# Fictional cards, setup and access

**Set out:** scrap paper, pencils, optional counters or cut paper `x` and unit tiles, a straight edge, and the three [A4 aids](print/TEXT-ALTERNATIVES.md). A calculator or offline graphing tool may check a completed setup; no account, internet, purchase, personal budget or actual class survey is needed. Give source values in text as well as print. A neutral reader can say every symbol, including brackets, signs and inequality relation, without supplying the operation to use. The separate [staff key](teacher/ANSWER-AND-NEXT.md) holds all practice/check answers.

## Week 3 card set

**D11 maker packs.** There are three identical invented packs. Each contains `x` plain cards and four marker cards. The count `3(x+4)` assumes each pack has the same non-negative whole `x`. A tile square labelled `x` is a variable amount, not the numeral 1. Point to each group before expanding.

**D12 signed terms.** In `4x+7+2x−3`, keep `−3` on one movable card so a learner cannot lose the sign while regrouping. The expression is abstract; do not invent a real refund or a debt where none was provided. A student can type or dictate `(4x+2x)+(7−3)`.

**D13 equal groups.** Six `x` tiles and twelve unit tiles may be laid into six equal rows. Text route: “Each of six groups gets one x tile and two unit tiles.” This represents `6x+12=6(x+2)` for any numeric `x` for which the model makes sense.

**D14 kit refill model.** A fictional club counts 8 setup tokens and 5 tokens per identical refill. `C=8+5n`; `n` is a non-negative whole number of refills. Tokens stand for a count, not a real price or actual resource claim. The model omits changing pack size or unavailable stock. D15 has a **different** check card in [the formative learner checks](STUDENT-CHECKS.md).

## Week 4 card set

**D16 equation balance.** `3x+7=25` is an abstract equality; both sides must undergo the same operation. A second example `2y+5=12` has a rational answer; no whole-count restriction has been imposed. Use a line of exact inverse steps before a decimal conversion.

**D17 two invented plan totals.** A `6+4n`; B `18+2n` tokens for `n` identical whole batches, `n≥0`. These are fictional teaching values with no service terms or quality evidence. Graph x as batches, y as tokens, and mark integer x-values as the available cases. Algebra determines exact crossing; drawing a line conveys relation between plotted points but does not make fractional batches offered.

**D18 poster desk.** Setup 9 points; 5 points per whole poster; 34 points available. `9+5n≤34`, `n∈{0,1,2,...}`. Points are invented and not money. If displaying graph, label the horizontal cap at `y=34` and the relation `y=9+5n`.

**D19 counter tray.** A fictional tray begins with 15 counters and loses exactly 3 per turn. The supplied domain is `t∈{0,1,2,3,4,5}`; after that this particular physical model is undefined. The question “more than 3 remain” corresponds to `15−3t>3`. The reversal when dividing by a negative is an algebraic fact; test boundary and a neighbouring value rather than relying on a memorised arrow.

## Access and classroom note

The [expression tiles](print/expression-tiles.pdf), [balance/rearrange mat](print/balance-rearrange.pdf) and [line/boundary board](print/line-and-boundary.pdf) have [complete text and tactile counterparts](print/TEXT-ALTERNATIVES.md). Do not assign a route based on a fixed “learning style” label; offer several ways to express the **same** mathematics. Make printed signs `−`, `≤`, `<` distinguishable in words. A tactile number line needs labelled tick numbers and an explicit open/closed boundary token. A student may need more time; protect the reasoning target and note the timing adjustment.

Original SubjectNest fictional cards and models © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).