# Algebra II

**Instructor**: Doug Guy

Curriculum Map, Class Page

Algebra II builds upon the foundation laid in Algebra I and Geometry. The students continue to use both functions and relations in the study of algebraic concepts with an emphasis on the application of algebraic principles and models in real-life situations. The students learn how individuals use algebraic knowledge to make decisions that change the world by translating real-life situations to mathematical models, obtaining solutions, and then translating the solutions back into the real-life context.

In Algebra II, students continue to learn how to think logically. They use mathematics to learn careful logical thought processes and how to spot logical fallacies in advertisers, politicians, and newscasters. Students examine how we use equations and inequalities to analyze the conclusions of public opinion surveys about politicians and what these individuals are doing to change the world. They analyze real-world situations where they develop systems of equations and inequalities and use these systems to decide how best to minimize costs but still meet nutritional requirements and make healthy decisions.

Students learn how individuals can use polynomial functions in their everyday lives as they make decisions. They apply this knowledge as they learn how to analyze data and make banking, economic, and business decisions and predictions. They apply their knowledge of powers, roots, radicals, and exponential and logarithmic functions in an integrated project on Industrialization. The students recreate some of the mathematical analysis of Thomas Malthus to understand how he used math as an argument for societal explanation and change. They analyze the impact of industrialization on the growth of large metropolitan areas in the United States, and they investigate how to use a power function to model the relationship between population and rank for large United States cities.

Finally, students investigate the algebraic analysis of rational functions, the conic sections, sequences, series, and trigonometry. They determine the most efficient shape and dimensions of a container that will minimize surface area, design a logo composed of conic sections, and prepare a photographic presentation of conic sections in everyday objects. In their final project, the students make a transit and use trigonometry to calculate indirect measurements.

Students consider the following questions:

- How do we use equations and inequalities to analyze what people believe about what individuals are doing to change the world? How do we use systems of equations and inequalities to see how to make nutritional and healthy lifestyle changes in our world?
- How do individuals use algebraic knowledge to make business, banking, and economic decisions that can change the world? How did an individual, Thomas Malthus, use mathematical analysis as an argument for changes in society?
- How can we use algebraic analysis to help us make efficient design decisions and calculate indirect measurements?

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