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Third Edition *Precalculus* meets all of the standards for a Common Core 4th Year high school math course, and includes an introduction to calculus with functions, graphs, limits, area under a curve, and rates of change. The course is designed similarly to the CPM Core Connections courses. On a daily basis, students work collaboratively with others as they use problem-solving strategies, complete investigations, gather evidence, critically analyze results, and communicate clear and effective arguments while justifying their thinking.

The course is well balanced among procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (application and extension). The course embeds the CCSS Standards for Mathematical Practice as an integral part of each lesson in the course. With the emergence of new technology, many lessons have moved beyond a traditional handheld device and are written with Desmos eTools as an integral component. The curriculum contains several key labs and hands-on activities throughout the course to introduce and connect concepts, with an emphasis on modeling.

Read More...The course starts with lessons that introduce the following big ideas of the course: functions, trigonometry, modeling, algebraic manipulation, rates of change, and area under a curve. Each of these major topics reemerges later in the course for students to revisit using new knowledge. For instance, the spring lab introduces modeling with mathematics, teamwork, and periodic functions early in the course. Then it is revisited two more times, connecting the situation to exponential decay and writing equations of trigonometric functions. The dirt bike course introduces area under a curve, optimization, and piecewise functions. This situation reemerges connected to instantaneous rates of change.

A focus on algebra is woven throughout the course. Students investigate equivalent expressions and practice setting up word problems right from the start. In Sections 1.2 and 2.1 students use algebra to manipulate inverse, composite, and piecewise-defined functions as well as investigate characteristics of functions and transformations of functions. Section 3.1 focuses on rewriting expressions, solving complicated equations and systems, and concludes with using algebra to solve word problems. Algebraic manipulation is practiced throughout the rest of the course as students work with limits, rates of change, trigonometric expressions, complex numbers, series, conic sections, and area under the curve.

Careful consideration was given to the sequencing of the concepts in the course to allow for mastery over time while meeting the content standards of a 4th year course. The book is designed to be a year-long course and allows teachers to choose topics that fit the needs of their students. One option using this text is a course that focuses on the 4th year math standards: algebra, functions, trigonometry, complex numbers, conic sections, probability, vectors, and matrices. Another option is a course that focuses on Calculus readiness with topics such as rates of change, limits, and area under the curve.

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