HS-ETS1-4: Using Computer Simulations to Test Engineering Solutions
In plain English: HS-ETS1-4 is the NGSS high school performance expectation that asks students to use a computer simulation to model how proposed solutions to a complex real-world problem affect the systems involved. Students run a solution under many criteria and constraints and trace how a change in one system affects the others. It is usually taught inside a high school science or engineering course.
Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints on interactions within and between systems relevant to the problem.
Next Generation Science Standards · Disciplinary Core Idea: Engineering Design · Official standard
Some solutions are too slow, too costly or too risky to try out in the real world first: nobody drains a real reservoir to see whether a water plan works. Engineers build a computer simulation instead, run each proposed solution through it, and watch what happens to every system the problem touches. In this lesson students build and run spreadsheet simulations of three complex problems: a city reservoir in a dry year, a fishery with a catch quota and a storm pond during heavy rain. Each has several criteria and constraints at once, and each solution changes more than one system: saving water for the city can take water from the river's fish, and making new water uses energy. Students compare solutions, test them under harder conditions, check the model against measured data and name what the model leaves out.
The practice is Using Mathematics and Computational Thinking: using computer simulations to predict the effects of a design solution on systems and the interactions between them. The core idea is ETS1.B, Developing Possible Solutions: computers can run simulations to test different ways of solving a problem and to see which one is most efficient or economical. NGSS gives no Clarification Statement and no Assessment Boundary for HS-ETS1-4, so the lesson stays with the wording of the performance expectation. Every simulation input on this page is invented for teaching and labeled as invented. The only hands-on part, an optional bucket check of the storm pond model, uses tap water with the computers kept away from the tub.
Learning Objectives
By the end of this lesson, students will be able to:
Describe a computer simulation in terms of its inputs, rules, time step, outputs and assumptions
Build and run a spreadsheet simulation that models proposed solutions to a problem with several criteria and constraints
Use simulation output to identify interactions within and between systems, such as a water supply, an ecosystem and an energy system
Test solutions under harder conditions and over long enough time spans, and compare them against every constraint
Check a simulation against measured data and explain how its assumptions limit what it can show
Prior Knowledge Required
Students should already be comfortable with:
Developing a model to generate data for testing and improving a design MS-ETS1-4
Evaluating solutions against criteria, constraints and trade-offs HS-ETS1-3
Entering formulas and filling them down in a spreadsheet
Reading line graphs and tables of values over time
Show a photo of a reservoir with a wide ring of dry shoreline. Give students three minutes alone and three with a partner.
Warm-Up Prompt
"A city's reservoir is low and the dry season is just starting. Three ideas are on the table: ask people to use less water, build a plant that cleans wastewater for reuse, or let less water out into the river below the dam. How could the city find out which idea works, and what else each idea would change, without trying it for real?"
Collect ideas. Students usually suggest asking an expert, looking at other cities, or calculating. Take the calculating idea further: if we know how much water comes in and goes out each month, a computer can add it up month by month for each idea. Point out the second half of the prompt: each idea also changes something else (people's daily lives, the energy the city uses, the fish in the river). HS-ETS1-4 asks students to use a simulation to see those effects too.
Direct Instruction20-25 minutes
What a simulation is. A computer simulation repeats a set of rules over many time steps. It needs inputs (starting values and data, such as monthly inflow), rules (how one step leads to the next), a time step (a month, a year, an hour), and it produces outputs (storage each month, the lowest storage, energy used). Every simulation also rests on assumptions, the things it leaves out or holds fixed.
Define the systems and the criteria and constraints. Here: the reservoir must stay at or above 30 hm³ (1 hm³ is one million m³), the river must get at least 1 hm³ a month for fish, and extra energy use must stay at or below 12 GWh a year.
Write the rule for one time step. Storage next month = storage this month + inflow - city demand - river release + recycled water.
Enter the inputs and run the baseline, the case with no new solution, to see the problem.
Change one input per solution and rerun. Record the outputs for every criterion and constraint, not only the one the solution targets.
Look across systems. Ask what each solution did to the other systems: the river, the energy grid and the people who use the water.
Stress-test and check. Rerun under a harder case (a drier year), and compare the model with measured data before trusting it.
Reservoir simulation, invented dry-year inputs (storage in hm³ at the end of each month)
Month
Inflow
Storage: baseline
Storage: combined plan
0
60
60
1
6
60
61.5
2
5
59
62
3
4
57
61.5
4
3
54
60
5
2
50
57.5
6
1
45
54
7
1
40
50.5
8
1
35
47
9
2
31
44.5
10
3
28
43
11
4
26
42.5
12
5
25
43
Run the baseline
Start at 60 hm³ with the dry-year inflows in the table, city demand 5 hm³ and river release 1 hm³ every month.
Result: Storage drops to 28 hm³ after month 10 and ends at 25 hm³: the 30 hm³ reserve is broken
Test conservation
Water restrictions cut city demand by 20%, from 5 to 4 hm³ a month.
Result: Lowest storage 37 hm³: the reserve holds, but households face restrictions and the utility sells 12 hm³ less water in the year
Test recycled water
A plant adds 1.5 hm³ a month of purified recycled water and uses 1 kWh per m³ (so 1 GWh per hm³).
Result: Lowest storage 42.5 hm³, but 1.5 × 12 = 18 GWh a year, over the 12 GWh energy limit
Test a smaller river release
Release 0.5 hm³ a month to the river instead of 1 hm³.
Result: Lowest storage 31 hm³: the reserve holds, but the fish-flow constraint is broken downstream
Combine and rerun
Conservation of 10% (demand 4.5 hm³) plus 1 hm³ a month of recycled water; the river release stays at 1 hm³.
Result: Lowest storage 42.5 hm³; energy 12 GWh a year; fish flow met: every constraint holds
Use Diagram 1 to compare the runs and Diagram 2 to show the interactions: each solution pulls on a different arrow. Cutting the release helps the reservoir by taking water from the river ecosystem, and recycled water helps the reservoir by drawing on the energy system. The combined plan works because it spreads the load. Point out that the lowest storage does not come in the driest months (6-8) but at the end of the year, because storage keeps falling as long as more water leaves than arrives.
Guided Practice15 minutes
Project a second spreadsheet and run it with the class: a fishery. Each year the fish stock grows by 0.4 × P × (1 - P/1,000) tonnes, where P is the stock and 1,000 t is the most the habitat can support; then the year's catch is removed. The stock starts at 400 t. Constraints: the stock must never fall below 300 t (the ecosystem), and the catch must be at least 80 t a year so fishing families can earn a living (the community). All values are invented.
Fishery simulation output: stock in tonnes (invented inputs)
Year
0
1
2
5
14
20
Quota 100 t
400
396.0
391.7
376.3
287.0
104.6
Quota 80 t
400
416.0
433.2
490.1
646.6
696.1
First show only years 0-5 and ask groups which quota they would choose. Many pick 100 t: the stock falls only 24 t in 5 years and the catch is larger. Then reveal years 14 and 20. With 100 t the stock drops below 300 t in year 14 and heads toward collapse; with 80 t it grows every year. Ask groups (1) to write the step rule in words, (2) to explain why a 5-year run was misleading, and (3) to name the interaction the model shows between the ecosystem and the fishing community. The key idea: at 400 t the stock grows about 96 t a year, so a 100 t catch takes a little more than the stock replaces, and the gap widens as the stock shrinks.
Independent Practice10-15 minutes
Each pair opens its reservoir spreadsheet from Activity 1 and stress-tests the combined plan: multiply every inflow by 0.8 for a year that is 20% drier, and rerun. Pairs record the lowest storage, decide whether every constraint still holds, and write one sentence about how confident they are in the plan. Pairs that finish early try a year 30% drier. Collect the results; they feed Homework Problem 6.
Closure10 minutes
Exit Ticket
"Cutting the river release kept the reservoir above its reserve. Explain in two sentences why the simulation still rules it out, and name one thing the reservoir model leaves out that could change its results."
Look for the interaction between systems (the saving comes from the river ecosystem and breaks the fish-flow constraint) and a real limitation, such as evaporation, a demand that changes with the weather, or a drier year than the one entered.
Differentiation Strategies
For Struggling Students
Give a spreadsheet with the columns and the first row of formulas filled in, so students fill down and change inputs
Have students work the first three months by hand in a table before they trust the spreadsheet
Provide a results table with one row per solution and one column per constraint, marked meets or fails
For Advanced Students
Ask students to make demand depend on the weather (higher in the hottest months) and test whether the combined plan still works
Have students find, by trial in the spreadsheet, the smallest conservation percentage that keeps the reserve with no recycled water
Ask students to rebuild one model in a block-based or agent-based modeling program and compare the two
Assessment Guidance
What to Look For
Strong work states the model's inputs, rule, time step and assumptions, changes one input per solution, and reports every criterion and constraint for every run. Students trace effects across systems, run long enough and under a harder case to catch slow failures, compare the model with measured data, and treat the output as a prediction that depends on assumptions rather than as proof. Watch for runs that report only the target system, a single scenario, a time span too short to show a trend, and spreadsheet formulas that were not checked by hand for the first step.
02
Classroom Activities
3 Activities
1
Build the Reservoir Simulation
30 minPairs, one computer per pair
Pairs build the reservoir model in a spreadsheet, reproduce the baseline from the worked example, and then design and test their own mix of solutions against all three constraints.
Set Up the Spreadsheet
Columns: A month, B inflow, C demand, D river release, E recycled water, F storage. Put the headings in row 1 and month 0 in row 2, with 60 in cell F2
Enter months 1-12 in rows 3-14 with the dry-year inflows from the table, 5 for demand, 1 for release and 0 for recycled water
In F3 type =F2+B3-C3-D3+E3 and fill it down to F14
Add outputs: lowest storage =MIN(F2:F14), extra energy in GWh =SUM(E3:E14) (1 hm³ of recycled water uses 1 GWh) and lowest release =MIN(D3:D14)
Check month 1 by hand: 60 + 6 - 5 - 1 + 0 = 60
Procedure
Confirm the baseline: lowest storage 25 hm³
Design a mix of conservation (lower demand), recycled water and release that meets all three constraints: storage at least 30 hm³, release at least 1 hm³ every month, energy at most 12 GWh a year
Record each run in the class table: the inputs, the three outputs, and one sentence on who is affected
Make a line graph of storage for your best run and the baseline
Discussion Questions
The driest months are 6-8, but the baseline storage is lowest at the end of month 12. Why?
Which constraint limited your mix the most?
Two teams met every constraint with different mixes. What would you need, beyond this model, to choose between them?
Modification for Distance Learning
Share one spreadsheet file with a tab per pair. Pairs post their best mix and its three outputs in a shared results table before the class discusses them.
2
Storm Pond Simulation: Pipe, Pond or Green Roofs
25 minGroups of 3
A neighborhood's stormwater drains into a pond, and a pipe lets water out of the pond into a creek. Groups simulate a heavy storm hour by hour and test three solutions against two systems: the street next to the pond and the creek downstream.
The Model (invented data)
Runoff into the pond each hour, in thousands of m³: 2, 6, 10, 8, 4, 2, 1, 0
The pipe lets out at most 3 thousand m³ an hour. Flows above 3 erode the creek banks
The pond holds 14 thousand m³; any water above that floods the street
Rule for each hour: water in the pond = previous amount + runoff - outflow, where the outflow is 3 or whatever is in the pond, whichever is less. In a spreadsheet: =MAX(0, B2+C3-3)
Procedure
Run the baseline and find the most water the pond would need to hold. Does the street flood?
Solution 1: a larger pipe that passes 4 thousand m³ an hour ($0.4 million)
Solution 2: a larger pond that holds 17 thousand m³ ($1.2 million, uses half a hectare of the park)
Solution 3: green roofs and rain gardens upstream that cut every hour's runoff by 15% ($2.5 million)
For each run, record the peak volume, whether the street floods and the highest flow into the creek
Discussion Questions
The baseline needs room for 16 thousand m³, so 2 thousand m³ reach the street. Which solution fixes the street by moving the problem to the creek?
Green roofs cost the most. What benefits might they have that this model does not count?
The storm in the model lasts 8 hours. What happens to your best solution if a second storm arrives 4 hours later?
Challenge Variation: Check the Model with a Bucket
Groups pour water into a plastic cup with a small hole (made by the teacher) at a steady rate and time how fast the level rises, then compare with a spreadsheet run of the same numbers. Work over a plastic tub, keep laptops and outlets on a separate table, wipe spills at once so nobody slips, and use tap water only.
3
Critique and Validate the Model
20 minPairs
Before a city trusts a simulation, it checks the model against what really happened. Pairs compare the baseline model with measured storage from the first half of a real dry year (invented values), find what the model is missing, and fix it.
Model and Measurements (invented)
Storage at the end of months 1-6. Model: 60, 59, 57, 54, 50, 45 hm³. Measured: 59.5, 58, 55.5, 52, 47.5, 42 hm³. The inflows, demand and release in the model match the utility's records for those months.
Procedure
Compute measured minus model for each month. Describe the pattern
Propose a process the model leaves out that could explain the pattern, and estimate its size per month
Add a column for it to your Activity 1 spreadsheet and rerun the combined plan. Does it still meet every constraint?
List two more assumptions of the reservoir model and say whether each one makes the results too hopeful or too cautious
Discussion Questions
The gap grows by the same amount every month. Why does that point to a steady loss such as evaporation, rather than a wrong starting value?
With the missing loss added, the combined plan's lowest storage is 37 hm³ instead of 42.5 hm³. How does that change your confidence in the plan?
What else would you add to the model or test before a city council relies on it?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Simulated Reservoir Storage Under Four Plans
Spreadsheet output for the invented dry year, drawn to scale. The red dashed line is the 30 hm³ emergency reserve. The baseline crosses it after month 10. Cutting the river release stays above it (31 hm³ at the end) but breaks the fish-flow constraint, so only conservation and the combined plan pass on every system; the combined plan also keeps the most water in storage.
Diagram 2: The Systems a Water Plan Touches
The reservoir sits between three other systems, and each proposed solution works through a different interaction: conservation lowers the supply the community draws, recycled water returns water but draws power from the energy system, and a smaller release takes water from the river ecosystem. A useful simulation reports what happens in every box, not only in the reservoir.
04
Homework Assignment
~30 min
HS-ETS1-4 Homework: Simulating Solutions Across Systems
Directions: Use a spreadsheet where you can, and write the rule you used for each simulation. Report every criterion and constraint for every run. All inputs are invented for practice.
Part 1: Running Simulations (Problems 1-3)
A town reservoir holds 40 hm³ at the start of a dry spell. Inflows for the next 6 months are 3, 2, 2, 1, 1 and 2 hm³. Town demand is 4 hm³ a month and the river release is 0.8 hm³ a month. The reservoir must stay at or above 24 hm³. (a) Simulate the 6 months and give the storage at the end of each month. (b) In which month is the constraint first broken? (c) Rerun with demand cut by 25%. Does the plan meet the constraint, and what is the lowest storage?
A fishery follows the rule: next year's stock = P + 0.5 × P × (1 - P/800) - catch, with P in tonnes. The stock starts at 300 t. (a) Simulate 3 years with a catch of 110 t a year and with a catch of 80 t a year, rounding to 0.1 t. (b) Which catch keeps the stock growing? (c) Fishing families say they need at least 100 t a year. Explain the conflict between the two systems and what a longer run could tell the town.
An invented simulation of another city's dry year gave these outputs for four plans. P1, 25% conservation: lowest storage 33 hm³, lowest release 1.0 hm³, extra energy 0 GWh, cost $5 million. P2, new groundwater wells: 36 hm³, 1.0 hm³, 15 GWh, $25 million. P3, reduced river release: 31 hm³, 0.6 hm³, 0 GWh, $1 million. P4, recycled water plus 10% conservation: 38 hm³, 1.0 hm³, 10 GWh, $38 million. Constraints: storage at least 30 hm³, release at least 1.0 hm³, energy at most 12 GWh, cost at most $40 million. (a) Which plans meet every constraint? (b) Which constraint does each failing plan break, and which system does it affect? (c) Choose between the passing plans and name one effect on people the table does not show.
Part 2: Designing and Checking (Problems 4-6)
A school parking lot drains into a storage tank with an outlet pipe. Runoff during a storm is 100, 400, 700, 600, 300 and 100 m³ in hours 1-6. The outlet passes at most 250 m³ an hour, the most the creek below can take without erosion, and the tank holds 800 m³. (a) Simulate the storm and find the most water the tank would need to hold. Does it overflow? (b) Test a larger outlet of 350 m³ an hour and a permeable pavement that cuts runoff by 20%. Report the peak volume and the highest creek flow for each. (c) Which solution meets both constraints?
A traffic simulation for a new school drop-off loop assumed that 240 cars arrive evenly over 30 minutes, 8 per minute. Video from a similar school shows that half the cars arrive in the last 10 minutes. (a) What arrival rate does that give for the last 10 minutes? (b) Explain why the original assumption could make a loop that is too short look adequate. (c) Describe a sensitivity test you would run in the simulation before building the loop.
Use the results of your Independent Practice stress test, or build a new simulation approved by your teacher. Write a one-page report: the problem and its systems, the criteria and constraints, the inputs, rule and time step, at least two proposed solutions and their outputs for every constraint, one harder case, one interaction between systems that the simulation revealed, and two assumptions that limit your conclusions.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Model Setup
Inputs, rule, time step and assumptions stated; first step checked by hand
Rule stated but inputs or assumptions unclear
No clear rule
Simulation Runs
Correct outputs for every solution and a harder case
Correct method with an error, or only one scenario
Runs missing or incorrect
Systems and Constraints
Every constraint reported for every run; interactions between systems explained
Some constraints or systems missing
Only the target system reported
Limits of the Model
Names specific assumptions and how they could change the conclusion
Limits named but vague
Output treated as proof
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Answer each multiple-choice question to see the explanation. For the six short-answer questions at the end, work on paper or in a spreadsheet, then open the sample answer. Reset quiz clears the page. All inputs in the questions are invented for practice.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Why do engineers use computer simulations to evaluate proposed solutions?
Answer: C
A simulation lets a team try many ideas, and harder conditions, without the cost or risk of building each one. It is a prediction based on assumptions, so choice A overstates it. Choice B is false: inputs and checks come from real data. Choice D is not true.
Question 2 of 20 · Multiple Choice
A reservoir model uses the rule: next storage = storage + inflow - demand - release + recycled. This month storage is 48 hm³, inflow 3, demand 5, release 1 and recycled 0.5. What is next month's storage?
Answer: A
48 + 3 - 5 - 1 + 0.5 = 45.5 hm³. Choice B leaves out the recycled water, choice C adds the demand instead of subtracting it, and choice D leaves out the river release.
Question 3 of 20 · Multiple Choice
In a reservoir simulation, which result shows an interaction between systems?
Answer: D
Choice D links two systems: a change in the water supply system (a low reservoir) has an effect on the river ecosystem (water temperature for trout). Choices A and B describe the reservoir or its inputs alone, and choice C is a feature of the model, not a result.
Question 4 of 20 · Multiple Choice
A storm pond model uses: water in pond = previous + runoff - outflow, with outflow at most 3 thousand m³ an hour. The pond now contains 9 thousand m³ and receives 5 thousand m³ of runoff this hour. Its capacity is 10 thousand m³. What happens?
Answer: B
9 + 5 - 3 = 11 thousand m³, which is 1 thousand more than the pond holds, so 1 thousand m³ overflows. Choice A forgets the outflow, choice C reverses the signs, and choice D forgets the pond's capacity.
Question 5 of 20 · Multiple Choice
A simulation of a town's groundwater pumping plan looks fine for 3 years, but a 30-year run shows the wells running dry. What is the lesson for running simulations?
Answer: A
Small yearly losses add up, so a drop in the water table that looks harmless for 3 years can empty the wells over 30. The time span is part of the model design. Choice B ignores the evidence, choice C wrongly claims the model can say nothing, and choice D changes the model to fit a preferred answer.
Question 6 of 20 · Multiple Choice
A fish stock grows by 0.3 × P × (1 - P/1,000) tonnes a year and then 60 t are caught. The stock is now 500 t. What is next year's stock?
Answer: C
Growth = 0.3 × 500 × (1 - 0.5) = 75 t, so next year's stock = 500 + 75 - 60 = 515 t. Choice A leaves out the growth, choice B leaves out the catch, and choice D leaves out the (1 - P/1,000) limit, so it uses growth of 150 t.
Question 7 of 20 · Multiple Choice
How can a team check whether its simulation can be trusted?
Answer: B
Comparing a model with a period whose results are already known (a hindcast) shows whether it captures the real processes. Choices A and D are about appearance and precision, not accuracy, and choice C is the bias a check is meant to prevent.
Question 8 of 20 · Multiple Choice
What is a sensitivity test in a simulation?
Answer: D
A sensitivity test changes uncertain inputs to see whether a solution still meets its constraints. If a small change flips the result, the team should be cautious. Choice B is a single run, and choice C throws away important information.
Question 9 of 20 · Multiple Choice
A proposed recycling plant would add 2 million m³ of water a month and use 1.2 kWh per m³. How much energy does it add to the energy system in a year?
Answer: A
2,000,000 m³ × 1.2 kWh = 2,400,000 kWh = 2.4 GWh a month, and 2.4 × 12 = 28.8 GWh a year. Choice B is one month only, choice C multiplies 2 by 12 and forgets the 1.2 kWh per m³, and choice D divides 2 by 1.2.
Question 10 of 20 · Multiple Choice
A water plan meets every constraint in a normal year, but in a simulated drought year the reservoir falls below its reserve. What should the team conclude?
Answer: C
Testing harder cases is what reveals weak plans, and a water plan exists for dry years. The team should strengthen the plan and state its limits. Choice A ignores the case that matters most, choice B blames the model without evidence, and choice D removes a safety constraint instead of solving the problem.
Question 11 of 20 · Multiple Choice
A reservoir model uses one time step per month. What is one limitation of that choice?
Answer: B
A monthly step averages everything within the month, so short peaks disappear. Choice A is false, since 12 steps cover a year. Choice C is false, and choice D claims a direction of error the time step does not guarantee.
Question 12 of 20 · Multiple Choice
A simulation gives the lowest storage for four plans: P 28 hm³, Q 34 hm³, R 31 hm³, S 26 hm³. The constraint is storage of at least 30 hm³. Which plans meet it?
Answer: D
Only 34 and 31 are at or above 30, so Q and R pass. Choice A misses R, choice B lists the two plans that fail, and choice C includes P at 28 hm³. A passing plan must still be checked against the other constraints and systems.
Question 13 of 20 · Multiple Choice
Which statement is an assumption of the reservoir model in this lesson rather than an output?
Answer: A
Leaving out seepage is a choice the modelers made; a real reservoir loses some water through the ground under and around it, so this assumption makes the results a little too hopeful. Choices B, C and D are results the simulation produced from its inputs and rule.
Question 14 of 20 · Multiple Choice
A model predicted a storage of 52 hm³, and the measured value was 49.5 hm³. What is the error as a percent of the measured value?
Answer: B
Error = 52 - 49.5 = 2.5 hm³, and 2.5 ÷ 49.5 ≈ 0.051, about 5.1%. Choice A divides by the model value instead of the measured one, choice C gives the error in hm³ as if it were a percent, and choice D is 49.5 ÷ 52.
Question 15 of 20 · Short Answer
A reservoir holds 50 hm³. Inflows for the next 4 months are 2, 1, 1 and 2 hm³, demand is 3.5 hm³ a month, the river release is 0.5 hm³ a month, and storage must stay at or above 42 hm³. Simulate the 4 months. Is the constraint met? What monthly cut in demand would just meet it?
Each month storage changes by inflow - 4: 50 → 48 → 45 → 42 → 40 hm³. The constraint is broken in month 4 (40 hm³). Storage falls every month, so the lowest value is at the end: 50 + 6 - 4 × (4 - x) ≥ 42 gives 4x ≥ 2, so demand must drop by at least 0.5 hm³ a month (to 3 hm³). Check: 48.5, 46, 43.5, 42 hm³.
Question 16 of 20 · Short Answer
Choose a complex problem (for example traffic near a school, a city's electricity supply on hot days, or coastal flooding). Name two systems involved, describe one way a proposed solution in one system could affect the other, and explain how a simulation could show that effect.
Sample answer: electricity on hot days. Systems: the power grid and city residents' health. A solution that shuts off power to some neighborhoods at peak times (rolling outages) protects the grid but leaves homes without air conditioning during a heat wave. A simulation that steps hour by hour through a heat wave could track grid demand and the hours each neighborhood spends without power, and compare it with a solution such as paying households to cut use at peak hours. Any two linked systems with a specific effect and a simulation output that would show it earn credit.
Question 17 of 20 · Short Answer
A fishery follows: next stock = P + 0.4 × P × (1 - P/1,000) - catch, with P in tonnes. The stock is 600 t and the catch is 110 t a year. Simulate 2 years (round to 0.1 t) and explain what the trend means for the fishing community.
Year 1: growth = 0.4 × 600 × 0.4 = 96 t, so 600 + 96 - 110 = 586 t. Year 2: growth = 0.4 × 586 × 0.414 ≈ 97.0 t, so 586 + 97.0 - 110 ≈ 573.0 t. The stock falls each year because the catch is larger than the growth. The largest growth this rule allows in any year is 0.4 × 1,000 ÷ 4 = 100 t, so a 110 t catch can never be replaced: over a long run the stock collapses and so does the catch. The community keeps a larger catch now at the cost of its future income; a quota at or below the stock's growth is needed.
Question 18 of 20 · Short Answer
A city council member says: "The simulation shows our plan keeps the reservoir above its reserve, so the model proves the plan will work." Write a short reply that explains what a simulation can and cannot show.
Sample answer: The simulation shows that the plan works if the inputs and assumptions are right: the inflows we entered, a steady demand and no losses the model leaves out, such as evaporation. It is a prediction, not proof. Before relying on it we should compare it with measured data from past years, rerun it for a drier year and for higher demand, and check its effects on the river and the energy supply. If the plan still meets every constraint under those tests, we can be much more confident.
Question 19 of 20 · Short Answer
A storage pond starts empty. Runoff in hours 1-4 is 3, 8, 6 and 2 thousand m³, the outlet passes at most 4 thousand m³ an hour, and the pond holds 8 thousand m³. Simulate the storm. Then a developer proposes paving that raises every hour's runoff by 25%. Rerun and say what the council should know.
Rule: pond = previous + runoff - outflow, outflow at most 4. Now: 0 (3 in, 3 out), 4, 6, 4 thousand m³; peak 6, within 8. With 25% more runoff (3.75, 10, 7.5, 2.5): 0, 6, 9.5, 8 thousand m³; the pond would need 9.5, so 1.5 thousand m³ would overflow at the peak. The council should know that the paving turns a safe design into a flooding one unless the pond is enlarged, runoff is reduced elsewhere, or the outlet is enlarged, which would send more water to whatever lies downstream.
Question 20 of 20 · Short Answer
Plan a simulation for this problem: a school cafeteria wants shorter lunch lines, but the line must not block the hallway and students need at least 20 minutes to eat. Name the inputs, the rule or time step, two outputs linked to criteria or constraints, and two solutions to test.
Sample answer. Inputs: students arriving per minute (counted at the door), the time to serve one student, the number of serving lines, the space before the hallway in places for students. Time step: one minute: line next minute = line + arrivals - students served. Outputs: the longest line compared with the space before the hallway (constraint: the hallway stays clear) and the longest wait (criterion: at most 10 minutes of a 30-minute lunch, so students get 20 minutes to eat). Solutions: open a second serving line, or release grades to lunch 5 minutes apart. Then rerun with 20% more students, as on a popular menu day, as a sensitivity test.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-ETS1-4 mean?
HS-ETS1-4 asks high school students to use a computer simulation to model how proposed solutions to a complex real-world problem affect the systems involved and the interactions between them.
The problem has many criteria and constraints, so students report every one of them for every solution they test. The code reads: HS (high school), ETS1 (Engineering Design), performance expectation 4.
Does a spreadsheet count as a computer simulation for HS-ETS1-4?
Yes. A spreadsheet that applies a rule step by step over time, from inputs to outputs, is a computer simulation.
It has an advantage for teaching: students can see every formula and check the first step by hand. Ready-made simulations are also fine, as long as students set the inputs, run the solutions and interpret the outputs.
Do students have to write code to meet HS-ETS1-4?
No. The standard says students use a computer simulation; it does not require programming.
Students can build a spreadsheet model, change the inputs of an existing simulation, or use a block-based or agent-based modeling environment such as NetLogo, which is free. Writing code can be an extension for students who want it.
What does "interactions within and between systems" mean in HS-ETS1-4?
It means the effects that one part of a problem has on other parts, inside one system and across systems.
In the reservoir example, storage and demand interact within the water system, while the river release links the water system to the river ecosystem, and recycled water links it to the energy system. A good simulation report shows what each solution does to all of them.
How do students know whether a simulation is right?
They check it: by working the first step by hand, comparing its output with measured data from a past period, and running sensitivity tests.
No model is exactly right. The goal is to know how far it can be trusted, which assumptions matter, and whether the choice of solution changes when those assumptions change.
What mistakes do students make with simulations?
Reporting only the system the solution targets, running a single scenario, and treating the output as proof.
Others include runs too short to show a slow trend, formulas that were never checked by hand, and changing several inputs at once so that nobody can tell which change caused the result.
How is HS-ETS1-4 different from HS-ETS1-3?
HS-ETS1-3 evaluates solutions against prioritized criteria and trade-offs; HS-ETS1-4 uses a computer simulation to predict what those solutions will do.
The two fit together: the simulation produces evidence, such as the lowest storage or the energy used, and the evaluation weighs that evidence with cost, safety and social impacts. HS-ETS1-1 and HS-ETS1-2 come earlier, defining and designing the solutions.
Which science course teaches HS-ETS1-4?
Any of them, since NGSS places engineering design inside the science courses.
Earth science classes often simulate water, climate or resources, biology classes populations and ecosystems, and physics classes energy systems. Simulations of human systems, such as traffic, also work well in any course.
Can HS-ETS1-4 be taught without a computer for every student?
Yes, with care: pairs can share one computer, or the teacher can run the simulation on a projector while groups choose the inputs.
Students still need to set up or change the model and interpret the outputs themselves. Working the first few steps by hand on paper is a good way to start before anyone touches a keyboard.
How is HS-ETS1-4 assessed?
Through tasks where students run or interpret a simulation of proposed solutions and report the effects on several systems, not through vocabulary recall.
State science tests aligned to NGSS handle engineering performance expectations in different ways, so check your state's test documents. In class, the homework rubric scores the model setup, the runs, the systems and constraints, and the limits of the model.
07
Related Standards
5 standards
These standards connect to HS-ETS1-4: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-ETS1-4Prerequisite
Develop a model to generate data for iterative testing and improvement of a design
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