HS-LS2-4: Using Math to Track Energy Flow and Matter Cycling in Ecosystems
In plain English: HS-LS2-4 is the NGSS high school performance expectation that asks students to use a mathematical representation, such as an energy pyramid or a carbon budget, to support claims about matter cycling and energy flow among organisms. Using percentages, students show that only part of the energy stored at one level reaches the next, while atoms are conserved. It is usually taught in Biology or Environmental Science.
Use a mathematical representation to support claims for the cycling of matter and flow of energy among organisms in an ecosystem.
Clarification Statement: Emphasis is on using a mathematical model of stored energy in biomass to describe the transfer of energy from one trophic level to another and that matter and energy are conserved as matter cycles and energy flows through ecosystems. Emphasis is on atoms and molecules such as carbon, oxygen, hydrogen and nitrogen being conserved as they move through an ecosystem.
Assessment Boundary: Assessment is limited to proportional reasoning to describe the cycling of matter and flow of energy.
Next Generation Science Standards · Disciplinary Core Idea: Ecosystems: Interactions, Energy, and Dynamics · Official standard
Students use numbers to back up two claims about ecosystems: energy flows through a food chain in one direction and a large share of it leaves each level as heat, while atoms of carbon, oxygen, hydrogen and nitrogen are conserved and cycle between organisms and the nonliving environment. The mathematical representations are energy pyramids, energy budgets for single organisms and carbon or nitrogen budgets that must add up. Every calculation is a ratio, a percentage or a proportion.
The NGSS Clarification Statement says: "Emphasis is on using a mathematical model of stored energy in biomass to describe the transfer of energy from one trophic level to another and that matter and energy are conserved as matter cycles and energy flows through ecosystems. Emphasis is on atoms and molecules such as carbon, oxygen, hydrogen and nitrogen being conserved as they move through an ecosystem." The Assessment Boundary says: "Assessment is limited to proportional reasoning to describe the cycling of matter and flow of energy." So this lesson uses only proportional reasoning: transfer efficiencies, percentages of a budget and scaling up or down by a ratio. All data sets are invented for teaching and labeled as invented. Students do the practice of using a mathematical representation to support a claim: they compute, check that a budget balances and write claims backed by the numbers.
Learning Objectives
By the end of this lesson, students will be able to:
Calculate the percentage of energy transferred from one trophic level to the next from stored-energy or biomass data
Use proportional reasoning to predict the energy available at a higher trophic level, or the producer energy needed to support it
Balance a carbon or nitrogen budget for an organism and use it to show that atoms are conserved
Explain with numbers why energy flows through an ecosystem and leaves as heat while matter cycles
Evaluate a claim about energy or matter in a food web by checking it against a mathematical representation
Prior Knowledge Required
Students should already be comfortable with:
Food chains, food webs and the roles of producers, consumers and decomposers MS-LS2-3
Photosynthesis and cellular respiration as processes that store and release energy MS-LS1-7
Project a photo of a grassy hillside with rabbits and one fox. Ask students to answer on a sticky note before any numbers appear:
Warm-Up Prompt
"This hillside feeds hundreds of rabbits but only a couple of foxes. Why? And when the fox dies, where do the carbon atoms in its body end up?"
Sort the notes into two piles on the board: ideas about energy and ideas about atoms. Many students say energy is "used up" or that matter "turns into energy". Keep both piles; students return to them in the Closure.
Direct Instruction15-20 minutes
Two accounts, one ecosystem. Producers capture light energy and store it as chemical energy in biomass. When a consumer eats, only part of that stored energy becomes new consumer tissue: much of it is released by cellular respiration to power the organism and leaves as heat, and some stays in waste and uneaten parts that decomposers use. Transfer efficiency is the ratio of the energy stored at one level to the energy stored at the level below it, written as a percentage. In many ecosystems it is roughly 10 percent, and measured values commonly fall between about 5 and 20 percent. Atoms follow a different account: every carbon, hydrogen, oxygen and nitrogen atom an organism takes in ends up in its tissue, in the carbon dioxide and water it releases, or in its waste, and decomposers return those atoms to the air and soil where producers take them up again. Use Diagram 1 for the energy account and Diagram 2 for the carbon account.
Energy pyramid (transfer efficiency)
In an invented grassland, producers store 20,000 kJ per m² per year, primary consumers store 1,600 kJ and secondary consumers store 120 kJ.
Result: 1,600 ÷ 20,000 = 0.08, so 8% passes to primary consumers. 120 ÷ 1,600 = 0.075, so 7.5% passes to secondary consumers. Only 120 ÷ 20,000 = 0.6% of the producer energy is stored in secondary consumers.
Energy budget of one organism
A caterpillar eats leaf tissue containing 250 J of chemical energy. 130 J leaves in its feces and 80 J is released by cellular respiration.
Result: Energy stored in new tissue = 250 - 130 - 80 = 40 J, which is 40 ÷ 250 = 16% of what it ate. Only those 40 J are available to a bird that eats the caterpillar.
Carbon budget (matter is conserved)
Over 10 days a young rabbit eats plants containing 480 g of carbon. It exhales 300 g of carbon as CO₂ and loses 156 g in droppings and urine.
Result: Carbon in new tissue = 480 - 300 - 156 = 24 g. Shares: 300 ÷ 480 = 62.5%, 156 ÷ 480 = 32.5%, 24 ÷ 480 = 5%. The parts add to 100%: no carbon atom is lost.
Nitrogen budget
A young beef steer eats 10 kg of dry grass a day. The grass is 2.5% nitrogen by mass, and the steer keeps 10% of that nitrogen in new tissue.
Result: Nitrogen eaten = 10,000 g × 0.025 = 250 g. Kept = 25 g. The other 225 g leaves in manure and urine, where decomposers release nitrogen compounds that grass roots take up again.
Scaling back down the food chain
Hawks here are third-level consumers (grass seeds, mice, snakes, hawks). How much producer energy is needed for 30 kJ to be stored in hawk tissue if each transfer is 10% efficient?
Result: Three transfers: 30 ÷ (0.1 × 0.1 × 0.1) = 30 ÷ 0.001 = 30,000 kJ of producer energy.
After each example ask: "Which number is the evidence, and what claim does it support?" Stress that the energy that is not passed on is not destroyed: it leaves the food chain, mostly as heat. The carbon that is not stored is not destroyed either: it is in the air as CO₂ or in waste that decomposers break down.
Guided Practice15 minutes
Pairs work through the invented data below from an ocean food chain. They compute each transfer efficiency and then answer a matter question about the same chain.
Guided practice data (invented): energy stored per year
Trophic level
Organism
Stored energy (kJ per m² per year)
Producers
Phytoplankton
15,000
Primary consumers
Zooplankton
1,800
Secondary consumers
Herring
162
Tertiary consumers
Seals
16.2
Compute the efficiency of each transfer. (Zooplankton 1,800 ÷ 15,000 = 12%, herring 162 ÷ 1,800 = 9%, seals 16.2 ÷ 162 = 10%.)
What percentage of the phytoplankton energy is stored in seals? (16.2 ÷ 15,000 = 0.108%, about one thousandth.)
Sketch the chain as an energy pyramid. Label each bar with its number and each step with its percentage.
A seal dies and sinks. Name the organisms that use its carbon and nitrogen next, and where those atoms go after that.
Write one claim about energy and one about matter, each citing a number from your work.
Independent Practice10-15 minutes
Each student analyzes a new invented data set from a pond, where producers store 8,000 kJ per m² per year, herbivorous insects store 720 kJ, dragonfly nymphs store 72 kJ and sunfish store 5.76 kJ.
Students find the three transfer efficiencies (9%, 10% and 8%) and the share of producer energy stored in sunfish (0.072%). They write a claim, evidence and reasoning paragraph answering: "Could this pond support a population of fish-eating herons that is as large, in stored energy, as the sunfish population? Why or why not?"
Closure5 minutes
Exit ticket: "A frog eats insects containing 60 kJ of stored energy and adds 6 kJ to its own tissue. What percentage was transferred, and where did the rest go? Were any carbon atoms destroyed?" (10%; the other 54 kJ was released as heat by respiration or left in waste; no atoms were destroyed.) Return to the warm-up piles and move each note into "energy flows" or "matter cycles".
Differentiation Strategies
For Struggling Students
Give a budget table with the rows already labeled (eaten, respired, waste, stored) so students only fill in numbers and check that they add up
Start with whole-number percentages (10%, 20%) before data that give decimals such as 7.5%
Provide a sentence frame: "The data show ___ kJ at one level and ___ kJ at the next, so ___% was passed on. The rest ___."
For Advanced Students
Ask students to compare two food chains of different lengths that start with the same producer energy and explain which can support more top-level biomass
Have students find the range of producer energy needed for a given top predator if each transfer could be anywhere from 5% to 20%
Ask students to design a mass budget experiment for a different decomposer, such as earthworms in leaf litter, and name the measurement that is hardest to make
Assessment Guidance
What to Look For
Check that students divide the higher level by the lower level when computing efficiency, not the other way around. Look for budgets that add up to the input, and for claims that cite a specific number. Listen for students who say energy is recycled by decomposers, that matter is turned into energy, or that the energy not passed on disappears. Correct answers say that the energy leaves as heat and that the atoms stay in the ecosystem.
02
Classroom Activities
3 Activities
1
Mealworm Matter Budget
25 min over two class days a week apartGroups of 3-4
Groups feed a known mass of wheat bran to a known mass of mealworms for one week, then measure how much bran was eaten, how much mass the mealworms gained and how much frass (droppings) they produced. The missing mass is the matter the mealworms released as carbon dioxide and water through cellular respiration.
Safety
Wear disposable gloves when handling mealworms, bran and frass, and wash hands with soap afterward, even with gloves.
Ask about allergies first: some people react to mealworms or their dust. Students with allergies take the recording and calculating role.
No eating or drinking at the lab tables, and never taste the bran.
Handle the mealworms gently. When the lab ends, keep them as a classroom culture or return them to the supplier; never release them outdoors.
Procedure
Day 1: mass the empty container, then 20 mealworms, then 10.00 g of wheat bran. Record every mass to 0.01 g.
Keep the container covered with a breathable lid at room temperature for 7 days.
Day 8: remove the mealworms and mass them. Sieve the remaining bran from the frass and mass each.
Compute bran eaten = starting bran - remaining bran, then the mass missing = bran eaten - mass gained - frass.
Sample Data (invented)
Mealworms 2.40 g on day 1 and 2.90 g on day 8. Bran 10.00 g on day 1 and 5.80 g on day 8. Frass 2.60 g. So the bran eaten is 4.20 g, the gain is 0.50 g (about 12% of the bran eaten), the frass is about 62% and the missing 1.10 g (about 26%) left as gases.
Discussion Questions
The largest share of the eaten bran left as frass. Which organisms will use the matter and energy in the frass next?
The missing 1.10 g was not destroyed. What molecules was it released as, and how could you test that with a carbon dioxide sensor?
The mealworm mass includes water but the bran is nearly dry. How does that affect the percentage you computed for growth?
Modification for Distance Learning
Students analyze the sample data in a spreadsheet, build a stacked bar like Diagram 2 and post a claim about conservation of matter with their numbers.
2
Beads and Chips: A Token Model of Matter and Energy
20 minGroups of 5
Each group runs a table-top model with five paper cups labeled Air and soil, Producer, Herbivore, Carnivore and Decomposers. Plastic beads stand for carbon atoms and stay in play. Paper chips stand for units of stored energy, and chips that are not passed on go into a Heat bin and never come back.
Rules
Energy: the Producer starts with 100 chips. When the Herbivore eats, it keeps 10 chips and the other 90 go to Heat. When the Carnivore eats, it keeps 1 of those 10 and 9 go to Heat.
Matter: start with 40 beads in Air and soil. Each round, the Producer takes 8 beads from Air and soil. Then the student at each living cup rolls a die for each bead: 1-2 the bead stays, 3-4 it goes back to Air and soil (respiration), 5 it moves up one level (eaten; a Carnivore bead stays), 6 it goes to Decomposers (waste or death). Decomposers send every bead back to Air and soil at the end of the round.
After the rolls in round 6, before the Decomposers return their beads, count the beads in every cup and the chips in Heat.
Sample Results (invented)
Energy: Heat holds 99 chips and the Carnivore holds 1. Matter after six rounds: Air and soil 17 beads, Producer 12, Herbivore 5, Carnivore 2, Decomposers 4.
Discussion Questions
The bead total is still 40 after six rounds. Which real-world principle does that model?
No chip ever leaves the Heat bin. Why is that a fair model of energy, and why would the model be wrong if chips went back to the Producer?
Name one way this model is unlike a real ecosystem, and suggest a rule change that would fix it.
Variation: Longer Food Chain
Add a fourth consumer cup. Groups predict how many of the 100 chips reach it before they play, then test the prediction.
3
Claim Check: Do the Numbers Support It?
20 minPairs
Pairs receive four claim cards. Each card has a claim and a small invented data set. Pairs use proportional reasoning to decide whether the data support the claim, then rewrite any unsupported claim so that it matches the numbers.
Claim Cards
Card A: "Lake producers store 12,000 kJ per m² per year, so the pike, which are third-level consumers, store about 1,200 kJ." Data: each transfer in this lake is about 10%.
Card B: "Decomposers recycle the energy in fallen leaves back to the trees." Data: fungi and bacteria break down leaf litter containing 400 g of carbon per m² each year, and a thermometer in a compost pile of the same litter reads warmer than the air.
Card C: "In a pasture, the carbon in 1,000 kg of eaten grass cannot all become sheep." Data: the grass eaten contains 450 kg of carbon, and the sheep that ate it gained body tissue containing 27 kg of carbon.
Card D: "Some carbon atoms in a wolf's breath were in the air a few months earlier." Data: the wolf eats deer, deer eat plants, and plants build sugars from carbon dioxide taken from the air during the growing season.
Discussion Questions
Which cards make claims the numbers do not support, and what calculation shows it?
For Card C, what percentage of the grass carbon became sheep tissue, and where did the rest of the carbon go?
Rewrite Card B so that it is accurate about both energy and matter.
Modification for Distance Learning
Post the cards on a shared slide deck. Pairs add a comment to each card with their verdict and the calculation that supports it.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Energy Stored at Three Trophic Levels
Invented data from the first worked example. Each arrow between levels shows the percentage of stored energy passed on: 8% and then 7.5%. The box areas are drawn to scale (area proportional to stored energy). The downward arrows show the energy that is not passed on, which leaves mostly as heat from respiration.
Diagram 2: A Carbon Budget That Adds Up
The young rabbit from the third worked example, drawn to scale. The three parts of the bar (300 g, 156 g and 24 g of carbon) add up to the 480 g the rabbit ate, which shows that the carbon atoms are conserved: they are exhaled, excreted or stored, never destroyed.
04
Homework Assignment
~30 min
HS-LS2-4 Homework: Energy and Matter by the Numbers
Directions: All data are invented for practice. Show every calculation with units, and end each problem with a one- or two-sentence claim that cites your numbers.
Part 1: Energy Flow (Problems 1-3)
In an invented desert, producers store 3,000 kJ per m² per year, herbivores store 270 kJ and lizards (secondary consumers) store 16.2 kJ. (a) Find the efficiency of each transfer. (b) What percentage of producer energy is stored in lizards? (c) Write a claim about why the desert supports far fewer lizards than plants.
Snakes here are secondary consumers (plants, then mice, then snakes). (a) How much producer energy is needed for 40 kJ to be stored in snake tissue if each transfer is 10% efficient? (b) How much if each transfer is only 5% efficient? (c) How many times as much producer energy does the 5% case need?
A grasshopper eats leaves containing 60 J of stored energy. It loses 24 J in its feces and releases 27 J by cellular respiration. (a) How much energy is stored in new grasshopper tissue? (b) What percentage of the energy it ate is that? (c) What percentage was released by respiration, and in what form does it leave the ecosystem?
Part 2: Matter Cycling (Problems 4-6)
In one day a deer eats plants containing 1,200 g of carbon. It stores 36 g of carbon in new tissue and exhales 780 g of carbon as CO₂. (a) How much carbon leaves in its feces and urine? (b) What percentage of the eaten carbon goes to each of the three destinations? (c) Show that the percentages add to 100% and explain what that shows about atoms.
Grass in an invented pasture takes up 18 g of nitrogen per m² per year. Sheep eat 40% of the grass and keep 10% of the nitrogen they eat in their bodies. (a) How much nitrogen do the sheep eat and keep? (b) How much leaves in their urine and dung? (c) The uneaten grass dies and decays. What total mass of nitrogen per m² returns to the soil through waste and decay, and what percentage of the uptake is that?
A student writes: "Energy and matter both cycle, because decomposers return them to the soil." In an invented forest, fallen leaves contain 400 g of carbon per m² each year. Decomposers release 380 g of it as CO₂ and 20 g stays in the soil as organic matter. (a) What percentage of the leaf carbon returns to the air? (b) Use the data and what happens to energy during respiration to write a response that corrects the student's claim.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Proportional Reasoning
Correct ratios, percentages and scaling with units for every problem
Correct method with one calculation or unit error
Budgets Balance
Every budget adds up to the input and the missing part is identified
Budget computed but not checked, or one part missing
Claim, Evidence, Reasoning
Claim cites specific numbers and explains that energy leaves as heat while atoms are conserved
Claim stated but evidence is general, or energy and matter are confused
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All data sets are invented. Energies are stored energy per year 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
In an invented marsh, producers store 40,000 kJ per m² per year and herbivores store 2,800 kJ. What is the transfer efficiency from producers to herbivores?
Answer: C
2,800 ÷ 40,000 = 0.07, so 7% of the stored energy is passed on. Choice A divides the lower level by the higher level (40,000 ÷ 2,800). Choices B and D misplace the decimal point when converting 0.07 to a percentage.
Question 2 of 20 · Multiple Choice
Producers in a meadow store 50,000 kJ per m² per year. If each transfer is 10% efficient, how much energy is stored in third-level (tertiary) consumers?
Answer: D
Tertiary consumers are three transfers above producers: 50,000 × 0.1 × 0.1 × 0.1 = 50 kJ. Choice A stops after one transfer (primary consumers) and choice B after two (secondary consumers). Choice C applies a fourth transfer.
Question 3 of 20 · Multiple Choice
In the energy pyramid of a forest, most of the energy stored at one level does not reach the next level. What happens to most of that energy?
Answer: A
Organisms use most of the energy in their food to stay alive, and cellular respiration releases it, ending as heat that leaves the ecosystem. Choice B is a frequent misconception: decomposers return matter, not energy, to producers. Choice C breaks conservation of energy, and choice D confuses energy with matter.
Question 4 of 20 · Multiple Choice
A rabbit exhales carbon dioxide. Where did the carbon atoms in that carbon dioxide come from most directly?
Answer: B
Cellular respiration breaks down food molecules such as sugars, and their carbon atoms leave as CO₂. Choice A is a common error: inhaled oxygen contains no carbon. Choice D confuses energy with matter: sunlight carries no atoms.
Question 5 of 20 · Multiple Choice
A mouse eats seeds containing 20 g of carbon. It stores 1 g of carbon in new tissue and exhales 14 g as CO₂. How much carbon leaves in its droppings and urine?
Answer: B
The carbon must balance: 20 - 1 - 14 = 5 g. Choice A forgets the carbon stored in new tissue (20 - 14). Choice C subtracts only the stored carbon, and choice D adds the numbers instead of balancing the budget.
Question 6 of 20 · Multiple Choice
Which statement best describes energy and matter in an ecosystem?
Answer: C
Atoms are reused again and again, while energy enters as light and leaves as heat, so it must be supplied continuously. Choice A is the error in many student models: energy does not return to producers. Choice B reverses the two, and choice D contradicts conservation of both matter and energy.
Question 7 of 20 · Multiple Choice
Why is an energy pyramid wider at the bottom than at the top?
Answer: B
Because each transfer passes on only a fraction (often about a tenth) of the stored energy, every level is smaller than the one below it. Choice A confuses body size with total energy. Choice C is wrong because producers are only at the bottom, and energy is transformed, not made.
Question 8 of 20 · Multiple Choice
In an invented lake, the transfer from herbivores to carnivores is 12% efficient and the carnivores store 90 kJ per m² per year. How much energy do the herbivores store?
Answer: C
Carnivores = 0.12 × herbivores, so herbivores = 90 ÷ 0.12 = 750 kJ. Choice A multiplies by 0.12 instead of dividing. Choice B assumes a 10% transfer instead of the 12% given. Choice D moves the decimal point one place.
Question 9 of 20 · Multiple Choice
Four students measured the carbon budget of a hamster over a week (grams of carbon). Which data set is consistent with conservation of matter?
Answer: A
Only in choice A do the three outputs add up to the input: 3 + 39 + 18 = 60 g. Choices B and C account for 63 g, more carbon than was eaten. Choice D accounts for only 51 g, as if 9 g of carbon had vanished.
Question 10 of 20 · Multiple Choice
An owl dies in a forest. How do the nitrogen atoms in its body return to producers?
Answer: B
Decomposers break down the proteins and release simple nitrogen compounds into the soil, and roots take these up. Choice A is wrong because plants cannot use nitrogen gas from the air through their leaves. Choice C breaks conservation of matter, and choice D skips the decomposers that make the nitrogen usable.
Question 11 of 20 · Multiple Choice
A wet year doubles the energy stored by producers in a grassland, and every transfer efficiency stays the same. What happens to the energy stored in the top predators?
Answer: A
Each level is a fixed fraction of the level below, so every level is proportional to the producer energy: doubling the base doubles the top. Choice C confuses the transfer efficiency with the change. Choice D would require the efficiencies themselves to change.
Question 12 of 20 · Multiple Choice
In an invented lake, algae store 9,000 kJ per m² per year. Chain 1: algae, zooplankton, trout. Chain 2: algae, snails, sunfish, bass. With 10% efficiency at every transfer, how does the energy stored in trout compare with the energy stored in bass?
Answer: D
Trout are two transfers up: 9,000 × 0.01 = 90 kJ. Bass are three transfers up: 9,000 × 0.001 = 9 kJ. 90 ÷ 9 = 10, so the trout store ten times as much. Choice B reverses the comparison. Choice A ignores the energy that leaves at each transfer.
Question 13 of 20 · Multiple Choice
A student claims: "A sealed glass jar holding a water plant and a snail can keep both alive forever in a dark closet, because the snail's waste feeds the plant and the plant feeds the snail." Which response is best supported by evidence?
Answer: B
Matter can cycle inside a sealed jar, but every organism in it releases energy by respiration, and that energy leaves as heat. Only light lets the plant store new chemical energy. Choice A confuses matter cycling with energy flow. Choice C is wrong because the atoms are conserved, and choice D is wrong because a plant cannot use heat to make sugar.
Question 14 of 20 · Multiple Choice
A caterpillar eats leaves containing 300 J of stored energy and adds 54 J to its own tissue. What percentage of the energy it ate could a bird get by eating it?
Answer: D
54 ÷ 300 = 0.18, so 18% is stored where a bird could get it. Choice A is the share that was not stored (100% - 18%). Choice B divides 300 by 54, and choice C misplaces the decimal point.
Question 15 of 20 · Short Answer
In an invented prairie, producers store 6,000 kJ per m² per year, primary consumers store 780 kJ and secondary consumers store 85.8 kJ. Find both transfer efficiencies and the percentage of producer energy stored in secondary consumers.
780 ÷ 6,000 = 13% and 85.8 ÷ 780 = 11%. The secondary consumers store 85.8 ÷ 6,000 = 1.43% of the producer energy. The rest left each level mostly as heat from respiration.
Question 16 of 20 · Short Answer
Over ten weeks a garden snail eats lettuce containing 2.0 g of carbon. Its body gains 0.10 g of carbon and it releases 1.3 g of carbon as CO₂. How much carbon is in its waste, and what percentage of the eaten carbon is that?
Carbon must balance: 2.0 - 0.10 - 1.3 = 0.60 g of carbon in waste, which is 0.60 ÷ 2.0 = 30%. The three parts (5%, 65%, 30%) add to 100%, so no carbon atoms are lost.
Question 17 of 20 · Short Answer
Explain, using an example with numbers you choose, why the energy stored in secondary consumers can never be larger than the energy stored in the primary consumers they eat.
A secondary consumer can only store energy it takes in from the primary consumers, and it releases most of that energy by respiration as heat. For example, if primary consumers store 1,000 kJ and a typical 10% is passed on, secondary consumers store about 100 kJ. Even at a high efficiency such as 20% they store only 200 kJ. An efficiency above 100% would mean energy was created, which is impossible.
Question 18 of 20 · Short Answer
A dairy calf eats hay containing 200 g of nitrogen. It keeps 20 g of that nitrogen in new tissue. How much nitrogen leaves in its manure and urine, what percentage is that, and what happens to it next?
200 - 20 = 180 g of nitrogen, which is 90% of what it ate. Decomposers in the soil break down the manure and urine and release nitrogen compounds that plant roots take up, so the nitrogen atoms cycle back into producers.
Question 19 of 20 · Short Answer
A student says: "When a fox uses the energy in its food, the heat is lost to the ecosystem, so the carbon in its food is lost too." Evaluate this claim.
The first half is right and the second half is wrong. The energy released by the fox's respiration leaves as heat and is not reused. The carbon atoms are conserved: they leave as CO₂ in the fox's breath, stay in its tissue or leave in its waste. Producers take the CO₂ back in by photosynthesis, and decomposers return the carbon in the waste and, later, in the fox's body.
Question 20 of 20 · Short Answer
In an invented pond, producers store 5,000 kJ per m² per year. The transfer to zooplankton is 11% efficient and the transfer from zooplankton to small fish is 9% efficient. How much energy is stored in each consumer level?
Zooplankton: 5,000 × 0.11 = 550 kJ. Small fish: 550 × 0.09 = 49.5 kJ, which is about 1% of the producer energy.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-LS2-4 mean?
HS-LS2-4 asks students to use a mathematical representation to support claims about how matter cycles and energy flows among the organisms in an ecosystem. In practice, students compute transfer percentages between trophic levels and check that carbon or nitrogen budgets add up. The code means High School, Life Science, core idea 2 (Ecosystems: Interactions, Energy, and Dynamics), performance expectation 4.
Is HS-LS2-4 taught in Biology or Environmental Science?
It is usually taught in the ecology unit of high school Biology, and it also fits Environmental Science or an integrated science course. The math is ratios and percentages, so it works for students in any high school math course.
What is the assessment boundary for HS-LS2-4?
Assessment is limited to proportional reasoning. Students compute ratios, percentages and scale factors, such as the share of energy passed from one level to the next. Exponential models, differential equations and detailed chemistry of nutrient cycles are beyond this standard.
Is the 10 percent rule exact?
No. It is a rough average for teaching. Measured transfer efficiencies vary with the organisms and the ecosystem, and values between about 5 and 20 percent are common. That is why this lesson gives students data and asks them to compute the efficiency rather than always assuming 10 percent.
Why does energy flow but matter cycle?
Because the two are accounted for differently. Atoms are conserved and can be reused by organism after organism, so matter cycles. Energy is also conserved, but each transfer releases part of it as heat, which organisms cannot use to build tissue, so the ecosystem needs a constant new supply of light energy.
Do decomposers get energy from dead organisms?
Yes. Decomposers are consumers of dead tissue and waste: they break it down by cellular respiration, keep a little energy in their own growth and release the rest as heat. What they return to producers is matter, such as carbon dioxide and nitrogen compounds, not energy.
What counts as a mathematical representation for HS-LS2-4?
Energy or biomass pyramids with numbers, tables of stored energy by trophic level, energy budgets for one organism, and carbon or nitrogen budgets shown as tables or to-scale bars. A good representation lets a reader check a claim, for example that the parts of a budget add up to the total.
How is HS-LS2-4 different from HS-LS2-3 and HS-LS2-5?
HS-LS2-3 asks for an explanation of matter and energy in aerobic and anaerobic conditions, and HS-LS2-5 asks for a model of the carbon cycle among the biosphere, atmosphere, hydrosphere and geosphere. HS-LS2-4 is the quantitative one: it uses numbers and proportions to support claims about energy and matter among organisms.
What mistakes do students make with energy pyramids?
Many students divide the wrong way (the lower level by the higher), think the missing energy was destroyed or recycled, or read the pyramid as a count of organisms. Asking "where did the rest go?" after every calculation and requiring budgets that add up catches these errors.
Is there a safe hands-on lab for HS-LS2-4?
Yes. A mealworm feeding lab uses only mealworms, wheat bran and a balance: students measure food eaten, growth and frass, and the missing mass shows matter released by respiration. Use gloves, wash hands, check for allergies and do not release the mealworms outdoors. A bead-and-chip token model works without live organisms.
07
Related Standards
6 standards
These standards connect to HS-LS2-4: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-LS2-3Prerequisite
Model the cycling of matter and flow of energy among living and nonliving parts
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