact or future change is established.

**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. Inline interactive code is Apache-2.0.