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Mathematics · Grade 11

A Calculus Investigation

In this capstone, learners investigate a fictional reservoir during a twelve-hour storm. Using inflow and outflow rates, they build an accumulation model, find when the water volume rises, falls and reaches its extremes, approximate integrals from data and judge their accuracy, connect volume and depth with related rates, extend the model with a differential equation, and write a complete, justified report.

  • 4 lessons
  • About 160 minutes
  • Reservoir investigation check: 12 questions
  • Ways to answer: choose an answer, type a number, place on a number line, put in order, sort into groups and true or false
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What learners will discover

  • Build and interpret an accumulation model from inflow and outflow rates, with units.
  • Use derivatives to determine when the quantity increases, decreases and reaches absolute extrema, with justification.
  • Approximate integrals from data, judge over- or underestimates, and compute related rates and averages.
  • Extend a model with a differential equation and communicate a complete investigation with justified conclusions.

Lessons

  1. Building the accumulation model 5 steps3 practiceabout 36 min
  2. When does the volume rise and fall? 6 steps4 practiceabout 40 min
  3. Estimates, averages and depth 5 steps4 practiceabout 40 min
  4. Extending the model and reporting 5 steps3 practiceabout 44 min
  5. Reservoir investigation check 12 questions at the end

Keep exploring

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Guide for grown-ups