• # Algebra 1A

• The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Algebra 1A (Year 1)

Unit 1- Relationships Between Quantities and Reasoning with Equations: By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. Now, students analyze and explain the process of solving an equation. Students develop fluency in writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations.

Unit 2- Linear and Exponential Relationships: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students explore systems of equations and inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.

# Algebra I and Algebra I Honors

• The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, called units, deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Standards for Mathematical Practice apply throughout each course, and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Unit 1- Relationships Between Quantities and Reasoning with Equations: By the end of eighth grade students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. This unit builds on these earlier experiences by asking students to analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. All of this work is grounded on understanding quantities and on relationships between them.

SKILLS TO MAINTAIN:
Reinforce understanding of the properties of integer exponents. The initial experience with exponential expressions, equations, and functions involves integer exponents and builds on this understanding.

Unit 2- Linear and Exponential Relationships: In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students will learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students explore systems of equations and inequalities, and they find and interpret their solutions. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions.

Unit 3- Descriptive Statistics: This unit builds upon students prior experiences with data, providing students with more formal means of assessing how a model fits data. Students use regression techniques to describe and approximate linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

Unit 4- Expressions and Equations: In this unit, students build on their knowledge from unit 2, where they extended the laws of exponents to rational exponents. Students apply this new understanding of number and strengthen their ability to see structure in and create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions.

Unit 5- Quadratic Functions and Modeling: In this unit, students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students expand their experience with functions to include more specialized functions, absolute value, step, and those that are piece wise-defined.

# Geometry & Geometry I Honors

• The fundamental purpose of the course in Geometry is to formalize and extend students' geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school standards. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical areas, organized into five units are as follows.

Unit 1-Congruence, Proof, and Constructions: In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions: translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems using a variety of formats and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.

Unit 2- Similarity, Proof, and Trigonometry: Students apply their earlier experience with dilation and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of triangles, use similarity to solve problems and apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean theorem. Students develop the Laws of Sines and Cosines in order to find missing measures of general (not necessarily right) triangles, building on students work with quadratic equations done in the first course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles.

Unit 3- Extending to Three Dimensions: Students' experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line.

Unit 4- Connecting Algebra and Geometry Through Coordinates: Building on their work with the Pythagorean theorem in 8th grade to find distances, students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in the first course. Students continue their study of quadratics by connecting the geometric and algebraic definitions of the parabola.

Unit 5-Circles With and Without Coordinates: In this unit students prove basic theorems about circles, such as a tangent line is perpendicular to a radius, inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations, which relates back to work done in the first course, to determine intersections between lines and circles or parabolas and between two circles.

# Algebra II & Algebra II Honors

• ## Version Description

Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and radical functions. Students work closely with the expressions that define the functions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. The Standards for Mathematical Practice apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. The critical areas for this course, organized into five units, are as follows:

Unit 1- Polynomial, Rational, and Radical Relationships:This unit develops the structural similarities between the system of polynomials and the system of integers. Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of polynomials with multiplication of multi-digit integers, and division of polynomials with long division of integers. Students identify zeros of polynomials, including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and solutions of polynomial equations. The unit culminates with the fundamental theorem of algebra. A central theme of this unit is that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers.

Unit 2- Trigonometric Functions: Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry, students now use the coordinate plane to extend trigonometry to model periodic phenomena.

Unit 3- Modeling with Functions: In this unit students synthesize and generalize what they have learned about a variety of function families. They extend their work with exponential functions to include solving exponential equations with logarithms. They explore the effects of transformations on graphs of diverse functions, including functions arising in an application, in order to abstract the general principle that transformations on a graph always have the same effect regardless of the type of the underlying function. They identify appropriate types of functions to model a situation, they adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as - the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions' is at the heart of this unit. The narrative discussion and diagram of the modeling cycle should be considered when knowledge of functions, statistics, and geometry is applied in a modeling context.

Unit 4- Inferences and Conclusions from Data: In this unit, students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify different ways of collecting data, including sample surveys, experiments, and simulations, and the role that randomness and careful design play in the conclusions that can be drawn.

Unit 5- Applications of Probability: Building on probability concepts that began in the middle grades, students use the languages of set theory to expand their ability to compute and interpret theoretical and experimental probabilities for compound events, attending to mutually exclusive events, independent events, and conditional probability. Students should make use of geometric probability models wherever possible. They use probability to make informed decisions.

• This course is targeted for students who are not yet "college ready" in mathematics or simply need some additional instruction in content to prepare them for success in college level mathematics.  This course incorporates the Florida Standards for Mathematical Practices as well as the following Florida Standards for Mathematical Content: Expressions and Equations, The Number System, Functions, Algebra, Geometry, Number and Quantity, Statistics and Probability, and the Florida Standards for High School Modeling.  The standards align with the Mathematics Postsecondary Readiness Competencies deemed necessary for entry-level college courses.

# Pre-Calculus

• Honors and Advanced Level Course Note: Advanced courses require a greater demand on students through increased academic rigor.  Academic rigor is obtained through the application, analysis, evaluation, and creation of complex ideas that are often abstract and multi-faceted.  Students are challenged to think and collaborate critically on the content they are learning. Honors level rigor will be achieved by increasing text complexity through text selection, focus on high-level qualitative measures, and complexity of task. Instruction will be structured to give students a deeper understanding of conceptual themes and organization within and across disciplines. Academic rigor is more than simply assigning to students a greater quantity of work.

# AP Calculus

• AP Calculus AB is an introductory college-level calculus course. 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.

Based on the Understanding by Design® (Wiggins and McTighe) model, this course framework provides a clear and detailed description of the course requirements necessary for student success. The framework specifies what students must know, be able to do, and understand, with a focus on big ideas that encompass core principles, theories, and processes of the discipline. The framework also encourages instruction that prepares students for advanced coursework in mathematics or other fields engaged in modeling change (e.g., pure sciences, engineering, or economics) and for creating useful, reasonable solutions to problems encountered in an ever-changing world.

The AP Calculus AB framework is organized into eight commonly taught units of study that provide one possible sequence for the course. As always, you have the flexibility to organize the course content as you like.

Unit

Exam Weighting (Multiple-Choice)

Unit 1: Limits and Continuity

10%–12%

Unit 2: Differentiation: Definition and Fundamental Properties

10%–12%

Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

9%–13%

Unit 4: Contextual Applications of Differentiation

10%–15%

Unit 5: Analytical Applications of Differentiation

15%–18%

Unit 6: Integration and Accumulation of Change

17%–20%

Unit 7: Differential Equations

6%–12%

Unit 8: Applications of Integration

10%–15%

### Mathematical Practices

The AP Calculus AB framework included in the course and exam description outlines distinct skills, called mathematical practices, that students should practice throughout the year—skills that will help them learn to think and act like mathematicians.

# AP Statistics

• AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem-solving, and writing as they explore concepts like variation and distribution; patterns and uncertainty; and data-based predictions, decisions, and conclusions.

Based on the Understanding by Design® (Wiggins and McTighe) model, this course framework provides a clear and detailed description of the course requirements necessary for student success. The framework specifies what students must know, be able to do, and understand, with a focus on three big ideas that encompass the principles and processes in the discipline of statistics. The framework also encourages instruction that prepares students for advanced coursework in statistics or other fields using statistical reasoning and for active, informed engagement with a world of data to be interpreted appropriately and applied wisely to make informed decisions.

The AP Statistics framework is organized into nine commonly taught units of study that provide one possible sequence for the course. As always, you have the flexibility to organize the course content as you like.

##### Exam Weighting (Multiple-Choice Section)
Unit 1: Exploring One-Variable Data  15%–23%
Unit 2: Exploring Two-Variable Data  5%–7%
Unit 3: Collecting Data  12%–15%
Unit 4: Probability, Random Variables, and Probability Distributions  10%–20%
Unit 5: Sampling Distributions  7%–12%
Unit 6: Inference for Categorical Data: Proportions  12%–15%
Unit 7: Inference for Quantitative Data: Means  10%–18%
Unit 8: Inference for Categorical Data: Chi-Square  2%–5%
Unit 9: Inference for Quantitative Data: Slopes  2%–5%

# MAT 1033 Intermediate Algebra- TCC

• Prerequisite(s): appropriate placement score or satisfactory completion of MAT0028. MAT1033 cannot be taken for credit by any student who has a grade of C or better in any higher mathematics course.

This course carries elective credit and does not count toward the six hours of mathematics required for the A.A. degree. Major topics include linear equations, linear inequalities, systems of linear equations, inequalities in two variables and their graphs, introduction to relations and functions, rational exponents, operations with rational expressions, complex fractions and rational equations, operations with radical expressions, and radical equations and quadratic equations. Application problems of various types are included to reinforce skills and concepts. This class includes a computer component that will require students to complete online computer assignments out of class, either at home or in the computer labs provided on campus. A scientific calculator is required for this course; it does not have to be a graphing calculator. Check with the instructor for the most appropriate type of calculator. Lecture: 3 hours. Elective credit only; does not satisfy the general education mathematics requirement.

# MAT 1105 College Algebra- TCC

• Prerequisite(s): grade of C or better in MAT1033, or appropriate score on the placement test.
Topics include characteristics of functions in general; inverse functions; linear, quadratic, rational, absolute value, radical, exponential and logarithmic functions and equations; systems of equations and inequalities; and applications. May not be taken for credit by any student having a grade of C or better in a higher-level math course. Does not satisfy degree requirements for students with credit in MAC1102. Lecture: 3 hours. A TI-83 or TI-84 graphing calculator is required.

# Personal Financial Literacy

• This grade 9-12 course consists of the following content area and literacy strands: Economics, Financial Literacy, Mathematics, Languages Arts for Literacy in History/Social Studies and Speaking and Listening. Basic economic concepts of scarcity, choice, opportunity cost, and cost/benefit analysis are interwoven throughout the standards and objectives. Emphasis will be placed on economic decision-making and real-life applications using real data.

The primary content for the course pertains to the study of learning the ideas, concepts, knowledge and skills that will enable students to implement beneficial personal decision-making choices; to become wise, successful, and knowledgeable consumers, savers, investors, users of credit and money managers; and to be participating members of a global workforce and society.

Content should include, but not be limited to:

• cost/Benefit analysis of economic decisions
• earning an income
• understanding state and federal taxes
• utilizing banking and financial services
• balancing a checkbook and managing a bank account
• savings, investment and planning for retirement
• understanding loans and borrowing money, including predatory lending and payday loans
• understanding interest, credit card debt and online commerce
• how to prevent identify fraud and theft
• rights and responsibilities of renting or buying a home
• understanding and planning for major financial purchases
• understanding the costs and benefits of insurance
• understanding the financial impact and consequence of gambling
• avoiding and filing bankruptcy
• reducing tax liability.
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