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# Our Classes

## AP European History Tue@12:30 PM EST

with SocSci Instructor (M.A. or PhD)

The study of European history since 1450 introduces students to cultural, economic, political, and social developments that played a fundamental role in shaping the world in which they live. Without this knowledge, we would lack the context for understanding the development of contemporary institutions, the role of continuity and change in present-day society and politics, and the evolution of current forms of artistic expression and intellectual discourse. In addition to providing a basic narrative of events and movements, the goals of the AP program in European History are to develop (a) an understanding of some of the principal themes in modern European History, (b) an ability to analyze historical evidence and historical interpretation, and (c) an ability to express historical understanding in writing. All AP courses are College Board audited (approved) and count from 6-12 hours college credit.

## 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 Chemistry Tue-Thu TBA

with STEM Instructor (M.S. or PhD)

AP Chemistry is an introductory college-level chemistry course. Students cultivate their understanding of chemistry through inquiry-based lab investigations as they explore the four Big Ideas: scale, proportion, and quantity; structure and properties of substances; transformations; and energy.

BIG IDEA 1: SCALE, PROPORTION, AND QUANTITY (SPQ) Quantities in chemistry are expressed at both the macroscopic and atomic scale. Explanations, predictions, and other forms of argumentation in chemistry require understanding the meaning of these quantities, and the relationship between quantities at the same scale and across scales.

BIG IDEA 2: STRUCTURE AND PROPERTIES (SAP) Properties of substances observable at the macroscopic scale emerge from the structures of atoms and molecules and the interactions between them. Chemical reasoning moves in both directions across these scales. Properties are predicted from known aspects of the structures and interactions at the atomic scale. Observed properties are used to infer aspects of the structures and interactions.

BIG IDEA 3: TRANSFORMATIONS (TRA) At its heart, chemistry is about the rearrangement of matter. Understanding the details of these transformations requires reasoning at many levels as one must quantify what is occurring both macroscopically and at the atomic level during the process. This reasoning can be as simple as monitoring amounts of products made or as complex as visualizing the intermolecular forces among the species in a mixture. The rate of a transformation is also of interest, as particles must move and collide to initiate reaction events.

BIG IDEA 4: ENERGY (ENE) Energy has two important roles in characterizing and controlling chemical systems. The first is accounting for the distribution of energy among the components of a system and the ways that heat exchanges, chemical reactions, and phase transitions redistribute this energy. The second is in considering the enthalpic and entropic driving forces for a chemical process. These are closely related to the dynamic equilibrium present in many chemical systems and the ways in which changes in experimental conditions alter the positions of these equilibria.

## AP Physics 1 (Algebra-based) Tue-Thu TBA

with Mark Kover, M.S.

AP Physics 1 is an algebra-based, introductory college-level physics course. Students cultivate their understanding of physics through classroom study, in-class activity, and hands-on, inquiry-based laboratory work as they explore concepts like systems, fields, force interactions, change, conservation, and waves.

BIG IDEA 1: SYSTEMS (SYS) Objects and systems have properties such as mass and charge. Systems may have internal structure.

BIG IDEA 2: FIELDS (FLD) Fields existing in space can be used to explain interactions.

BIG IDEA 3: FORCE INTERACTIONS (INT) The interactions of an object with other objects can be described by forces.

BIG IDEA 4: CHANGE (CHA) Interactions between systems can result in changes in those systems.

BIG IDEA 5: CONSERVATION (CON) Changes that occur as a result of interactions are constrained by conservation laws

Prerequisites: Students should have completed Geometry and be concurrently taking Algebra II or an equivalent course. Although the Physics 1 course includes basic use of trigonometric functions, this understanding can be gained either in the concurrent math course or in the AP Physics 1 course itself.

## AP Physics 2 (Algebra-based) Tue-Thu TBA

with Mark Kover, M.S.

**AP Physics 2** is an algebra-based, introductory college-level physics course. Students cultivate their understanding of physics through classroom study, in-class activity, and hands-on, inquiry-based laboratory work as they explore concepts like systems, fields, force interactions, change, conservation, waves, and probability.\

The course content is organized into seven commonly taught units, which have been arranged in the following suggested, logical sequence: ■ Unit 1: Fluids ■ Unit 2: Thermodynamics ■ Unit 3: Electric Force, Field, and Potential ■ Unit 4: Electric Circuits ■ Unit 5: Magnetism and Electromagnetic Induction ■ Unit 6: Geometric and Physical Optics ■ Unit 7: Quantum, Atomic, and Nuclear Physics Each unit is broken down into teachable segments called topics.

In addition, the following BIG IDEAS serve as the foundation of the course, enabling students to create meaningful connections among concepts and develop deeper conceptual understanding:

■ Systems: Objects and systems have properties such as mass and charge. ■ Fields: Fields existing in space can be used to explain interactions. ■ Force Interactions: The interactions of an object with other objects can be described by forces. ■ Change: Interactions between systems can result in changes in those systems. ■ Conservation: Changes that occur as a result of interactions are constrained by conservation laws. ■ Waves: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass. ■ Probability: The mathematics of probability can be used to describe the behavior of complex systems.

**College Course Equivalent** AP Physics 2 is a full-year course that is the equivalent of a second-semester introductory college course in algebra-based physics.

**Prerequisites** Students should have completed AP Physics 1 or a comparable introductory physics course and should have taken or be concurrently taking pre-calculus or an equivalent course.