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.
Common Core Math · High School
HSA-REI.C.6 Solve systems of linear equations
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Why water teaches this standard well
Students compare two water utility rate structures, a flat monthly fee versus a per-gallon charge, by solving the system both algebraically and graphically to find the exact usage level where the two plans cost the same. This is the high school version of the same rate-comparison problem introduced in grade 8, now solved with full algebraic and graphical methods.
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12 materials aligned to HSA-REI.C.6
Lesson plans
Grade 9 Lesson plan
Garrowby Water Authority: Two Entry Paths as a System of Equations
A 55-minute grade 9 lesson where students model cumulative earnings for two routes into a water utility and solve the system for the year the totals meet.
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.
Grade 10 Lesson plan
Amberlin Water District: Comparing Two Billing Plans by Equation
A grade 10 lesson where students solve and graph a system of linear equations to find the break-even usage point between two fictional water utility billing plans.
Grade 9 Lesson plan
Wrenfield's Two Water Rate Plans: A Systems of Equations Lesson
A grade 9 lesson where students set up and solve a system of linear equations to find the usage level where two water utility billing plans cost the same.
Worksheets
Grade 11 Worksheet
Rodmell's Digester Blend: Solving a Two-Stream Solids Balance
A grade 11 worksheet solving a system of two linear equations for the blend of thickened and primary sludge a digester needs, then checking solids in pounds per day.
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 10 Math problem set
Nyefield Blending Plan: A Two-Source System of Equations
A grade 10 problem set where students solve a two-variable system to blend purified recycled water with hard groundwater for a fictional district in drought.
Grade 10 Math problem set
Saltcombe Reverse Osmosis Plant: Flow Balance and Energy Problems
A grade 10 problem set solving a feed-permeate-concentrate system of equations for a fictional desalter, then finding recovery, salt rejection, and energy use.
Grade 9 Math problem set
Pinebluff Water Rates: Tiered Billing and Break-Even
A grade 9 problem set on the fictional Pinebluff utility, building a tiered water bill as a linear equation and solving for where two rate plans cost the same.
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.