Common Core Math · High School
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Why water teaches this standard well
Students calculate the average rate of change in a reservoir's level over a summer from a table of monthly readings, then compare that rate to one estimated directly from the reservoir's graph. Average rate of change here is the same statistic used to describe a drought's severity in a real water-supply report.
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Grade 11 Lesson plan
A 55-minute grade 11 lesson where students read key features of a granular activated carbon breakthrough curve and compute average rates of change across its intervals.
Grade 12 Lesson plan
Students act as dam safety technicians, computing average rates of change in seepage and piezometer data and weighing three surveillance responses against criteria.
Grade 9 Lesson plan
A grade 9 consumer-science lesson where students model a fictional tiered water bill as equations and test it against an affordability threshold.
Grade 11 Lesson plan
A grade 11 lesson fitting an exponential decay model to six fictional streamflow readings, then predicting when the brook drops below an intake.
Grade 12 Lesson plan
A grade 12 lesson where students read key features off a fictional reservoir's water-level graph and compute average rates of change across a drought and recovery.
Grade 12 Lesson plan
A 50-minute grade 12 lesson where students track a fictional reservoir's monthly storage with a water-budget equation and model its decline.
Grade 11 Lesson plan
A grade 11 lesson tracing the snow-albedo feedback, then using rates of change and a runoff table to show how earlier melt shifts a city's summer water supply.
Grade 10 Lesson plan
A grade 10 lesson comparing linear phosphorus loading to exponential algae-coverage growth in a fictional pond, using explicit formulas to distinguish the two models.
Grade 9 Worksheet
A grade 9 worksheet where students read a spillway rating table, compute rates of change across intervals, and convert discharge between cfs, MGD, and gpm.
Grade 9 Worksheet
A grade 9 worksheet using a sequential flush profile from one home's lead service line to practice average rate of change and one-variable equations.
Grade 11 Worksheet
A grade 11 worksheet on a new municipal well: students find drawdown, specific capacity, an average rate of change, and a pump discharge pressure in feet of head.
Grade 11 Worksheet
A grade 11 worksheet computing average rate of change from a fictional digester's biogas startup table and interpreting how a maturing digester levels off.
Grade 9 Worksheet
A grade 9 worksheet using a fictional river's dissolved oxygen readings to find average rate of change and build a linear model against the 5 mg/L fish threshold.
Grade 11 Math problem set
A grade 11 careers problem set in which a groundwater monitoring technician fits a line to nitrate readings from eight wells, computes residuals, and judges the fit.
Grade 11 Math problem set
A grade 11 problem set contrasting a fixed-percent water rate increase with a steady pipe leak, using function models and average rate of change.
Grade 11 Math problem set
A grade 11 problem set building a running tank balance from a fictional district's 24-hour demand table, then sizing the tank in gallons and in feet.
Grade 9 Math problem set
A grade 9 math problem set where students build and graph linear equations for a fictional reservoir's storage under current withdrawal versus a conservation order.
Grade 10 Lab / experiment
Students cool bottles of warm water four ways, from still air to an ice-water tub, calculate cooling rates, and advise a fictional school on heat stroke first aid.
Grade 9 Classroom activity
A grade 9 station-rotation activity where teams read six fictional water meters, convert CCF to gallons per day, and rank which address the leak crew should visit.
Grade 9 Classroom activity
A grade 9 relay activity where teams match pump-station flow data tables to scenario cards and calculate the average rate of change for each.
Grade 12 Quiz & test questions
A 45-minute, 40-point grade 12 test on a fictional basin: converting runoff depth to acre-feet and MGD, then reading average rates of change from a storage table.
Grade 9 Quiz & test questions
A grade 9 quiz on six days of fictional gauge readings, covering average rate of change, conversions among cfs, gpm, and MGD, and reading a storm rise.