Project Grade 8 Math
Brindlecombe Constructed Wetland: A Grade 8 Sizing Project
A four-session grade 8 project where teams build a flow function, size a treatment wetland and a holding tank, and pitch the design to a fictional village board.
Objectives
- Students will construct a linear function from a table and interpret its rate of change and initial value.
- Students will size a treatment wetland and a cylindrical tank so that both meet stated design rules.
- Students will write a proposal that shows how a design meets a land limit and a budget limit.
Vocabulary
Key words: constructed wetland, design flow, rate of change, initial value, budget
Teacher overview
Small villages sometimes treat their wastewater in a constructed wetland, a shallow planted basin where plants and bacteria break down the waste, because a wetland costs less to run than a mechanical plant and needs no full-time operator. Sizing one is a mathematics problem: the village has to predict its flow years ahead, convert that flow into an area of wetland and a volume of storage, and then check both against the land and money it has. Over four sessions, teams do that work for the fictional village of Brindlecombe and present a proposal to its village board. For teachers, the flow table is built so that Milestone 1 produces a design flow of 99,000 gallons per day, which is a quick way to check that step before teams build the rest of the design on it.
Project Brief
Driving question: How large a treatment wetland and holding tank does the village of Brindlecombe need, and will both fit on the land and inside the budget the village has?
Scenario: Brindlecombe is a fictional village with a creamery and about 1,100 residents. Its old septic system is failing. The village board has asked your team to propose a constructed wetland and a holding tank sized for the village 20 years from now, when planners expect 1,300 residents.
The flow table. The village recorded its wastewater flow at three different population levels.
| Population | Flow (gallons per day) |
|---|---|
| 900 | 71,000 |
| 1,000 | 78,000 |
| 1,100 | 85,000 |
Constraints:
- The site is 1.5 acres. One acre equals 43,560 square feet.
- Design rule for the wetland: it needs 1 square foot of surface for every 2 gallons per day of design flow.
- Design rule for the tank: it must hold 6 hours of the design flow. One cubic foot holds 7.48 gallons.
- The tank must be a cylinder. No tank may be deeper than 14 feet.
- Budget: $180,000 for both pieces. Use 3.14 for pi in every calculation.
- Price sheet for this fictional village: wetland construction costs $2 for each square foot, and tank construction costs $12 for each cubic foot of capacity.
Final deliverable: A site plan drawn to scale on grid paper showing the wetland and the tank, a two-page written proposal to the village board, and a five-minute team presentation. The proposal must show the flow function, the wetland area, the tank dimensions, and an itemized cost.
Milestones
- Session 1, build the flow function. Use the flow table to find the rate of change and the
initial value. Write the flow f as a function of the population p. Say in a sentence what each
number means for the village. Then use the function to find the design flow at 1,300 residents.
Output: a signed function sheet showing the two numbers, the rule, and the design flow. - Session 2, size the wetland. Use the design rule of 1 square foot for every 2 gallons per day to find the wetland area. Convert the 1.5-acre site into square feet. Show that the wetland fits, and state how much land is left over. Draw the wetland to scale on grid paper. Output: an area calculation and a scaled outline of the wetland on the site.
- Session 3, size the tank. Find the number of gallons in 6 hours of design flow, then convert that to cubic feet. Choose a diameter, then use the cylinder volume formula to find the depth your tank needs. Check the depth against the 14-foot limit and adjust the diameter if it does not pass. Output: a tank drawing labeled with diameter, depth, and volume, with all work shown.
- Session 4, cost the design and present. Use the price sheet to find the cost of the wetland
and the cost of the tank, then add them. Compare the total with the budget. Write the two-page
proposal, add the tank to the site plan, and present to the class acting as the village board.
Output: an itemized cost sheet, the finished proposal, the scaled site plan, and the presentation.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Rubric
| Criterion | Emerging | Developing | Proficient | Advanced |
|---|---|---|---|---|
| Flow function | The team reports a flow with no rule or no supporting work | The team writes a rule but misreads the rate of change or the initial value | The team writes a correct rule, explains both numbers in village terms, and finds the design flow | The team also checks the rule against all three table rows and explains why the flow is not proportional to population |
| Wetland sizing and fit | The area is missing or does not use the design rule | The area follows the design rule but the site is not converted to square feet | The area follows the design rule, the site is converted correctly, and the plan shows the wetland fits with land left over | The plan also shows the leftover land clearly and names one use the village could make of it |
| Tank sizing | The tank has no volume calculation, or the volume ignores the 6-hour rule | The volume is correct but the cylinder dimensions are not checked against the depth limit | The volume, diameter, and depth are correct and the depth meets the 14-foot limit | The team compares two diameters, shows the depth each produces, and explains which is the better choice |
| Proposal and cost | The proposal has no itemized cost or exceeds the budget without comment | The cost is itemized but at least one piece is unpriced or the total is not compared with the budget | The cost is itemized, totaled, and compared with the budget, and the proposal shows every calculation | The proposal also states one tradeoff the team considered and what it would cost to change the design |
Differentiation
Support
Give these teams the flow function already written, so Session 1 becomes the task of explaining what the rate of change and the initial value mean rather than finding them. Provide a partly completed conversion sheet for the acre-to-square-foot step and for the gallons-to-cubic-feet step, and reduce the written proposal to one page with headings supplied.
Extension
Ask teams to design a second option in which the wetland is split into two equal cells with a 10-foot path between them, then determine whether that layout still fits the site and what it adds to the cost. Have them recommend one of the two layouts to the board and defend the choice in the presentation.
ELL supports
Provide a labeled cross-section drawing of a constructed wetland showing the inlet, the plants, the gravel bed, and the outlet, so the vocabulary attaches to a picture. Supply a bilingual glossary for "flow," "design flow," "area," "volume," and "budget," and allow the presentation to be delivered from a labeled poster rather than from a script.
Extensions
Invite an operator or engineer from a nearby wastewater utility to hear two team presentations and respond with the questions a real board would ask, or have teams send their proposals to a classroom in another school and review each other's cost sheets for arithmetic and for missing items.