Grade 10 Lesson plan
Farrowdean Combined Sewer: Storm Storage as a Constraint
A 55-minute grade 10 lesson in which students model a fictional town's storm storage tank as an inequality in rate and duration, then judge four storms as viable or not.
Common Core Math · High School
HSA-CED.A.3 Represent constraints and interpret viable solutions
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
Why water teaches this standard well
Students model a household's water budget as a system of inequalities balancing indoor and outdoor use, then identify which combinations of uses are viable under a conservation target and which are not. Distinguishing viable from non-viable solutions is essential when a model's answer must make sense in the real world, not just on paper.
Materials tagged with this code are written to the full standard , and each carries a written note explaining the alignment. See how we review materials.
37 materials aligned to HSA-CED.A.3
Lesson plans
Grade 12 Lesson plan
Fetterly's Rate Increase: When Customers Use Less Water
A 55-minute grade 12 lesson where students model a water utility's revenue against a demand response and solve a quadratic for the rate increase that hits a target.
Grade 12 Lesson plan
Quillsdale Canal Allotment: Choosing Acreage by Corner Points
A 55-minute grade 12 lesson where students model an irrigation allotment as a system of inequalities and test corner points to maximize a grower's net return.
Grade 9 Lesson plan
Thrushmere Well Field Permit: Pumping Limits as Inequalities
A 50-minute grade 9 lesson where students write a system of inequalities for two wells' permit caps and test proposed pumping plans for viability.
Grade 12 Lesson plan
The Freshwater Lens Under Selvey Point
A 55-minute grade 12 lesson building a spreadsheet model of a barrier island's freshwater lens and testing which withdrawal rates keep seawater below the well screen.
Grade 11 Lesson plan
Meddingham's Water Main Budget: Which Segments Get Replaced
A 55-minute grade 11 careers lesson in which students act as an asset management analyst, scoring five water main segments by risk and fitting them to a budget.
Grade 11 Lesson plan
Birch Hollow's Three Rate Plans: Break-Even Systems and Intervals
A grade 11 lesson where students solve three systems of equations comparing three water-rate plans and determine which plan is cheapest across each usage interval.
Worksheets
Grade 9 Worksheet
One Acre, One Vote in the Pennyfold Irrigation District
A grade 9 worksheet comparing acreage-weighted and per-owner voting in a fictional irrigation district, with vote shares, a majority inequality, and a vote cap.
Grade 11 Worksheet
Thornleigh's Aging Water Mains: A Replacement Plan Under Two Limits
A grade 11 worksheet writing budget and crew-capacity inequalities for a fictional city's main replacement program, then solving the system they form.
Math problem sets
Grade 12 Math problem set
Halbrook Water: Uniform Versus Inclining Block Rate Break-Evens
A grade 12 set comparing a uniform water rate with a three-block piecewise rate: two break-evens, interval answers, and a year of seasonal bills.
Grade 9 Math problem set
Rennick Valley Center Pivots: Run Times and Canal Capacity
A grade 9 problem set on scheduling six center pivots under a canal limit using acre-inches, run times, inequalities, and wheat water use per pound.
Grade 11 Math problem set
Torvale Coast RO Blending: Recovery and a TDS Mass Balance
A grade 11 problem set on a fictional brackish RO plant: find recovery, solve a blended-TDS mass balance for the bypass fraction, and estimate daily energy.
Grade 9 Math problem set
Cravenshaw Meadows Detention Basin: Storage and Release
A grade 9 problem set applying the rational method to a fictional subdivision, then testing whether the detention basin fits the site under a depth limit.
Grade 9 Math problem set
Crestline Reservoir's Drought Drawdown: Equations and Rationing Limits
A grade 9 problem set where students write and solve one-variable equations for a drought-stricken reservoir's drawdown and a household's rationing constraints.
Grade 9 Math problem set
Larkspur Flats Well Drawdown: A Grade 9 Linear Equations Problem Set
Eight algebra problems that model a subdivision's groundwater well as a linear equation, using drawdown rate, a safety shutoff, and unit conversions.
Classroom activities
Grade 10 Classroom activity
Wistmere Drought Board: A Four-Station Constraint Rotation
A 55-minute grade 10 activity where teams collect one constraint per station, build a feasible region for a fictional town, and test four proposed plans.
Grade 11 Classroom activity
Eastmere Bay Nutrient Trading Floor: Cutting a Load at Least Cost
A 60-minute grade 11 activity where three teams trade phosphorus reduction projects across a watershed cap and then find the least expensive package that meets it.
Grade 12 Classroom activity
Verrindale Leak Survey Round: Ranking Segments by Expected Value
A 45-minute grade 12 team round where students compute expected water-loss recovery per survey dollar and choose a leak survey plan under a fixed budget.
Projects
Grade 10 Project
Duncannon Elevated Tank: A Storage and Pressure Design Project
A four-session grade 10 project where teams size an elevated tank for a fictional town to meet storage, pressure-range and budget limits at low cost.
Grade 12 Project
Sandalford's New Water Source: Desalination, Reuse, or Conservation
A grade 12 project where teams test desalination, reuse, conservation and a hybrid against supply and budget inequalities, then recommend one to a board.
Grade 9 Project
Thurlby's Stormwater Fee: Setting a Rate and a Credit Schedule
A five-session grade 9 project where teams measure hard surfaces, build a revenue equation for a town stormwater fee, and defend a credit schedule to a council panel.
Grade 9 Project
Whitmoor Creek Dam: A Repair, Retrofit, or Removal Study
A grade 9 project where teams model twenty-year costs for three options at a fictional mill dam and recommend one to a river district board.
Grade 10 Project
Draythorne's Pump Overhaul Plan: A Maintenance Planner Project
A grade 10 careers project where teams act as maintenance planners, ranking seven pumps by cost per added service year and scheduling a year of overhauls.
Grade 11 Project
Okemont Booster Station: A Pump Replacement Recommendation
A grade 11 careers project in which teams screen three pump options against stated constraints and recommend one to a fictional maintenance superintendent.
Grade 12 Project
Standen Ford Water Reclamation: Build the Shift Staffing Plan
A four-session grade 12 careers project scheduling round-the-clock licensed coverage for a fictional reclamation plant within staffing and labor cost limits.
Grade 10 Project
Kelmarsh Valley Irrigation District: Allocating a Short Supply
A five-session grade 10 project in which teams display thirty fictional parcel requests, model district constraints, and propose a seasonal allocation rule.
Grade 11 Project
Varnwell's Pumping Schedule: Least Cost Under a Time-of-Use Tariff
A four-session grade 11 project where teams build an hourly tank balance, design a 24-hour pumping schedule under storage limits, and defend its cost to a board panel.
Grade 12 Project
Jarrowdene Drought Reliability: A Simulated Ten-Year Study
A six-session grade 12 project in which students simulate reservoir storage under three drought policies and report a failure probability with its margin of error.
Grade 10 Project
Hollowdale Farm Irrigation Water Budget Design Project
A grade 10 project where teams design a season's irrigation plan for a fictional 40-acre field, comparing flood and drip efficiency to fit a water and equipment budget.
Grade 10 Project
Tarnbury Pressure Zones: Designing for 40 to 80 psi on a Hillside
A five-session grade 10 project where teams divide a fictional hillside town into pressure zones, size each zone's tank, and defend the plan against a capital budget.
Grade 11 Project
Amberly Landing's Drought Plan for Corvie Reservoir
A five-session grade 11 project building a monthly reservoir balance for a fictional district, then designing drought stages that hold a protected level.
Grade 12 Project
Dorwyn Water District: A 20-Year Drought Supply Plan
A grade 12 project where teams forecast a fictional city's water demand with an exponential model and design a supply portfolio that closes the drought gap on budget.
Grade 12 Project
Ravelston Field Cistern: A Rainwater Harvesting Design Proposal
A four-session grade 12 project sizing a cistern for a fictional school field, using a budget inequality and cylinder geometry under height and footprint limits.
Grade 9 Project
Ambervale Irrigation District: A Water Budget Project
A grade 9 project for the fictional Ambervale Irrigation District, where teams model a season of water use as a constraint system within an allocation and budget.
Grade 10 Project
Sundown Bay Water Budget: Conservation and Desalination Project
A 4-session grade 10 project where teams use a system of inequalities to design a feasible conservation-and-desalination plan within a fictional town's budget.
Grade 12 Project
Fenwick County Water Utility: A Capital Plan and Rate Proposal Project
A grade 12 multi-session project where student teams build a capital improvement and rate plan for a fictional utility, constrained by an affordability limit.
Grade 9 Project
Aldergate's Aging Pipes: A Water-Main Break Trend and Budget Project
A grade 9 project where students model a fictional town's rising water-main break trend and propose a pipe-replacement plan within budget and construction limits.