Day 4 facilitator guide: Compare linear models
Before class
Ask students to label a cost model as starting fee + rate × quantity. All questions specify the same quantity for both plans. Optional Pearson 15705 or 28018 can supplement the shared-cost example.
30-minute facilitation
| Minutes | Facilitation |
|---|---|
| 0–3 | Use W1–W2 to retrieve evaluation and one-step solving. |
| 3–10 | Model writing two expressions, equating them, solving, and checking both costs. Explain equality as a crossover, not always the best plan. |
| 10–14 | Work G1–G2 together. Label the input and its unit. |
| 14–22 | Students complete P1–P4. Confer with students comparing only the hourly prices. |
| 22–27 | Collect E1–E2 independently. |
| 27–30 | Ask what changes before versus after the crossover. |
Listen for
- Comparing hourly rates without the initial fee.
- Giving the common cost when the question asks for hours.
- Assuming the lower starting fee makes a plan always cheaper.
- Reporting fractional units when the situation allows only whole units; all required examples here have valid whole-number crossover inputs.
Support and extension
Support: build a two-column cost table for h = 0, 1, 2, … before writing an equation. Extension: determine when A = 12 + 3h is cheaper than B = 6 + 5h. A is cheaper for h > 3; at h = 3 costs are equal.
Next action
E1 checks a crossover; E2 checks a comparison at a specific input. Use Day 5 results to separate equation-solving gaps from model-selection gaps.