Five-day instruction, worked calculations, learning progressions, misconceptions, rubric and print-friendly synthetic lab alternatives.
Purpose, alignment and safety
Essential question: Why can two machines do the same work at different rates? Students connect energy transfer to average power and improve a modeled conversion device within numerical constraints. The design activity is relevant to HS-PS3-3, but these five sessions alone do not cover its full engineering design performance expectation.
Prerequisites: joules, watts, positive time intervals, work, kinetic and other forms of energy, unit conversion, conservation and percent ratios. Week 11 introduced the complete energy ledger. Provide a formula card with P=E/t and η=E_useful/E_input before independent work.
Monday — Same Energy, Different Time
Starter (8 min): Imagine two devices delivering the same 360 J in 6 s and 3 s. Ask which did more work and which was more powerful.
Core reading (15 min): Average output power is useful energy divided by time. Work and energy are in joules; power is in watts (J/s). Do not infer instantaneous power from interval averages.
Worked answer (12 min): 360/6=60 W and 360/3=120 W; useful work remains 360 J in both cases. Halving the interval doubles average power.
Controlled data (15 min): Three runs with unchanged energy and different durations; written misconception check.
Starter: Draw a device boundary and arrows for incoming energy, useful output and other forms.
Model: E_input=E_useful+E_other for the same interval and a device without net stored-energy change. Input, useful and other powers are each category's energy divided by the SAME time interval.
Worked answer: E_in=400 J, E_useful=300 J, E_other=100 J, t=5 s → input 80 W, useful 60 W, other 20 W. All transfers are accounted, not destroyed.
Exit: What if the machine were charging a battery? Require an additional stored-energy-change term.
Model: η=E_useful/E_input=mean useful power/mean input power for a shared interval under the stated assumptions. Efficiency is dimensionless, not a watt or joule.
Worked: 400 J input and 75% useful output give 300 J useful and 100 J other. Compare with 60% at the same energy/time: 240 J useful. Neither amount is real measurement. Device efficiency depends on chosen intended output.
Practice: Hold input and time fixed; test 50%, 75%, and 90%. Explain why a high efficiency percentage need not imply higher absolute power.
Design brief: energy input ≤500 J, useful output ≥300 J, elapsed time ≤6 s. Test designs in the Efficiency Lab; learners must satisfy all three constraints.
Worked: 400 J at 75% over 5 s gives useful 300 J and passes. 400 J at 60% over 5 s gives useful 240 J and fails. 600 J at 75% over 5 s would exceed the input budget even if other criteria passed.
Evidence: Three rate trials and three design trials, matched comparisons, exported journals, a defensible numerical recommendation and one unmodeled realistic engineering constraint (such as reliability or cost).
Claim: Two devices can transfer the same joules at different watts, because their time intervals differ. Efficiency separately characterizes the fraction of incoming energy serving the intended goal.
Evidence: Calculate 360 J/6 s and 360 J/3 s. Demonstrate 400 J in at 75% produces 300 J useful, 100 J other and 60 W useful over five seconds. Identify source and interval for every displayed quantity.
Assessment: Ten randomized open-book formative questions from a 20-question bank, with explanatory feedback and an 80% correction goal. These public exercises are not official proctored midterms or finals.
Correctly distinguishes power, total energy and efficiency.
Numerical calculations · 4
At least two examples with appropriate joules, seconds, watts and percentages.
Conservation ledger · 4
Complete useful/other/input account with one defined common interval.
Engineering design evidence · 4
Applies all three constraints and supports a recommendation with controlled trial results.
Limitations and revisions · 4
Identifies a real-world missing criterion and corrects a misconception using scientific reasoning.
Target: 16/20 (80%). The teacher reviews the exported and written evidence. Confidential formal exams are assessed in a separate supervised environment.
Differentiate instruction
Foundation: provide precomputed tables, calculator assistance, unit labels and a percent-to-decimal reference. Core: vary one control per investigation and explain ledger equations in words. Extension: discuss start/stop transients, changes in stored energy and why mean useful/input power ratios require matched time windows.
The five khae_high_science_evidence_v1: student journal keys are preserved. Supplemental Week 12 lessons/labs use separate browser-local keys and export/import portability. Dormant STOS content is untouched.