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# Modeling with Mathematics: A Fourth Year Course

## Second EditionNancy Crisler; Gary Simundza; Region IV Educational Service Center; COMAP

©2012With the emphasis the Common Core State Standards (CCSS) places on modeling, *Modeling With Mathematics: A Fourth Year Course* (Fourth Year 2e) addresses these modeling requirements while exploring how mathematics is ever-present in solving real-world problems. Intended for students fulfilling a fourth year math credit, the Fourth Year 2e program helps solidify students’ understanding by providing a different kind of learning experience. With Fourth Year 2e students model real-world applications with a functions approach netting a deeper grasp of the important concepts necessary for success on the forthcoming Common Core assessments.

## Table of Contents

**1. Mathematical Modeling***What is a Mathematical Model?***2. Direct Variation***How is Mathematics Related to Bungee Jumping?***3. Solving Equations and Inequalities***How Can We Care for Our Forests?***4. Measurement: Perimeter, Area and Volume***Why is Package Design Important?***5. Functions and Their Representations***How Can You Find the Value of an Unknown Quantity?***6. Describing Data***How Does the Census Help Us Understand Our Country?***7. Linear Models from Data***What Happened to Amelia Earhart?***8. Systems of Equations and Inequalities***How Are Business Decisions Made?*

**9. Symmetry and Transformations**

*How Do Archaeologists Use Mathematics to Study Past Civilizations?*

**10. Exponential Functions**

*Will the World Have Enough Water?*

**11. Quadratic Functions**

*Is it a Parabola?*

**12. Indirect Measurement**

*How Can You Determine the Height of a Model Rocket?*

**13. Periodic Functions and Sound**

*How Are Music and Repeated Motion Related?*

**14. Probability**

*What Are the Chances?*

**15. The Mathematics of Personal Finance**

*How Much Do I Need to Cover My Personal Expenses?*

**Appendices:** Fractions, Decimals, Ratio, Proportions, Percents as Fractions and Decimals, Percent Calculations, Absolute Value, Order of Operations, Operations with Positive and Negative Numbers, Properties of Real Numbers, Scientific Notation, Solving One- and Two-step Equations, Simplifying Radicals, Mean, Median, Mode, and Range, Coordinate Plane, Square Roots