What’s inside:
- Part 1 · The Blueprint Scaler — a gridded blueprint rectangle beside the actual room it becomes, with three sliders (drawing width, height, and the scale 1 cm : k m). The actual room visibly grows/shrinks, and three stat cards track lengths (× k), perimeter (× k), and — highlighted in gold — area (× k²!), with a caption explaining why area stretches in two directions.
- Part 2 · Triangle Commissions — random client “orders” of either three sides or three angles, with three commit buttons: Exactly ONE / MANY sizes / NONE. The drafting table then draws the truth: valid sides close into a rigid triangle built from the actual lengths; impossible sides show two dashed “reach” circles that never meet; valid angles render two different-size similar triangles side by side; impossible angles stack the three wedges along a straight 180° line so the overshoot or shortfall is visible.
- Part 3 · Studio Machines — 📏 Scale Converter (both directions, narrating why drawing→actual multiplies and actual→drawing divides, with the adding-trap called out numerically), 📐 Triangle Tester (sorts sides, runs the one reach test that matters, handles the degenerate “collapses flat” equality case, and classifies valid triangles), and 🔪 Slice Visualizer (rectangular prism and square pyramid drawn in oblique projection with a gold cut plane, all five slices: prism parallel/vertical, pyramid parallel/through-apex/off-apex, each with the resulting cross-section drawn and explained).
- Part 4 · Quiz — 10 questions across scale (including the k² area question), triangle conditions (unique/many/none), and cross-sections, with four tiers routing back by tag.
Misconception coverage summary: Questions 1–3 target scale errors — adding or subtracting the scale number instead of multiplying, converting in the wrong direction (dividing drawing→actual or multiplying actual→drawing), and the big one: scaling area by k instead of k², plus believing area doesn’t scale at all. Questions 4–7 target triangle-condition traps: assuming any three lengths work, checking the wrong pairs in the inequality (longest + anything), believing fixed sides allow many shapes or that a mirror flip counts as a second triangle, thinking three angles force one unique triangle, and missing the exact-180° requirement. Questions 8–10 target cross-section confusions — expecting prism slices to shrink or pyramid slices to match the base, and mixing up the through-apex triangle with the off-apex trapezoid.
