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Classroom activity Grade 11 Science

Vellacott Lake's Mussels: Modeling How Fast a Lake Clears

A grade 11 activity where teams calculate the clearance time of a fictional lake invaded by filter-feeding mussels, then evaluate three management responses.

Objectives

  1. Students will model how fast a filter-feeding population can process the volume of a lake.
  2. Students will explain why clearer water does not mean less phosphorus in a lake.
  3. Students will evaluate three management responses against stated criteria and defend one.

Vocabulary

Key words: filter feeder, clearance time, population density, benthic, nutrient shunt, veliger

Teacher overview

A single small mussel filters only about 40 milliliters of water an hour, yet the population on a lake's hard bottom can process the whole lake in under a week. In this activity, teams of three build that model from a fictional lake's dimensions and mussel counts, then meet as a board to evaluate three responses. The activity pairs the clearance calculation with the phosphorus result, which shows that clearer water is not the same as cleaner water, since the nutrient did not leave the lake but moved from the open water to the bottom. The sequence follows the work a utility biologist does when a new population appears near an intake.

Activity Directions

  1. Before class. Print one handout per student and one set of three management option cards per team. Every place and figure in this activity is fictional. Arrange desks in groups of three.
  2. Framing (7 min). Define filter feeder, clearance time, and benthic. Explain that the mussels in this scenario attach to hard surfaces, that they arrive as microscopic larvae called veligers carried in bilge and live wells, and that they colonize the inside of raw water intake pipes as readily as they colonize rock. State the guiding question at the top of the handout.
  3. Modeling round (20 min). Teams complete items 1 through 8 of the handout. Circulate and check two things at each table: that units are written on every line, and that the two clearance times in items 6 and 7 are compared rather than just calculated.
  4. Checkpoint (4 min). Ask every team to hold up their answer to item 6 on chart paper. Any team more than a factor of two away from the class median has a unit error; send them back to the line where liters per hour became liters per day before continuing.
  5. Mechanism discussion (6 min). Have teams answer items 9 and 10, which ask why the lake got clearer without losing phosphorus. Take two answers aloud before moving on.
  6. Board round (14 min). Deal the three management option cards to each team. Teams rank the options against three stated criteria: effect on the lake, effect on the intake, and whether the action prevents spread to other lakes. Each team writes its ranking and one sentence of justification per option on chart paper, then answers item 11.
  7. Debrief (4 min). Ask two questions. First, which of your calculated values changed a team's ranking, and how? Second, the population in this scenario grew from the earlier survey to the current one; what would you need to measure to know whether it has stopped growing?

Management option cards. Card A: chlorinate the raw water intake line continuously to keep the pipe clear. Card B: fund a boat inspection and wash station at every public ramp on the fictional lake. Card C: take no action and accept the clearer water, adjusting the treatment plant as needed.

Vellacott Lake's Mussels: Modeling How Fast a Lake Clears — Grade 11 Science
Name: ____________________________ Date: ______________

Student Handout

Guiding question: How fast can a mussel population filter a whole lake, and does clearer water mean a cleaner lake?

Vellacott Lake and its water utility are fictional, and every figure below is invented for this activity. Show units on every line of work.

Use these values for items 1 through 8.

  • Lake surface area: 2,000,000 square meters
  • Mean depth: 5.0 meters
  • Hard bottom suitable for mussels: 25 percent of the lake bed
  • Current mussel density on hard bottom: 4,000 mussels per square meter
  • Filtration rate: 0.04 liters per mussel per hour
  • Conversion: 1 cubic meter equals 1,000 liters
  1. Calculate the volume of the lake in cubic meters.
  2. Convert the lake volume from cubic meters to liters.
  3. Calculate the area of hard bottom in square meters.
  4. Calculate the total number of mussels living on the hard bottom.
  5. Calculate the volume the whole population filters in one day, in liters per day.
  6. Calculate the clearance time of the lake in days, meaning the number of days for the population to filter a volume equal to the whole lake.
  7. A survey five years earlier found 900 mussels per square meter on the same area of hard bottom. Calculate the clearance time in days at that earlier density.
  8. Each mussel releases about 0.9 micrograms of dissolved phosphorus per day. Calculate the mass of dissolved phosphorus the current population releases in one day, in kilograms per day.
  9. Water clarity in the fictional lake improved from a Secchi depth of 1.8 meters to 5.4 meters over the same five years. Explain how the mussels produced that change.
  10. Total phosphorus in the lake did not fall over those five years, yet the open water grew clearer and a thick mat of green algae now covers the rocks in the shallows. Explain where the phosphorus went and why the shallow rocks changed.
  11. Rank the three management option cards from most to least effective at protecting other lakes from this species, and defend your first choice in two sentences using a value you calculated.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 10,000,000 cubic meters. Volume equals surface area times mean depth, so 2,000,000 square meters times 5.0 meters gives 10,000,000 cubic meters, or 1.0 x 10^7 cubic meters.
  2. Answer: 1.0 x 10^10 liters. Multiply 10,000,000 cubic meters by 1,000 liters per cubic meter.
  3. Answer: 500,000 square meters. One quarter of the 2,000,000 square meter lake bed is hard bottom.
  4. Answer: 2.0 x 10^9 mussels. Multiply 4,000 mussels per square meter by 500,000 square meters.
  5. Answer: 1.92 x 10^9 liters per day. The population filters 2.0 x 10^9 mussels times 0.04 liters per mussel per hour, which is 8.0 x 10^7 liters per hour, and 24 hours of that gives 1.92 x 10^9 liters per day.
  6. Answer: 5.2 days. Divide the lake volume of 1.0 x 10^10 liters by 1.92 x 10^9 liters per day.
  7. Answer: 23.1 days. At 900 mussels per square meter the population is 4.5 x 10^8 mussels, which filters 4.32 x 10^8 liters per day, and 1.0 x 10^10 divided by that is 23.1 days. The population became more than four times faster at processing the lake in five years.
  8. Answer: 1.8 kilograms per day. Multiply 2.0 x 10^9 mussels by 0.9 micrograms per mussel per day to get 1.8 x 10^9 micrograms, which is 1,800 grams, or 1.8 kilograms per day.
  9. Answer: The mussels removed the suspended particles that scattered light. Filter feeders strain algae, silt, and other fine particles out of the water column, and with those particles gone, light travels much farther before it is scattered, which is what a Secchi disk measures.
  10. Answer: The phosphorus moved from the open water to the bottom. Mussels eat algae from the open water and release phosphorus in dissolved form near the lake bed, where they live. Light now reaches that same bed because the water above is clear, so attached algae on the shallow rocks have both the light and the nutrient they need and they grow into thick mats. The lake did not lose phosphorus; the mussels moved it and made it easier to use in the shallows.
  11. Answer: Card B, the boat inspection and wash station, ranks first for protecting other lakes. Accept any ranking defended with a calculated value. A strong answer notes that the population reached a clearance time of 5.2 days from a much lower density in five years, so a few veligers carried in a live well are enough to establish a population in a new lake, and only Card B addresses that transport. Card A protects the intake pipe but does nothing outside it, and Card C leaves both the lake and the transport route unaddressed.

Differentiation

Support

Give these students a handout with the calculation chain laid out as labeled boxes, so each item shows which quantity feeds the next, and supply the first line of work for items 5 and 6. Provide a conversion reference card and allow a partner check after every second item.

Extension

Ask these students to calculate what mussel density would be required to reach a clearance time of one day, then explain why lakes rarely reach that value. They can also write a short paragraph predicting what happens to the mussel population itself once the open water runs short of algae.

ELL supports

Pre-teach filter feeder, clearance, density, and benthic with a labeled cross-section of a lake showing mussels on the bottom and algae in the water column. Provide the frames "First I found ___, which let me find ___" and "The water is clearer because ___." Allow teams to talk through the model in their home languages while writing the work in English.

Extensions

Have students look up whether their state requires boat inspection at public ramps, and write a paragraph comparing that requirement with Card B in this activity. Students can also extend the model by asking what happens to clearance time if half the hard bottom is buried by sediment, recalculating and explaining the result.