# Mathematics

## MISSION

The mission of the ChiArts mathematics department is to provide all students with a complete understanding of the logical structure of mathematics and how it prepares adolescents to become successful citizens in an ever-changing society. Through the study of mathematics, students will conceptualize math as a unique language in order to be effective problem solvers and critical thinkers. Students will further develop their abstract and quantitative reasoning skills to creatively solve mathematically modeled situations.

## PROGRAM GOALS

Understand that mathematics is a language the can be used to interpret and conceptualize the world we live in; Construct and communicate viable mathematical arguments; Determine the meaning of a problem and persevere in solving it through various avenues; Reason abstractly and quantitatively by making sense of different relationships in problem situations; Model real life situations as mathematical problems and apply learned knowledge to creatively solve them; And analyze problems closely to discern a pattern or structure and then generalize that discovered pattern.

## COURSES

Numeracy
The goal of this course is to reinforce fundamental algebra concepts by developing quantitative thinking necessary in a college preparatory class. The teacher will foster a classroom environment so students can develop mathematical confidence by honing their problem solving skills. The students will learn about concepts including but not limited to: order of operations, numerical fractions, decimals & percents, Cartesian plane, ratios, rates, & proportions.

Integrated Math I
The goal of this course is to expose students to abstract thinking through algebraic structures and challenge students to solve problems logically. This course is designed to help students conceptualize math as a language. Students will apply learned skills through modeling real-world situations. Topics investigated are expressions, exponents, functions, solving equations/inequalities, linear functions, linear systems, patterns/sequences, comparing linear and exponential functions, properties of angle pairs, properties of triangles and quadrilaterals, parallel lines, perpendicular lines, scatterplots, correlation, and box plots.

Integrated Math II
This course is an extension of the Math I course. Students expand on their prior knowledge of Algebra with further investigation of functions such as quadratic functions. Students will analyze, interpret, build, transform, and model quadratics. In addition, students explore concepts of geometric similarity, right triangle trigonometry, and geometric proofs. An emphasis on integrating geometric concepts with algebraic skills is reinforced throughout the year. Lastly, students will extend the number system beyond their prior knowledge of non-real solutions and students will analyze applications of probability. Students apply learned skills via real-world applications and approach problem solving both logically and creatively. Overall, we want our students to leave our course with a strong sense of problem solving while understanding that mistakes are part of the problem solving process.

Integrated Math III
This course is designed to help students conceptualize math as a language, expose students to abstract thinking through algebraic structures, and challenge students to solve problems both logically and creatively. Students will master mathematical concepts and skills such as data analysis; fitting data to equations; linear, quadratic, exponential, rational, radical, logarithmic, and trigonometric models; and formulas.

Pre-Calculus
In order to prepare students for calculus and other higher-level math, this course is designed to have students develop a deeper understanding of such topics as exponential, logarithmic, and trigonometric functions. We will focus on these functions’ properties and graphs and apply them to real-world situations. Students will apply many of the learned skills from previous courses and will find their algebra and graphing skills very useful. To do well, problems in this course must be approached both logically and creatively. At the completion of this course, students with interest should have the necessary skill set to pursue a specific branch of mathematics, whether Calculus, Statistics, Theory, Physics, Engineering, and even the biological and medical sciences.

Financial Statistics
Financial Statistics takes the math skills that students have acquired since freshmen year and reveals their value and purpose in the real world of finance. Students will explore how math is used and applied in the stock market, modeling of businesses, marketing and advertising, credit, loans, taxes, income, budgeting, and more. This course is designed to reinforce previously taught concepts from a different, more relatable perspective while preparing students for life after high school.

AP Calculus
AP Calculus is a challenging, college-level course applying previously learned concepts in math (ie. slope, rates of change, functions) along with many new concepts such as limits, derivatives, and integrals. The course provides students with the opportunity to work with functions represented in a variety of ways — graphically, numerically, analytically, and verbally — and emphasizes the connections among these representations. Students are expected to learn and apply multiple definitions and proofs of theorems that will help in completing problems and exploring the general properties of mathematics. AP Calculus explores math on infinitesimally large and small scales, so students should have open, creative minds and be willing to think outside the box. AP Calculus is challenging and fast-paced as well as extremely interesting and rewarding. Those who work hard will find the beauty of mathematics while uncovering many applications for the sciences.

AP Statistics
AP Statistics is the high school equivalent of a one semester, introductory college statistics course. In this course, students develop strategies for collecting, organizing, analyzing, and drawing conclusions from data. Students design, administer, and tabulate results from surveys and experiments. Probability and simulations aid students in constructing models for chance behavior. Sampling distributions provide the logical structure for confidence intervals and hypothesis tests. Students use a TI-83/84 graphing calculator, Fathom and Minitab statistical software, and Web-based java applets to investigate statistical concepts. To develop effective statistical communication skills, students are required to prepare frequent written and oral analyses of real data.