HS-ESS3-2NGSS*ScienceEarth and Space ScienceGrades 9-12
HS-ESS3-2: Evaluating Energy and Mineral Resource Designs with Cost-Benefit Ratios
In plain English: HS-ESS3-2 is the NGSS high school performance expectation that asks students to evaluate competing design solutions for developing, managing and using energy and mineral resources by comparing their cost-benefit ratios. Students weigh mining, drilling, recycling and soil practices, including environmental costs. It is usually taught in Earth and Space Science or Environmental Science.
Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.
Clarification Statement: Emphasis is on the conservation, recycling, and reuse of resources (such as minerals and metals) where possible, and on minimizing impacts where it is not. Examples include developing best practices for agricultural soil use, mining (for coal, tar sands, and oil shales), and pumping (for petroleum and natural gas). Science knowledge indicates what can happen in natural systems—not what should happen.
Next Generation Science Standards · Disciplinary Core Idea: Earth and Human Activity · Official standard
Students evaluate competing design solutions for developing, managing and using energy and mineral resources, and they base the evaluation on cost-benefit ratios. They compute the ratio (total benefits divided by total costs), decide which costs and benefits belong in it, and test how the ranking changes when environmental costs, recycling or a price change are included. The cases cover mining for coal, tar sands and oil shale, pumping petroleum and natural gas, recycling metals and managing farm soil. All numbers are invented for teaching and labeled as invented.
The NGSS Clarification Statement says: "Emphasis is on the conservation, recycling, and reuse of resources (such as minerals and metals) where possible, and on minimizing impacts where it is not. Examples include developing best practices for agricultural soil use, mining (for coal, tar sands, and oil shales), and pumping (for petroleum and natural gas)." It adds that science knowledge indicates what can happen in natural systems, not what should happen, so students separate the parts of an evaluation that science can predict (how much land a mine disturbs, how much energy a process uses) from the value choices people make. HS-ESS3-2 has no official Assessment Boundary.
Learning Objectives
By the end of this lesson, students will be able to:
Compute a benefit-cost ratio from a list of costs and benefits and interpret values above, at and below 1
Compare competing designs for developing, managing and using an energy or mineral resource, including recycling and reuse
Explain how adding environmental costs, recycling benefits or a price change can change which design ranks best
Evaluate mining, pumping and soil-management practices for ways to minimize impacts when a resource cannot be recycled
Distinguish what science can predict about a design from the value judgments involved in choosing it
Prior Knowledge Required
Students should already be comfortable with:
How Earth's mineral, energy and groundwater resources are unevenly distributed MS-ESS3-1
Evaluating competing design solutions against criteria and constraints MS-ETS1-2
Renewable and nonrenewable resources and where fossil fuels come from
Ratios, percents and multi-step arithmetic with money
Hold up an aluminum can and a steel can. Ask students to list everything it took to make each one, from the ground to the store.
Warm-Up Prompt
"A town can get the metal it needs by opening a new mine or by collecting and recycling old cans. List two costs and two benefits of each choice. Which of your costs are easy to put a price on, and which are hard?"
Sort the answers on the board into money costs (equipment, wages, fuel) and impact costs (land disturbed, water used, emissions). Tell students that the lesson uses one number, the benefit-cost ratio, to compare choices, and that deciding what goes into that number is part of the science and part of the judgment.
Direct Instruction15-20 minutes
The benefit-cost ratio. Add up all benefits over the life of a design and divide by all costs over the same period: B/C = total benefits ÷ total costs. A ratio above 1 means the benefits are larger than the costs, a ratio of 1 is break-even, and a ratio below 1 means the costs are larger. When two designs are compared, the ratio shows the return per dollar spent, but it does not show the size of the project, who pays the costs or how certain the estimates are. Diagram 2 shows where costs arise across a resource's life cycle, from developing a deposit to recycling or disposal. For an energy resource, a second ratio is useful: the energy returned on energy invested (EROI), the energy a source delivers divided by the energy spent to get it. The examples below use invented numbers.
Recycling metals (utilizing and conserving a mineral resource)
An invented city runs a can and scrap-metal recycling program. Collection and sorting cost $180,000 per year. Selling the metal earns $150,000 per year, and the city avoids $90,000 per year in landfill fees.
Result: B/C = (150,000 + 90,000) ÷ 180,000 = 240,000 ÷ 180,000 ≈ 1.33. Without the avoided landfill fees, B/C = 150,000 ÷ 180,000 ≈ 0.83, so leaving out one benefit reverses the decision.
Mining coal: surface mine or underground mine
Two invented designs would recover coal worth $900 million. The surface mine costs $500 million to run, $100 million to reclaim and $60 million for water treatment, and disturbs 1,200 ha. The underground mine costs $700 million to run, $20 million to repair subsidence and $30 million for water treatment, and disturbs 150 ha.
Result: Surface: 900 ÷ (500 + 100 + 60) = 900 ÷ 660 ≈ 1.36. Underground: 900 ÷ (700 + 20 + 30) = 900 ÷ 750 = 1.20. The surface mine has the higher ratio, but it disturbs 8 times as much land, a cost that is only partly counted in the reclamation budget.
Tar sands and oil shale: energy returned on energy invested
Illustrative values: a conventional oil well returns 18 units of energy for each unit invested, a tar sands operation returns 5, and an oil shale operation returns 2. Each must deliver 1,000 units of energy.
Result: Energy invested = 1,000 ÷ EROI: about 56 units for the well, 200 units for tar sands and 500 units for oil shale. Lower-ratio sources spend more energy, land and water to deliver the same energy.
Pumping natural gas: capturing gas that would be vented
At an invented gas well site, a vapor recovery unit costs $85,000 to buy and install. The gas it captures sells for $34,000 per year over its 5-year life, and it also cuts methane released to the air.
Result: Benefits = 34,000 × 5 = $170,000, so B/C = 170,000 ÷ 85,000 = 2.0 before any value is placed on the reduced methane, which would raise the ratio further.
Best practices for agricultural soil use
An invented farm compares a cover crop with bare winter fields. The cover crop costs $60/ha per year. It saves $25/ha in fuel and labor and $20/ha in fertilizer, adds $10/ha in yield, and keeps 8 t/ha of soil in place, which the farm values at $5/t.
Result: With the soil counted: (25 + 20 + 10 + 8 × 5) ÷ 60 = 95 ÷ 60 ≈ 1.58. Without it: 55 ÷ 60 ≈ 0.92. The practice pays only when the lost soil is counted as a cost of bare fields.
After each example, ask: "Which costs and benefits were counted, which were left out, and who would pay the costs that were left out?" Then ask which part of the evaluation is a scientific prediction (how much soil erodes, how much energy is spent) and which part is a value choice (how much a ton of soil or a hectare of habitat is worth). Science knowledge tells us what can happen; people decide what should happen.
Guided Practice15 minutes
Pairs evaluate three invented designs for supplying copper to a region over the next 20 years. The region needs about 450 thousand metric tons (kt) of copper. Benefits are the value of the copper; costs include operation and environmental management (tailings storage and water treatment).
Compute the benefit-cost ratio for each design (A ≈ 1.33, B = 1.20, C ≈ 1.55). Compare with Diagram 1.
Which design has the highest ratio? Can it supply the copper the region needs by itself?
Find a combination of designs that meets the 450 kt need, and compute its combined ratio (total benefits ÷ total costs).
Write a recommendation that names the ratio, the land disturbed and one cost that is not in the table.
Independent Practice10-15 minutes
Each student evaluates two invented designs for pumping petroleum from a small oil field that holds about 2.0 million barrels. At an assumed price of $70 per barrel, the oil is worth $140 million under either design.
Two ways to develop one oil field (invented data, $ million)
Cost item
Design 1: 12 vertical wells on 12 pads
Design 2: 12 directional wells from 1 pad
Drilling
60
78
Operation
30
28
Land and habitat restoration
12
1
Spill prevention and cleanup reserve
8
4
Students compute both ratios, compare the land each design disturbs, and write a short evaluation. They then state which design they would choose if the ratios were nearly equal, and which part of that choice is science and which is a value judgment.
Closure5 minutes
Exit ticket: "A plan has a benefit-cost ratio below 1 when only money is counted and above 1 when avoided health costs are included. What would you need to know before deciding? Name one question science can answer about the plan and one question it cannot."
Differentiation Strategies
For Struggling Students
Give a two-column organizer (benefits, costs) with a total row and the division already set up, so students focus on what belongs in each column
Use whole-number costs in the first example and add environmental costs one at a time
Provide a sentence frame: "Design ___ has a ratio of ___, which means ___. But it also ___, so I recommend ___."
For Advanced Students
Ask students to vary one uncertain cost (such as reclamation) over a range and find the value at which the ranking of two designs flips
Have students compute the net benefit (benefits minus costs) alongside the ratio and explain when the two measures point to different designs
Ask students to research how a real reclamation bond or recycling deposit law works and describe how it changes a company's cost-benefit ratio
Assessment Guidance
What to Look For
Check that students divide total benefits by total costs over the same period, and that they read a ratio below 1 as costs larger than benefits. Look for evaluations that compare at least two designs, name costs left out of the ratio (land, water, emissions, risk) and consider recycling or reuse where the resource allows it. Strong answers separate what science predicts from what people value. Watch for students who pick the highest ratio without checking whether the design meets the need.
02
Classroom Activities
3 Activities
1
Cookie Mining: Develop, Extract and Reclaim
25 minIndividuals, then groups of 4
Each student "buys" a cookie as a mining claim, chooses mining tools, extracts chocolate chips (the ore) and then reclaims the land by fitting the cookie back into its traced outline. Everyone computes a benefit-cost ratio, and groups compare the two tool designs.
Procedure and Prices
Before class, check students' food allergies and use an allergy-safe substitute (for example, raisin-studded modeling dough) if needed. Cookies used in the activity are lab materials: nobody eats them.
Place the cookie on grid paper and trace its outline. Costs: claim (cookie) $3, flat toothpick $2 or paper clip $4, mining time $1 per minute (5 minutes maximum).
Mine chips without using fingers to hold the cookie. Each whole chip sells for $2.
Reclaim: push the crumbs back inside the outline. Every grid square outside the outline that still has crumbs costs $1.
Safety: point toothpicks and paper clips away from yourself and others, wipe crumbs off desks when done, and wash hands before and after.
Sample Results (invented)
Miner
Tool
Chips
Time (min)
Squares outside
Student 1
Toothpick
14
5
6
Student 2
Paper clip
18
5
15
Discussion Questions
In the sample results, the paper-clip miner extracted more chips but ended with the lower benefit-cost ratio. Which cost made the difference?
How is the $1-per-square reclamation charge like a real reclamation requirement for a surface coal mine?
Which real mining costs does this model leave out (for example, water pollution or lost habitat)?
Modification for Distance Learning
Students use the sample results above, compute both ratios, and then design a third tool with a price and predicted results that would beat both.
2
Recycle or Mine? Can Sorting and School Program Designs
20 minGroups of 3-4
Groups sort a bag of clean cans with a magnet (steel cans stick, aluminum cans do not), weigh each metal, and then evaluate two competing designs for a school recycling program.
Procedure
Use only rinsed cans with no sharp or torn edges. Wear work gloves while handling them. Do not include glass, batteries or aerosol cans.
Test each can with the magnet, sort into steel and aluminum, and weigh each pile.
Use the design data below to compute a benefit-cost ratio for each program design.
Design Data (invented, one school year)
Item
Design A: single mixed bin
Design B: separate metal bins, sorted by students
Bins
$400
$700
Hauling
$1,200
$1,000
Training
$0
$300
Sale of metal
$600
$1,500
Avoided trash fees
$900
$900
Discussion Questions
In this data set, only one design has a benefit-cost ratio above 1. Why does sorting raise the value of the metal?
Design B costs more to set up. Which benefits make up for it?
Recycled aluminum replaces metal that would otherwise be mined and smelted. What mining and energy costs does that avoid, and how could you add them to the ratio?
Modification for Distance Learning
Students sort the cans in their own recycling bin at home with a refrigerator magnet, report the counts, and complete the design comparison from the table.
3
Design Review Panel: Fuel for a Regional Power Plant
20 minGroups of 4
Each group acts as a review panel for three competing proposals to meet a region's electricity needs for 20 years. The panel computes each ratio twice, once with direct costs only and once with estimated environmental and health costs, and then writes a recommendation.
Proposals (invented, $ million over 20 years)
Proposal
Benefits
Direct costs
Estimated environmental and health costs
1. Natural gas from nearby wells, with a leak detection program
520
340
90
2. Coal from a surface mine 80 km away, with reclamation
520
300
200
3. Efficiency upgrades that cut the region's demand by 30%
160
80
0
Discussion Questions
Of the two fuel proposals, coal has the higher ratio when only direct costs count, but the lower ratio when environmental and health costs are added. Which ratio should the panel report, and why?
Proposal 3 has the highest ratio in both columns. Why can't it be the whole plan?
The environmental estimates are uncertain. How would the panel's recommendation change if the coal estimate were half as large?
Challenge Variation
Panels design a combined plan (for example, efficiency plus one fuel) and compute its overall ratio with all costs counted.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Benefit-Cost Ratios of Three Copper Supply Designs
The guided-practice designs, drawn to scale. Bars show benefits ÷ costs for each design; the dashed line marks break-even (B/C = 1). The recycling design has the highest ratio and the smallest footprint but supplies the least copper, so a ratio alone does not settle the choice.
Diagram 2: Where Costs Arise in a Resource Life Cycle
A mineral or energy resource is developed, processed, used and then recycled, reused or discarded. Each stage has costs to count in a benefit-cost ratio. Recycling (green loop) returns metal to processing and skips the costs of developing a new deposit.
04
Homework Assignment
~30 min
HS-ESS3-2 Homework: Evaluating Resource Designs
Directions: All numbers are invented for practice. Show every sum and ratio. Round ratios to two decimal places. For each evaluation, name at least one cost or benefit that the numbers leave out.
Part 1: Mineral Resources (Problems 1-2)
A county e-waste program collects old phones and computers. Collection costs $210,000 per year and processing costs $140,000 per year. The recovered gold, copper and other metals sell for $290,000 per year, and the county avoids $120,000 per year in hazardous-waste disposal. (a) Compute the benefit-cost ratio. (b) Metal prices fall 20%. Compute the new ratio. (c) Should the program continue? Explain, naming one benefit not in the numbers.
A metal mine must store its tailings (crushed waste rock and water). Design W, a wet tailings dam, costs $40 million to build and $5 million to monitor, and has a 2% chance of failing over the mine's life, with damage estimated at $600 million. Design D, dry-stacked filtered tailings, costs $65 million to build and $3 million to monitor, with a 0.2% chance of failure and the same damage estimate. Both designs let the mine earn benefits of $120 million. (a) Find each design's expected failure cost (chance × damage). (b) Compute each ratio, counting the expected failure cost as a cost. (c) Evaluate the two designs, and explain why a panel might choose the one with the lower ratio.
Part 2: Energy Resources (Problems 3-4)
An oil shale project has an energy return on energy invested (EROI) of 3, and a conventional oil field has an EROI of 15. Each must deliver 900 units of net energy (energy out minus energy in). (a) Find the energy invested and the total energy produced for each. (b) Explain why the oil shale project needs more land, water and equipment for the same net energy.
A company runs 40 natural gas well sites. A leak detection and repair program costs $12,000 per site per year. At each site it saves gas worth $9,000 per year and prevents methane emissions that a state program values at $6,000 per year. (a) Compute the ratio counting only the saved gas. (b) Compute the ratio counting the methane value too. (c) Explain how the choice of what to count changes the decision, and which part of that choice is science and which is a value.
Part 3: Managing and Using Resources (Problems 5-6)
A farm on a steep slope compares two soil practices. Terraces cost $1,800/ha to build and last 20 years, and they cut soil loss from 30 to 3 t/ha per year. Contour grass strips cost $25/ha per year and cut soil loss from 30 to 12 t/ha per year. Value saved soil at $4/t. (a) Find the yearly cost per hectare of the terraces. (b) Compute each practice's benefit-cost ratio. (c) Which practice would you recommend, and when might the other be better?
A closed surface coal mine can be (a) left as it is, (b) reclaimed with topsoil and native plants for $8 million, which brings benefits of $10 million in cleaner water, grazing and land value, or (c) reclaimed and then covered by a solar farm, which costs another $30 million and sells $42 million of electricity over 20 years. Compute the ratio for (b), for the solar farm alone, and for (b) and (c) together. Then write a recommendation that names the ratio, one impact that is hard to price, and one value judgment.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Ratios
Totals and ratios correct, with costs and benefits over the same period
Correct method with one arithmetic error
Comparison
Compares designs using the ratio and at least one factor it leaves out (land, risk, supply)
Compares ratios only
Science and Values
Separates what science predicts from the value choices in the decision
Mentions values but does not separate them from predictions
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All numbers in these questions are invented for practice. Round ratios to two decimal places unless a question says otherwise. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
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
An invented mine expansion would bring benefits of $3.6 million and costs of $2.4 million. What is its benefit-cost ratio?
Answer: C
B/C = 3.6 ÷ 2.4 = 1.5, so each dollar of cost returns $1.50 of benefit. Choice A divides costs by benefits. Choice B is the difference, 3.6 - 2.4 = 1.2, not a ratio. Choice D adds the two numbers.
Question 2 of 20 · Multiple Choice
An invented pipeline repair plan has benefits of $1.4 million and costs of $2.0 million. Which statement is correct?
Answer: B
1.4 ÷ 2.0 = 0.7, which is below 1, so the costs are larger. Choice A divides the costs by the benefits. Choice C subtracts (2.0 - 1.4 = 0.6), and break-even would be a ratio of 1. Choice D adds the numbers.
Question 3 of 20 · Multiple Choice
An invented foundry can make 2,000 t of steel from recycled scrap at a cost of $340 per ton, or from iron ore at $470 per ton. How much does recycling save on this order?
Answer: D
The saving is (470 - 340) × 2,000 = 130 × 2,000 = $260,000. Choice A is the saving per ton only. Choice B is the full cost of the recycled steel (340 × 2,000), and choice C is the full cost of the ore-based steel (470 × 2,000).
Question 4 of 20 · Multiple Choice
An invented tar sands operation delivers 4 units of energy for every 1 unit invested (EROI = 4). How much net energy (out minus in) does it provide when it produces 400 units?
Answer: A
Energy invested = 400 ÷ 4 = 100 units, so net energy = 400 - 100 = 300 units. Choice B is the energy invested, not the net. Choice C multiplies instead of dividing. Choice D subtracts the ratio itself as if it were an energy amount.
Question 5 of 20 · Multiple Choice
An invented farm's cover-crop plan costs $50/ha. It saves $35/ha in fuel and fertilizer and keeps soil in place that the farm values at $30/ha. What is the benefit-cost ratio when the soil is counted?
Answer: B
Benefits = 35 + 30 = $65/ha, so B/C = 65 ÷ 50 = 1.3. Choice A leaves the soil out (35 ÷ 50 = 0.7). Choice C divides the costs by the benefits (50 ÷ 65). Choice D is the net benefit in dollars per hectare (65 - 50 = 15), not a ratio.
Question 6 of 20 · Multiple Choice
Two invented mine designs each have a benefit-cost ratio of 1.4. Design X disturbs 400 ha of forest and Design Y disturbs 40 ha. The land cost is not in either ratio. Which evaluation fits the emphasis on minimizing impacts?
Answer: C
With equal ratios, the uncounted impact decides: Design Y disturbs 40 ÷ 400 = one tenth of the land. Choice B ignores a cost the ratio leaves out. Choice A confuses size with value. Choice D invents a cutoff: any ratio above 1 means benefits exceed costs.
Question 7 of 20 · Multiple Choice
A town is evaluating a proposed gravel mine near a river. Which question can science answer?
Answer: A
The change in the water table can be predicted from measurements of the aquifer and the pumping rate, so it is a science question. Choices B and C ask what should happen, which depends on values. Choice D is a political question.
Question 8 of 20 · Multiple Choice
At an invented oil well, gas that is burned off could instead be captured. The equipment costs $250,000, and the captured gas sells for $60,000 per year for 5 years. What is the benefit-cost ratio?
Answer: C
Benefits = 60,000 × 5 = $300,000, so B/C = 300,000 ÷ 250,000 = 1.2. Choice A uses one year of benefits (60,000 ÷ 250,000). Choice D divides costs by benefits (250,000 ÷ 300,000). Choice B divides the cost by one year of benefits, which gives the payback time in years.
Question 9 of 20 · Multiple Choice
An invented surface coal mine has benefits of $500 million and operating costs of $380 million. A reclamation requirement adds $70 million in costs. What is the ratio with reclamation included?
Answer: B
Total costs = 380 + 70 = $450 million, so B/C = 500 ÷ 450 ≈ 1.11. The mine still has benefits larger than costs, but by a smaller margin. Choice A leaves out reclamation (500 ÷ 380). Choice C divides costs by benefits. Choice D subtracts the reclamation cost from the operating costs instead of adding it (500 ÷ 310 ≈ 1.61).
Question 10 of 20 · Multiple Choice
An invented school replaces its lights with LEDs for $12,000. The new lights save $4,000 per year in electricity for 6 years. What is the benefit-cost ratio over those 6 years?
Answer: D
Benefits = 4,000 × 6 = $24,000, so B/C = 24,000 ÷ 12,000 = 2.0. Choice A uses one year only (4,000 ÷ 12,000). Choice B divides the cost by one year of savings, which gives the payback time in years, not a ratio. Choice C divides costs by benefits.
Question 11 of 20 · Multiple Choice
An invented copper project has benefits of $50 million and costs of $40 million. If the copper price falls so that the benefits drop by 20%, what happens to the ratio?
Answer: A
The original ratio is 50 ÷ 40 = 1.25. A 20% drop leaves 50 × 0.8 = $40 million of benefits, and 40 ÷ 40 = 1.0. Choice C divides the costs by the original benefits (40 ÷ 50 = 0.8). Choice B ignores the price change.
Question 12 of 20 · Multiple Choice
An invented tailings dam has a 1% chance of failing during the mine's life, and a failure would cause about $450 million in damage. What expected failure cost should an evaluation include?
Answer: C
Expected cost = chance × damage = 0.01 × 450 = $4.5 million. Choice A counts the full damage as certain. Choices B and D misplace the decimal point (10% and 0.1%).
Question 13 of 20 · Multiple Choice
A benefit-cost ratio for a new tar sands mine counts digging, heating and shipping costs only. Which cost does the emphasis on minimizing impacts most clearly call for adding?
Answer: B
Land reclamation and tailings water treatment deal with impacts on natural systems that the mine itself creates, so they belong in an evaluation that aims to minimize impacts. The other choices are ordinary business costs unrelated to the resource's effect on land or water.
Question 14 of 20 · Multiple Choice
Four invented designs for developing a mineral deposit have these benefits and costs ($ million). Which has the highest benefit-cost ratio?
Answer: D
The ratios are 1.2, 1.125, 1.2 and 1.5, so the design with benefits of 90 and costs of 60 returns the most per dollar. Choice C has the largest benefits and the largest net benefit (50), but its ratio is lower: size and ratio are different measures.
Question 15 of 20 · Short Answer
An invented school district's aluminum recycling program costs $18,000 per year. It earns $11,000 from selling cans and avoids $4,500 in landfill fees. (a) Compute the benefit-cost ratio. (b) The district also counts the energy saved by not making new aluminum from ore, valued at $5,000 per year. Compute the new ratio and state whether the program should continue.
(a) B/C = (11,000 + 4,500) ÷ 18,000 = 15,500 ÷ 18,000 ≈ 0.86, so the costs are larger. (b) With the energy value, B/C = 20,500 ÷ 18,000 ≈ 1.14, above 1. Making aluminum from recycled cans takes far less energy than smelting it from bauxite ore, so counting that benefit is reasonable, and the program is worth continuing if the district accepts the energy estimate.
Question 16 of 20 · Short Answer
An invented oil shale operation has an EROI of 2.5. (a) If 1,000 units of energy are invested, how much energy is produced, and what is the net energy? (b) How much energy would a conventional field with an EROI of 12 need to invest to deliver the same net energy?
(a) Energy produced = 2.5 × 1,000 = 2,500 units, so net energy = 2,500 - 1,000 = 1,500 units. (b) For EROI 12, net = 12x - x = 11x, so 11x = 1,500 and x ≈ 136 units. The conventional field needs about one seventh of the energy input for the same net energy, which is why oil shale is costly in energy, water and land.
Question 17 of 20 · Short Answer
Two invented designs could mine the same ore body. An open pit recovers ore worth $800 million for $560 million in costs and disturbs 700 ha. An underground mine recovers ore worth $600 million for $450 million and disturbs 50 ha. (a) Compute both ratios. (b) Land restoration would add $120 million for the pit and $10 million for the underground mine. Compute the new ratios. (c) Which design do you recommend?
(a) Pit: 800 ÷ 560 ≈ 1.43; underground: 600 ÷ 450 ≈ 1.33. (b) Pit: 800 ÷ 680 ≈ 1.18; underground: 600 ÷ 460 ≈ 1.30. (c) Once land restoration is counted, the underground mine has the higher ratio and disturbs far less land, so it is the stronger choice. The pit still recovers more ore, which matters if supply is the main need.
Question 18 of 20 · Short Answer
An invented farm is deciding whether to switch to no-till planting. The switch costs $40/ha per year (mostly a new planter). It saves $18/ha in fuel and $10/ha in labor, and the soil it keeps in place is valued at $24/ha. (a) Compute the ratio. (b) In the first few years, yields drop by an amount worth $15/ha. Compute the ratio for those years. Explain what the farm should consider.
(a) B/C = (18 + 10 + 24) ÷ 40 = 52 ÷ 40 = 1.3. (b) With the yield loss counted as a cost, B/C = 52 ÷ 55 ≈ 0.95. (Subtracting the loss from the benefits gives 37 ÷ 40 ≈ 0.93; either way the ratio is below 1.) The farm should consider how long the yield dip lasts, since the soil benefits build up over many years, and whether it values soil loss at $24/ha.
Question 19 of 20 · Short Answer
An invented pipeline company can install leak sensors for $2.4 million. Without them, it estimates a 5% chance each year of a spill costing $20 million. Over 10 years, what is the expected avoided spill cost, and what is the benefit-cost ratio if the sensors prevent all such spills? Name one source of uncertainty.
Expected avoided cost = 0.05 × 20 × 10 = $10 million, so B/C = 10 ÷ 2.4 ≈ 4.2. The ratio is high, but it depends on the 5% estimate, the damage estimate and the claim that the sensors stop every spill. If the sensors stop only half of the spills, the ratio falls to about 2.1, still above 1.
Question 20 of 20 · Short Answer
A regional council must choose between expanding a natural gas field and funding energy efficiency. Write a short evaluation that uses the phrase "benefit-cost ratio", and label one sentence as a scientific prediction and one as a value judgment.
A strong answer compares both options with a benefit-cost ratio and names what each ratio includes (for example, leak costs for the gas field, and the share of demand efficiency can meet). Scientific prediction: "Expanding the field will add about 20 new well pads and increase methane leakage unless leaks are repaired." Value judgment: "The council should give more weight to lower emissions than to the lower price of gas." Full credit separates the two clearly.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-ESS3-2 mean?
HS-ESS3-2 asks students to compare competing ways of developing, managing and using energy and mineral resources, and to judge them by their cost-benefit ratios. Students compute ratios, decide which costs and benefits belong in them, and explain their choice. The code means High School, Earth and Space Science, core idea 3 (Earth and Human Activity), performance expectation 2.
What is a cost-benefit ratio in HS-ESS3-2?
It is a single number that compares what a design delivers with what it costs: total benefits divided by total costs, over the same period. Some sources write the same idea as a benefit-cost ratio. The important work is deciding what to count: money, energy, land, water, emissions and risk can all be part of it.
Is HS-ESS3-2 taught in Earth science or environmental science?
It is usually taught in Earth and Space Science, and it fits naturally in Environmental Science. It also pairs well with an engineering unit, because evaluating competing designs is an engineering practice.
Does HS-ESS3-2 have an assessment boundary?
No. HS-ESS3-2 has no official Assessment Boundary. The Clarification Statement sets the emphasis instead: conservation, recycling and reuse of resources where possible, and minimizing impacts where not, with examples from soil use, mining and pumping.
What does "science indicates what can happen, not what should happen" mean here?
Science can predict the results of a design: how much land a mine disturbs, how much energy a process uses, how much soil a practice saves. Choosing among designs also depends on what people value, such as jobs, habitat or low prices. Students should keep the two apart in their evaluations.
How do you put a dollar value on environmental costs?
Common approaches use the cost of repairing the damage (reclamation, water treatment), the cost of preventing it, or an estimate of lost services such as clean water. These estimates are uncertain, so students should test how the ratio changes over a range of values. Impacts that cannot be priced can be listed beside the ratio.
What are tar sands and oil shale?
Tar sands (also called oil sands) are sand and clay mixed with bitumen, a very thick form of petroleum that must be mined or heated underground before it flows. Oil shale is rock that contains kerogen, an organic material that yields oil only when the rock is heated strongly. Both take more energy and water to produce than oil pumped from a conventional well.
Is the cookie mining activity safe for a science class?
Yes, with a few steps. Check food allergies first and use an allergy-safe substitute if needed, treat the cookies as lab materials that nobody eats, have students point toothpicks and paper clips away from people, and have everyone wash their hands before and after. Wipe desks clean at the end.
How does HS-ESS3-2 connect to engineering standards?
It uses the same practice as HS-ETS1-3, which asks students to evaluate a solution using prioritized criteria and trade-offs. HS-ESS3-2 adds the Earth science: the costs and benefits come from how resources form, how they are extracted and what extraction does to land, water and air.
What comes after HS-ESS3-2?
HS-ESS3-4 asks students to evaluate or refine a technology that reduces human impacts on natural systems, and HS-ESS3-3 asks them to build a computational simulation of resource management, human sustainability and biodiversity. Both use the idea that every design has costs and benefits that can be measured and compared.
07
Related Standards
6 standards
These standards connect to HS-ESS3-2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-ESS3-1Prerequisite
Explain how uneven distributions of Earth's resources result from geologic processes
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