Goal/materials: evaluate what a linear quote can and cannot justify; C/D card, optional graph and model-audit strip.
- Notice, 3: Ask whether C(10) is a supported price. Key: arithmetic gives 72, but stated domain ends at 8; the pack does not supply a real quote for 10.
- Model, 5: Teacher says “Within 0–8 whole hours, the rule compares stated charges. It omits availability, print quality, taxes and any extra fee. ‘D is always cheaper’ fails at h=3.” Show model → interpretation → check of assumption.
- Together, 8: Consider three claims: “C cheaper at 3” (supported); “D cheaper at 8” (supported); “D prints better quality” (unknown). Learners identify the exact number or missing evidence behind each.
- Try, 6: Fresh concert-prop hire H(t)=18+2t, J(t)=6+5t for t=0–6 whole days. Keys: equal when 18+2t=6+5t ⇒ t=4, cost 26; H lower at day 6 (30 vs 36); J lower at day 2 (16 vs 22). Learner names one omitted condition.
- Check, 3: “If a real supplier adds a delivery fee, what must we do?” Key: revise the cost model using sourced terms; we cannot assume the given graph still applies. If learner answers only ‘choose cheap line’, revisit assumption card.