Fixing Lake Vesipuro: Test a Restoration Plan on Paper

Investigation question: Which combination of cutting nutrient inflow, netting out plankton-eating fish and stocking predatory fish will bring a fictional murky lake back to clear water within four years, within budget, and keep it clear afterward?

Scientific purpose

Students read three years of simulated monitoring data from a fictional lake, state the food-web bet behind each possible fix, and then use a simple rule-based model to generate year-by-year predictions for two plans. They compare the output with the criteria and the budget, modify a plan, run it again, and commit to a decision with a written justification. The lab makes the engineering spread's test-measure-modify cycle something students do themselves, and it ties nutrient inflow (matter) to algae and predators (food-web effects) in one system.

Why this helps students with this chapter

The textbook tells the lake story as a finished success in two steps. Running the numbers themselves shows students that a plan can help without succeeding, that stopping an action can undo it, that a cheap plan and an expensive plan can both meet the criteria for different reasons, and that a simple model gives directions and rough sizes, not certainty. Having to spend a budget forces a real decision instead of 'do everything'.

Standards connections

MS-ETS1-4 (practice, using a model to generate data for iterative testing and modification of a proposed process): Students run a supplied rule-based lake model to produce four years of predicted data for each plan, compare the results with criteria and constraints, modify the plan and run it again. The model is given rather than developed by students, so the lab practices the PE rather than fully assessing it.

MS-LS2-4 (practice, arguing from evidence that a change to a biological component affects populations): The decision must be justified with model output and the baseline data, tracing how removing or adding fish populations changes zooplankton, algae and clarity; the evidence is simulated, so this is practice toward the PE.

MS-LS2-3 (supports, nutrient inflow as matter entering the system and driving producer growth): The nutrient rule in the model makes visible that the matter arriving in sewage and runoff becomes algae; this reinforces the matter-cycling model from Lab 1 without being the main target of the lab.

Roles (rotate each session)

• Modeler: Applies the five model rules in order for each year and reads the results aloud.
• Checker: Recomputes every row independently before it is accepted, and flags any step where the rules were applied out of order.
• Accountant: Tracks the cost of each plan year by year, checks every criterion and constraint, and fills the criteria table.
• Spokesperson: Drafts the group's justification from the recorded numbers and presents the decision to the class.

Materials

Estimated cost: 2 to 4 per class (an estimate; Printing only; calculators and colored pencils are classroom stock.)

Safety

• Paper and pencil only; no physical hazards. Keep the discussion about the fictional lake, not about any named local water body, unless you have checked the facts.

Teacher preparation and setup

1. Run the model yourself for the five plans in the answer key so you can spot arithmetic slips quickly; the most common error is applying the predator rule in the stocking year instead of the year after.
2. Print the recording sheet; the rule card is on it, but a large copy on the board helps every group apply the rules in the same order.
3. Decide whether to tell students before they start that the fictional lake is based on the textbook's Finnish lake story, or to let them discover the resemblance in the debrief.
4. Post the criteria and constraints where every group can see them: clarity at least 2.0 m in year 4, still at least 2.0 m in year 5 with no new spending, predatory fish for anglers by year 4, and a total cost of at most 9 units over years 1 to 4.

Investigation design

Student procedure

1. Session 1. Read the baseline dataset and answer q1 and q2: describe the lake's problem with numbers, and write the sign chain the food-web model is betting on (fewer roach → more zooplankton → fewer algae → clearer water).
2. Read the rule card together. Practice the rules on the 'no action' plan for one year: N stays 8, R stays 10, Z = 0, A = 8, clarity = 0.8 m. Every group should get these numbers before going on.
3. Choose two plans from the plan menu that fit the budget (at most 9 units over years 1 to 4). Write each plan's actions in the first column of run sheets A and B.
4. Run plan A for years 1 to 5, one year at a time, applying the rules in order: nutrients, roach, zooplankton, algae, clarity, then cost. The checker recomputes each row before the group moves on. Year 5 has no spending; it tests whether the result holds.
5. Run plan B the same way. Plot clarity against year for both plans on the graph in two colors, and draw the 2.0 m criterion line across the graph.
6. Fill the criteria table for plans A and B. Answer q3: which criteria did each plan meet or miss, and by how much?
7. Session 2. Modify one plan to fix its biggest miss. You may add, remove or move an action, as long as the total stays within budget. Write the modified plan C and your reason for the change (q4). Run plan C for years 1 to 5 and plot it in the third color.
8. Decide. Compare all three plans against every criterion and constraint. Choose one, and write the justification (q5): the numbers that show it meets the criteria, why you preferred it over the other plans, and one limitation of the model that could make the real lake behave differently.
9. Present your decision in under two minutes. Listen for groups that chose a different plan and record what they valued more (cost, speed, holding, anglers). Answer the analysis questions individually.

Expected observations

• No action: N 8, R 10, Z 0, A 8, clarity 0.8 m every year.
• Net in year 1 plus stock in year 1 (cost 5): clarity 2.2, 2.4, 2.6, 2.6 m in years 1 to 4 and 2.6 m in year 5; meets C1, C2, C3 and K1.
• Divert plus stock in year 1 (cost 9): clarity 1.2, 2.2, 2.8, 3.4 m, and 3.6 m in year 5; meets everything with the clearest water, using the whole budget.
• Divert only (cost 6): clarity 1.2, 1.6, 2.0, 2.4 m, then 2.4 m; meets C1 and C2 but fails C3. Stock only (cost 3): 0.8, 1.4, 1.6, 1.8 m, then 2.0 m; fails C1. Net every year (cost 8): 2.2 m for four years, then 1.8 m; fails C2 and C3.
• Groups that try all three actions in year 1 find the cost is 11 and must drop something, which is the intended budget squeeze.

Likely difficulties

• Applying the predator rule in the stocking year. The rule says 'starting the year after'; the checker role exists to catch this.
• Forgetting the cap of 10 on R after regrowth, which makes R = 12 and Z negative. Z can never be below 0.
• Decimals in A and clarity (4.5, 2.6). Allow one decimal place throughout; do not round A before computing clarity.
• Treating year 5 as another spending year. It is the 'does it hold' test and has no actions.
• Groups who want to 'do everything' and exceed the budget. The constraint is the point; make them choose.

Structured debrief

1. Collect every group's chosen plan on the board with its cost and year-4 clarity. Usually two camps appear: the cheap food-web plan (net plus stock, 5 units, 2.6 m) and the expensive combined plan (divert plus stock, 9 units, 3.4 m). Ask each camp what it valued, and point out that both are defensible when the criteria are met; engineering choices between working solutions are about trade-offs.
2. Ask who ran 'divert only'. It reaches 2.0 m in year 3 and meets both clarity criteria, but it fails the anglers criterion and does nothing about the roach. Then reveal the real history: in the Finnish lake the textbook describes, diverting the sewage in the mid-1970s did much of the work, and the fish steps came later and overlapped. The textbook's clean two-step story is the model's prediction, and the scientists themselves say the exact mechanism is still debated.
3. Walk through the 'net every year' relapse. The roach rule stands for a real fact: small plankton-eating fish breed fast, so removal without a predator is a treadmill. Ask what the equivalent would be in the kelp forest from the connection slide (removing urchins by hand without a predator to keep them down).
4. Close on the model's limits from q9: weather, nutrients stored in the mud, zooplankton being eaten by things other than roach, the phosphorus that leaves the lake inside netted fish. A model with five rules is a thinking tool, not a forecast. That is why the real team measured every year and was ready to modify.

Recording sheet: what students fill in

Lab 3 recording sheet: Fixing Lake Vesipuro

Lake Vesipuro is a fictional lake, and every number here is a teaching dataset built to behave the way the chapter's food-web model predicts. For decades a town piped sewage into the lake. The sewage carried nutrients that fed the algae, and the water turned green and murky. Fish died in late summer when decomposers breaking down dead algae used up the oxygen. Small plankton-eating fish called roach now swarm; big predatory fish are rare. Your team has four years and nine budget units to bring the lake back.

Criteria (what success means): C1, clarity at least 2.0 m in year 4. C2, clarity still at least 2.0 m in year 5 with no new spending. C3, predatory fish stocked by year 2, so anglers have fish by year 4. Constraints (limits): K1, total cost over years 1 to 4 at most 9 units. K2, each action can be taken at most once per year.

Analysis questions: answer key

Individual evidence of learning

Each student submits their own run sheets A, B and C, the clarity graph, the criteria table, and answers to q1 through q11. The run sheets and criteria table are evidence of using a model to generate data for iterative testing; q5 is the evidence-based argument; q9 and q10 show understanding of model limits and of the matter-versus-food-web routes to the same outcome.

Assessment criteria

Accessibility adaptations

• Provide run sheets with year 1 of each plan already computed, and a laminated copy of the rule card with the five steps numbered in large print.
• Allow a calculator app that shows the running expression, and accept a spoken justification for q5 recorded on a device.
• Pair a student who struggles with multistep arithmetic as the accountant (tracking cost and criteria) with a confident modeler, and swap roles for plan C.
• Offer the sign-chain sentence frame for q2 and q10: 'Fewer ___ means more ___, which means fewer ___, so ___.'

Low-cost alternative

No materials beyond printing are needed. If printing is limited, project the rule card and plan menu and have students draw the run sheets in their notebooks with eight columns.

Model limitations

Lake Vesipuro is fictional and every number is simulated; the five rules were written so that the plans behave the way the chapter's food-web model predicts, and they use whole-number indices rather than real population measurements. The real lake the textbook describes recovered through a messier history in which sewage diversion did much of the work and the fish steps overlapped, and the researchers themselves do not treat extra zooplankton grazing as the proven cause of the algae decline. The model leaves out weather, nutrients stored in the bottom mud (beyond the slow N decline), other predators of zooplankton, the phosphorus removed inside netted fish, and chance. Use it to practice test-measure-modify, not to predict any real lake.

Teacher notes

Reference runs (N, R, Z, A, clarity by year): net Y1 + stock Y1: Y1 8,3,7,4.5,2.2; Y2 8,2,8,4.0,2.4; Y3 8,1,9,3.5,2.6; Y4 8,1,9,3.5,2.6; Y5 same. Divert + stock Y1: Y1 7,10,0,7,1.2; Y2 6,7,3,4.5,2.2; Y3 5,6,4,3.0,2.8; Y4 4,5,5,1.5,3.4; Y5 4,4,6,1.0,3.6. Divert only: Y1 7,10,0,7,1.2; Y2 6,10,0,6,1.6; Y3 5,10,0,5,2.0; Y4 4,10,0,4,2.4; Y5 same. Stock only: Y1 8,10,0,8,0.8; Y2 8,7,3,6.5,1.4; Y3 8,6,4,6.0,1.6; Y4 8,5,5,5.5,1.8; Y5 8,4,6,5.0,2.0. Net every year: 8,3,7,4.5,2.2 for Y1-Y4; Y5 8,5,5,5.5,1.8. Divert + net Y1: Y1 7,3,7,3.5,2.6; Y2 6,5,5,3.5,2.6; Y3 5,7,3,3.5,2.6; Y4 4,9,1,3.5,2.6; Y5 4,10,0,4.0,2.4. Grade q5 on the match between the numbers and the verdicts, not on which plan was chosen.