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# Math

## Accelerated Algebra 1 Tue-Thu TBA

with Mark Kover, M.S.

***FALL Semester course**

Course Description: This course is a full-year Algebra 1 course, taught to advanced students & completed in 1 semester's time.

**Classical to the CORE**:

Areas of focus are vertically aligned to the mathematical practices that are fundamental to the discipline of mathematics in high school, AP courses, and beyond. This gives students multiple opportunities to think and work like mathematicians as they develop and strengthen these disciplinary reasoning skills throughout their education:

- Connections among multiple representations: Students represent mathematical concepts in a variety of forms and move fluently among the forms.
- Greater authenticity of applications and modeling: Students create and use mathematical models to understand and explain authentic scenarios.
- Engagement in mathematical argumentation: Students use evidence to craft mathematical conjectures and prove or disprove them.

Algebra 1 has four main units --> Unit 1: Linear Functions and Linear Equations (~9 weeks); Unit 2: Systems of Linear Equations and Inequalities (~5 weeks); Unit 3: Quadratic Functions (~9 weeks); Unit 4: Exponent Properties and Exponential Functions (~5 weeks); Unit 5: Physical & Social Science Applications of Algebra 1 (~3 weeks)

Topics covered include:

Foundations for Algebra (variables and expressions, operations with real numbers, functions), Equations (solving equations, proportion and percent, Inequalities – solving simple and compound inequalities), Functions (function concepts, applying functions), Linear Functions (characteristics of linear functions, using a variety of forms of linear functions), Systems of Equations and Inequalities (solving systems by graphing, substitution, and elimination), Exponents and Polynomials, Factoring Polynomials, Quadratic Functions and Equations, Data Analysis and Probability, Exponential and Radical Functions, & Rational Functions and Equations.

## Accelerated Algebra 2 / Pre-Calc Tue-Thu TBA

with Mark Kover, M.S.

*** SPRING Semester Course**

**Course Description:** This course is a full-year Algebra 2 / Pre-Calc course, taught to advanced students & completed in 1 semester's time.

**Classical to the CORE:**

Areas of focus are vertically aligned to the mathematical practices that are fundamental to the discipline of mathematics in high school, AP courses, and beyond. This gives students multiple opportunities to think and work like mathematicians as they develop and strengthen these disciplinary reasoning skills throughout their education:

- Connections among multiple representations: Students represent mathematical concepts in a variety of forms and move fluently among the forms.
- Greater authenticity of applications and modeling: Students create and use mathematical models to understand and explain authentic scenarios.
- Engagement in mathematical argumentation: Students use evidence to craft mathematical conjectures and prove or disprove them.

Algebra 2 / Pre-Calc has 4main units --> Unit 1: Modeling with Function (~7 weeks); Unit 2: Algebra of Functions (~6 weeks); Unit 3: Function Families (~9 weeks); Unit 4: Trigonometric Functions (~6 weeks)

**Prerequisite**: Accelerated Algebra 1

## Accelerated Geometry & Trig Tue-Thu TBA

with Mark Kover, M.S.

**Geometry & Trigonometry**

Students create and use mathematical models to understand and explain authentic scenarios. Mathematical modeling is a process that helps people analyze and explain the world. In Accelerated Geometry & Trig, students explore real-world contexts where mathematics can be used to make sense of a situation. They engage in the modeling process by making choices about what aspects of the situation to model, assessing how well the model represents the available data, drawing conclusions from their model, justifying decisions they make through the process, and identifying what the model helps clarify and what it does not. In addition to mathematical modeling, Accelerated Geometry & Trig students engage in mathematics through authentic applications. Applications are similar to modeling problems in that they are drawn from real-world phenomena, but they differ because the applications dictate the appropriate mathematics to use to solve the problem.

Often, geometric reasoning is used to make sense of algebraic calculations. Likewise, algebraic techniques can be used to solve problems involving geometry. Patterns in data can emerge by depicting the data visually. Statistical calculations are important and valuable, but they make more sense to students when they are conceptually grounded in and related to graphical representations of data.

Skills Summary: After successful completion of this course, students will be able to:

- Use the formulas for distance, slope, and midpoint and derive them.
- Verify whether lines are parallel, perpendicular, or neither using formulas
- Determine the equation of a line that passes through a particular point and is parallel or perpendicular to a given line
- Transform figures in a plane by dilating, translating, reflecting, and rotating them.
- Describe a transformation in words and in coordinate notation
- Identify a sequence of transformations that will move one object onto another.
- Distinguish and identify objects that have reflectional and rotational symmetry
- Determine whether a conditional statement is true or false; and if it is true, give a reasonable counterexample.
- Identify, compare, and contrast a conditional statement with its converse, inverse, and contrapositive.
- Contrast Euclidean and spherical geometries through examining the concepts of parallel lines and the sum of the angles in a triangle.
- Prove various theorems about angles and apply these theorems to solve problems.
- Prove triangles are congruent using triangle congruence theorems.
- Apply the definition of triangle congruence to identify congruent sides and angles.
- Verify theorems about triangles, such as the Pythagorean Theorem, and apply these theorems to solve problems.

**Prerequisites**: Accelerated Algebra 1

## AP Calc AB Tue-Thu TBA

with Mark Kover, M.S.

**AP Calculus AB** is roughly equivalent to a first semester college calculus course devoted to topics in differential and integral calculus. The AP course covers topics in the areas, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections amongst these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

Course Content:

- Unit 1: Limits and Continuity
- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration

**Big Ideas** serve as the foundation of the course, enabling students to create meaningful connections among concepts and develop deeper conceptual understanding:

**Change**: Using derivatives to describe rates of change of one variable with respect to another or using definite integrals to describe the net change in one variable over an interval of another allows students to understand change in a variety of contexts.**Limits**: Beginning with a discrete model and then considering the consequences of a limiting case allows us to model real-world behavior and to discover and understand important ideas, definitions, formulas, and theorems in calculus.**Analysis of Functions**: Calculus allows us to analyze the behaviors of functions by relating limits to differentiation, integration, and infinite series and relating each of these concepts to the others.

**Prerequisites**: Before studying calculus, all students should complete the equivalent of four years of secondary mathematics designed for college-bound students: courses that should prepare them with a strong foundation in reasoning with algebraic symbols and working with algebraic structures. Prospective calculus students should take courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the composition of functions, the algebra of functions, and the graphs of functions.

## AP Statistics Tue-Thu TBA

with STEM Instructor (M.S. or PhD)

The AP Statistics course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data.

There are four themes evident in the content, skills, and assessment in the AP Statistics course:(1) Exploring Data, (2) Sampling & Experimentation, (3) Probability & Simulation, and (4) Statistical Inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.

**College Course Equivalent** The AP Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics.

**Prerequisites** The AP Statistics course is an excellent option for any secondary school student who has successfully completed a second-year course in algebra and who possesses sufficient mathematical maturity and quantitative reasoning ability. Because second-year algebra is the prerequisite course, AP Statistics is usually taken in either the junior or senior year. Decisions about whether to take AP Statistics and when to take it depend on a student’s plans:

- Students planning to take a science course in their senior year will benefit greatly from taking AP Statistics in their junior year.
- For students who would otherwise take no mathematics in their senior year, AP Statistics allows them to continue to develop their quantitative skills.
- Students who wish to leave open the option of taking calculus in college should include precalculus in their high school program and perhaps take AP Statistics concurrently with precalculus.

## AP Calc BC Sat TBA

with STEM Instructor (M.S. or PhD)

**AP Calculus BC**

AP Calculus BC is designed to be the equivalent to both first and second semester college calculus courses. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions.

AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series.

- Unit 1: Limits and Continuity
- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration
- Unit 9: Parametric Equations, Polar Coordinates, & Vector-Valued Functions
- Unit 10: Infinite Sequences and Series

**Prerequisites **Beyond AP Calc AB, students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and descriptors such as increasing and decreasing). Students should also know how the sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions at the numbers 0, π/6, π/4, π/3, π/2, and their multiples. Students who take AP Calculus BC should have basic familiarity with sequences and series, as well as some exposure to parametric and polar equations.