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Mathematics · Grade 9

An Algebra Modeling Investigation

A capstone investigation that pulls the year together. Learners help a fictional town plan its community fair: they formulate questions and assumptions, choose between linear and exponential models of attendance and advertising reach, build a quadratic revenue model to set a ticket price under a crowd constraint, and validate their models against new data before writing a recommendation with stated limitations.

  • 4 lessons
  • About 150 minutes
  • Modeling investigation check: 11 questions
  • Ways to answer: choose an answer, draw a graph, type a number, put in order, sort into groups and true or false
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What learners will discover

  • Formulate a modeling problem: identify quantities, variables, assumptions and constraints, and choose a model type from patterns in data.
  • Build, use and compare linear and exponential models, including finding when one overtakes the other and where a model must stop.
  • Build and analyze a quadratic revenue model to find and interpret a maximum, and adjust the decision for a real constraint.
  • Validate models against new data using residuals and reasonableness, revise assumptions, and communicate a recommendation with its limitations.

Lessons

  1. Formulating the problem 6 steps2 practiceabout 30 min
  2. Linear and exponential growth: attendance and advertising 7 steps4 practiceabout 38 min
  3. Setting a ticket price: a quadratic revenue model 7 steps4 practiceabout 40 min
  4. Validate, revise and report 5 steps3 practiceabout 32 min
  5. Modeling investigation check 11 questions at the end

Keep exploring

More 9th grade math

Guide for grown-ups