Set out: scrap paper, pencils, optional counters or cut paper x and unit tiles, a straight edge, and the three A4 aids. 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 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.
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, balance/rearrange mat and line/boundary board have complete text and tactile counterparts. 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.
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