Lesson plan Grade 10 Engineering & Design

Pinewattle Flats Aquifer Storage and Recovery Feasibility

A grade 10 lesson sizing an aquifer storage and recovery scheme for a fictional town, from winter surplus and recovery efficiency to the number of injection wells.

Grade: Grade 10
Subject: Engineering & Design
Material: Lesson plan
Time: 55 min
Prep: Low prep
Materials: Printed Student Handout, one per student, Calculators, Board space for the worked example

Standards

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Students carry million gallons per day, days, and gallons per minute through a linked chain of conversions to a well count.

All materials for HSN-Q.A.1 →

HS-ETS1-3 NGSS

Evaluate a solution to a complex real-world problem based on prioritized criteria and trade-offs that account for a range of constraints, including cost, safety, reliability, and aesthetics as well as possible social, cultural, and environmental impacts.

How this material aligns: Students test the recoverable volume against the summer deficit, then judge the scheme on the margin it leaves and the number of injection wells the injection rate requires.

All materials for HS-ETS1-3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-03.

Objectives

Students will calculate the seasonal surplus a treatment plant can inject into an aquifer and the volume recoverable after losses.
Students will compare the recoverable volume against a summer supply deficit and state whether the scheme closes the gap.
Students will convert an injection rate into gallons per minute and determine how many wells the rate requires.

Vocabulary

Key words: aquifer storage and recovery, injection well, recovery efficiency, seasonal surplus, supply deficit

Teacher overview

Aquifer storage and recovery treats drinking water when a system has spare capacity, pumps it down a well into an aquifer, and pulls it back out months later when demand exceeds what the plant can make. This lesson has students size such a scheme for the fictional town of Pinewattle Flats, which runs a plant with idle winter capacity and a summer shortfall, and asks whether the stored water can cover the shortfall and how many wells the injection rate demands. The misconception worth addressing directly is that stored water comes back in full; a share of every injected volume mixes with native groundwater, moves beyond the recovery zone, or fails to meet drinking-water quality on return, so recovery efficiency is well below one hundred percent and the design has to account for it.

Procedure

Hook, 5 minutes. Ask the class where a utility could put treated water it does not need in February so that it is available in August. Take a few answers, then note that above-ground tanks large enough to hold months of supply are usually impractical, which is the constraint that makes an aquifer worth considering as a storage vessel.
Direct instruction, the recovery cycle, 10 minutes. Sketch the three phases on the board: injection during the surplus season, storage while the water sits in the aquifer, and recovery during the deficit season. Define recovery efficiency as the share of injected water that can be pumped back at drinking-water quality, and explain the three ways water is lost, which are mixing with native groundwater, movement away from the well, and quality changes underground.
Worked example, teacher modeled, 10 minutes. Use a separate fictional system on the board, not the numbers on the handout. Suppose a plant with 4.0 MGD of capacity serves a 3.0 MGD winter demand for 100 days at a recovery efficiency of 80 percent. Work the chain aloud: the surplus is 1.0 MGD, the injected volume is 100 million gallons, and the recoverable volume is 80 million gallons. Then convert 1.0 MGD to 694 gpm and note that at 500 gpm per well the system needs two wells, since a partial well is not something a utility can build.
Guided and independent work, 20 minutes. Distribute the Student Handout and have students work questions 1 through 9 in pairs, with the requirement that each partner writes the full chain rather than copying a final number. Circulate and check two things: that students subtract demand from plant capacity rather than the reverse, and that they multiply by 0.78 rather than dividing when they apply recovery efficiency.
Formative check, 5 minutes. Call for answers to question 3 on a show of fingers, with three fingers for a value near 243 million gallons. If fewer than three quarters of the class lands there, rework questions 2 and 3 on the board before continuing.
Debrief and decision, 5 minutes. Ask whether Pinewattle Flats should build the scheme, and require each answer to cite question 6 for the margin and question 8 for the well count. Close by asking what would have to change in the numbers before four wells stopped being enough.

Pinewattle Flats Aquifer Storage and Recovery Feasibility — Grade 10 Engineering & Design

Name: ____________________________ Date: ______________

Student Handout

Pinewattle Flats is a fictional town created for this lesson. Its water treatment plant can produce 6.0 MGD. Winter demand averages 3.4 MGD, and the utility can inject its surplus for 120 days each winter. Pilot testing shows a recovery efficiency of 78 percent. Summer demand averages 7.1 MGD for 75 days while the plant capacity stays at 6.0 MGD. Each aquifer storage and recovery well can accept 550 gpm. One MGD equals 694 gpm. Show the full chain for every answer.

Find the daily surplus available for injection in winter, in MGD, using the 6.0 MGD plant capacity and the 3.4 MGD winter demand.
Find the total volume injected over the 120-day injection season, in million gallons.
At a recovery efficiency of 78 percent, find the volume that can be recovered, in million gallons.
Find the daily summer supply deficit in MGD, using the 7.1 MGD summer demand and the 6.0 MGD plant capacity.
Find the total summer deficit over the 75-day deficit period, in million gallons.
How many million gallons larger is the recoverable volume from question 3 than the summer deficit from question 5?
Convert the winter injection rate from question 1 into gallons per minute, using 694 gpm per MGD.
Each well accepts 550 gpm. How many wells does the utility need to inject the full rate from question 7?
How many million gallons of the injected water cannot be recovered?

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

Answer Key

Answer: 2.6 MGD.
The surplus is plant capacity minus winter demand: 6.0 minus 3.4 equals 2.6 MGD available for injection each winter day.
Answer: 312 million gallons.
Multiplying the 2.6 MGD surplus by 120 days gives 312 million gallons injected over the season.
Answer: about 243.4 million gallons.
Applying the recovery efficiency: 312 multiplied by 0.78 equals 243.36, which rounds to about 243.4 million gallons.
Answer: 1.1 MGD.
The deficit is summer demand minus plant capacity: 7.1 minus 6.0 equals 1.1 MGD short every summer day.
Answer: 82.5 million gallons.
Multiplying the 1.1 MGD deficit by 75 days gives 82.5 million gallons of shortfall for the season.
Answer: about 160.9 million gallons.
Subtracting the deficit from the recoverable volume: 243.36 minus 82.5 equals 160.86, which rounds to about 160.9 million gallons of margin. The scheme covers the summer shortfall almost three times over.
Answer: about 1,804 gpm.
Converting the injection rate: 2.6 MGD multiplied by 694 gpm per MGD equals 1,804.4 gpm, which rounds to about 1,804 gpm.
Answer: 4 wells.
Dividing 1,804.4 gpm by 550 gpm per well gives 3.28 wells, and since a utility cannot build a partial well, the answer rounds up to 4 wells. Three wells would accept only 1,650 gpm, leaving part of the surplus with nowhere to go.
Answer: about 68.6 million gallons.
Subtracting the recoverable volume from the injected volume: 312 minus 243.36 equals 68.64, which rounds to about 68.6 million gallons that stays in the aquifer or fails to return at drinking-water quality.

Differentiation

Support

Give these students the handout with questions 1, 2, and 4 already answered, so their independent work begins at question 3 where the reasoning becomes less mechanical. Provide a one-page conversion card showing that one MGD equals 694 gpm and that a volume in million gallons equals a rate in MGD multiplied by a number of days, and let them use the teacher worked example as a side-by-side model.

Extension

Ask these students to find the recovery efficiency at which the recoverable volume would exactly equal the summer deficit for the fictional Pinewattle Flats scheme, then explain what that number means for the value of pilot testing before construction. Have them also determine how short the injection season could become before the recoverable volume stopped covering the summer deficit.

ELL supports

Post a labeled cross-section of an aquifer storage and recovery well showing the injection phase, the stored bubble of treated water, and the recovery phase, and keep it visible during the independent work. Provide a vocabulary strip pairing surplus with extra, deficit with shortfall, and recovery with getting back, and allow students to explain their chain for question 6 orally before writing it.

Extensions

Have students research whether their state's regulations require a permit to inject treated drinking water underground, and what water-quality testing the permit demands before and after injection. Students can also compare aquifer storage and recovery with two alternatives for the same fictional deficit, which are expanding the treatment plant and buying wholesale water from a neighboring system, and rank the three on cost, reliability, and the time each would take to build.