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Modeling with Math, Algebra I and II

Examples and exercises illustrate modeling concepts using mathematics from Algebra I and II topics. Some examples are simple models with discrete time steps. Others have functions with continuous variables, such as time or number of dollars; for example, piecewise defined functions show how to calculate federal taxes from specific income levels. Some open-ended scenarios to practice creating models are included.

Additionally, two presentations demonstrate the construction of functions to fit data and the use of probability in biology models. An Excel file is provided to iterate and to illustrate discrete models with sequences.

The teacher workshop for which these materials were developed was conducted in cooperation with Lynn Hodge, associate professor of mathematics education at the UT-Knoxville, and was partially supported by the East TN STEM Hub and the Center for Enhancement Education in Mathematics and Sciences.

Activity files

Illustration Recursive Model (xlsx)
Biodiversity Modeling Handout (pdf)
Presentation Modeing Biodiversity (pdf)
Presentation DATA rescalce Logs (pdf)
Discrete Models background and exercises (pdf)
Discerte Model Open Exercise Trout (pdf)
Solving Geometry Problem With Algebra (pdf)
Solving Diophantine Equation with Algebra (pdf)
Discrete Model Brim Lake (pdf)
Discrete Model Brim answers (pdf)
Inverse Functions with Euros (pdf)
Inverse functions with Euros Conversion answers (pdf)
Modeling Functions Ironman Model (pdf)
Modeling Functions Ironman Race answers (pdf)
Modeling Functions Marathon Race (pdf)
Modeling Functions Marathon Example answers (pdf)
Modeling Taxes with Piecewise Functions (pdf)
NCTM paper BIodiversity (pdf)
NCTM paper Biodiversity answers (pdf)
Rate Conversion Medical Example (pdf)
Tree Rings Regression (pdf)

Education and Outreach Contacts:

Suzanne Lenhart
Associate Director for Education and Outreach
Ph: (865) 974-4270 (Math)   (865) 974-9349 (NIMBioS)   Fax: (865) 974-9300

National Institute for Mathematical and Biological Synthesis
University of Tennessee
1122 Volunteer Blvd., Suite 106
Knoxville, TN 37996-3410

1122 Volunteer Blvd., Suite 106
University of Tennessee
Knoxville, TN 37996-3410
PH: (865) 974-9334
FAX: (865) 974-9461
Contact NIMBioS

From 2008 until early 2021, NIMBioS was supported by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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