Math is often a favorite subject at AIM due to the use of multisensory, individualized and rigorous instruction. Our math teachers use the extensive research of the NCTM (National Council of Teachers of Mathematics) to drive the focus of their instruction. We continue to approach concepts from a conceptual level and build toward the more abstract procedures.
Look deeply into mathematical ideas of expression, equations, and polynomials.
Algebra is what is known as a foundational math class. The material students take on in this class will help prepare them for all their future mathematics classes in high school and college; it will also help them sharpen the quantitative and abstract reasoning skills that they will find so valuable in their lives and future careers. Algebra I will look deeply into some mathematical ideas students may have seen before (like expressions and equations). It also introduces some concepts that may be brand new to them (like polynomials).
Sample Topics: Solving and graphing advanced linear equations, exponents and scientific notation, Pythagorean theorem and irrational numbers, systems of linear equations and inequalities, congruence and similarity, bivariate data analysis, probability
Algebra is a tool that is used to solve problems in virtual every profession. Owners of sports teams use it to determine how much the athletes should be paid. Lawyers use it to determine how much to sue a defendant. Doctors use it to determine how much medicine to prescribe to a patient. This course will continue your study of the language of algebra and develop the skills that will enable you solve more complex problems. Students will be able to confidently, patiently, and persistently solve real-world math problems, document their thinking in an organized way, communicate their ideas using academic language, and collaborate with other students to compare strategies and determine which are most effective.
Sample Topics: Quadratic functions and factoring, polynomials and polynomial functions, rational exponents and radical functions, exponential and logarithmic functions, rational functions ,data analysis and statistics, sequences and series, quadratic relations and conic sections, trigonometric ratios and functions, trigonometric graphs, identities, and equations
Focus on problem solving and reasoning skills as they relate to geometric shapes.
Geometry is one of the oldest fields of mathematical study. Its origins trace back to the third century. Our study of geometry will focus on problem solving and reasoning skills as they relate to lines, triangles, quadrilaterals and circles. We will also learn how to calculate the perimeter, circumference, surface area, and volume for polygons and solids. Their number sense will be enhanced throughout this course.
Sample Topics: Points, lines, planes, congruence, proofs, parallel and perpendicular lines, triangles, quadrilaterals, properties of transformations, properties of circles, measurements of figures and solids.
Precalculus is designed to reinforce students' knowledge of algebra in order to prepare them to be successful in a calculus class next year. Students will encounter a mixture of topics they have seen before and new concepts. If a topic is not new to the students, it will be examined more deeply and from a different standpoint than in the past. Someone once said that no one fails calculus, they fail the algebra that is needed to complete the calculus problems. This course is designed to keep that from happening to AIM students.
Sample Topics: Quadratic functions, polynomial functions, polynomial expressions and equations, sequences and series, rational functions, solving rational equations, limits.
The intent of this course is to teach a solid foundation in the fundamentals of calculus. Calculus does a few things really well that other math struggles with: it's good at looking at how things change — especially when they change in a non-linear way — and it's good at breaking things apart and putting them together. It accomplishes these feats using two new operations called derivatives and integrals, which modify lots of functions that you already know about. Most of the year will be spent learning how these two things work and how they can be applied. Students will also discuss limits as they provide a foundation for the definition of derivatives. a secondary, concurrent goal of the course is to prepare students for the rigors of college study,, particularly in mathematics and the natural sciences. With that in mind students will be given more freedom than a normal high school class, and part of their success in the class will be based on how they handle this freedom.
Sample Topics: Functions and graphs, exponential functions, parametric equations, functions and logarithms, trigonometric functions, limits and continuity, derivatives, the definite integral, differential equations and mathematical modeling, L'Hopital's Rule, improper integrals, and partial fractions.
The structure of this Statistics course follows a cycle of introduction of a topic and hands-on activities to better grasp the concept and ideas presented. Major themes will be:
- Exploring data
- Planning a study
- Anticipating Patterns
- Statistical Inference
Statistics is as much about numbers as it is about communicating what those numbers mean. Therefore, students will be reading and writing more than a typical math class. The course includes several units on statisitical research which will include short papers and presentations.
Sample Topics: Sampling, statistic measurement, errors, visual displays of data, distribution, describing data, probability, correlation and causation, hypothesis testing, statistic tests.
Quantitative & Financial Literacy
As the name suggests, the class is designed to teach two things:
- Quantitative Literacy, which means that students should be able to perform everyday calculations such as leaving a tip, determining the final cost of something that is on sale, figuring taxes, understanding recipes, and analyzing investments. These calculations require that you have some ability to handle fractions and percents.
- Financial Literacy, which is the ability to understand your paycheck, your mortgage, your car loan, your credit card payments, your income taxes, and other financial aspects of your life. In this part of the class, students will learn new vocabulary and new concepts and be able to make a plan for their future.
Sample Topics: Budgeting, tracking spending, check writing, choosing a loan, demystifying pay check allocations, and investing.