Algebra 1 Mathematics

Texts The Cognitive Tutor, www.CarnegieLearning.com

Course Overview

This course teaches Algebra of real numbers, with technology-reinforced emphasis on functions, evaluating, simplifying, and factoring polynomial, rational, and radical expressions; solving and graphing linear and quadratic equations and inequalities; solving related story problems.

Skills Taught

The student will be able to: • Analyze and solve linear, quadratic, exponential, proportional,

inequality, absolute value, systems of equations and radical word problems.

• Understand and explain linear, inequality, and quadratic graphs. • Acquire the unknown value in a multi-step linear equation,

quadratic equation, absolute value equation and system of linear equations.

• Communicate the steps in solving equations and the procedure to finding an unknown quantity.

• Explore the relationship between independent and dependent variables graphically through the study of functions.

• Express the relationship between independent and dependent variables found in word problems through equations.

• Demonstrate understanding of algebraic vocabulary and algebraic properties used to simplify and solve equations.

• Determine the reasonableness of an answer. • Explore how Algebra applies to the real world and how we can use

it to help us in our everyday lives after high school. • Acquire a love and appreciation of mathematics.

Assessments Quizzes, Tests, Cognitive Tutor, Daily Worksheets Sample Activities

Matho Jeopardy Partner Competitions Working problems posted around the room Collecting real world data to analyze ratios, proportions, and percents I have, Who has? Bungee Barbie & Kamikazee Ken Exponents Magic Square Radicals Baseball Basketball Video about Parabolas White Board Races Graphing on Individual White Boards

Technology

The Cognitive Tutor, www.CarnegieLearning.com Graphing Calculator (TI-84 Plus Silver Edition) Classroom Technology Document Camera with Wireless Projector

Geometry Mathematics

Texts Geometry, Larson, Boswell, Kanold, Stiff; Holt McDougal, 2011.

Course Overview

This course introduces students to concepts of plane, solid, and coordinate geometry, with emphasis on the development of student’s skills in inductive and deductive reasoning, spatial visualization, pictorial representation, and problem-solving. A variety of proof forms, both written and oral, will be used to develop logical reasoning. Connections between algebra and geometry will be reinforced through the use of coordinate geometry and review of algebra concepts.

Skills Taught

The student will be able to: • Analyze how and why geometric theorems work. • Articulate their reasoning in the problem-solving process. • Compare and contrast problems and their solutions for

reasonableness and accuracy. • Connect the structure of a mathematical system, connecting

definitions, postulates, logical reasoning, and theorems. • Cooperate with other students to facilitate learning and problem-

solving. • Describe geometric relationships using correct vocabulary and

standard symbols • Listen carefully in order to follow directions completely and to

identify relevant information for well-defining and solving problems. • Participate actively in the learning process so as “to own” the

learning. • Persevere in the learning process, despite whatever difficulties are

encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. • Prove inductively or deductively, as appropriate, the mathematical

results (properties, formulae, theorem conclusions, etc.) studied in the course.

• Synthesize mathematical concepts and problem-solving strategies together to create strategies to solve unfamiliar problems.

Assessments Unit test and quizzes. The Cognitive Tutor.

Sample Activities

Proof Puzzles: Statements and reasons in proofs can be cut up for students in groups to rearrange to form a logical proof. Use Geometer’s Sketchpad to create polygon designs and line art Use Geometer’s Sketchpad to draw a Serpienski’s Triangle Use models of rectangles and parallelograms on dot paper to derive the

formula for area of a parallelogram, triangle, and trapezoid Create a movie showing various geometric relationships in the world around us Create a family tree to organize the relationships between the quadrilaterals

Technology

The Cognitive Tutor, www.CarnegieLearning.com Graphing Calculator (TI-84 Plus Silver Edition) Geometer’s Sketchpad iMovie

Geometry Honors Mathematics

Texts

Geometry, Jurgensen, Ray; Brown, Richard; and Jurgensen, John; McDougal Littell, 2004.

Course Overview

This course introduces students to concepts of plane, solid, and coordinate geometry, with emphasis on the development of students’ skills in inductive and deductive reasoning, spatial visualization, pictorial representation, and problem solving. A variety of proof forms, both written and oral, will be used to develop logical reasoning. Connections between algebra and geometry will be reinforced through the use of coordinate geometry and review of algebra concepts. The honors level involves accelerated and deeper study of geometry topics, with emphasis on deductive reasoning and formal proof.

Skills Taught

The student will be able to: • Describe geometric relationships using correct vocabulary and

standard symbols. • Appreciate the structure of a mathematical system, connecting

definitions, postulates, logical reasoning, and theorems. • Create a logical argument to justify and prove mathematical

statements deductively with symbolic logic, two-column proofs, paragraph proofs, or indirect proofs.

• See numeric and geometric patterns and formulate generalizations or conjectures about properties of geometric figures.

• Analyze characteristics and properties of two- and three-dimensional geometric objects.

• Determine appropriate formulas for measurable attributes of geometric objects and perform calculations with formulas for measurements such as perimeter, area, and volume.

• Connect algebraic skills to geometric concepts and describe special relationships such as collinearity, perpendicularity, and parallelism using coordinate geometry.

• Synthesize geometric ideas, relationships, and properties to solve meaningful real-world problems, with a variety of representations (concrete, pictorial, numerical, symbolic, graphical and verbal), tools, and technology.

• Articulate reasoning in the problem-solving process. • Connect transformations and symmetry to geometric concepts such

as congruence and similarity. Assessments Daily assignments

Tests and quizzes Mid-year and final exams Sketchpad activities and projects

Sample Activities

Proof Puzzles: Statements and reasons in proofs can be cut up for students in groups to rearrange to form a logical proof.

Use Geometer’s Sketchpad to discover and test conjectures. Polygon design project and Fractals with Geometer’s Sketchpad.

Day Scavenger Hunt on the Internet Make a Tetralope, a pyramid made out of an envelope. Create a family tree or flow chart to classify types of quadrilaterals and organize their properties.

Technology

Graphing Calculator (TI-84 Plus Silver Edition) Geometer’s Sketchpad Dynamic Software You-tube videos, Numberphile, channel for numbers and math Hotmath.com website for hints and step-by-step explanations for the odd-numbered homework problems in our text.

Algebra 2 Mathematics

Texts Algebra II, Holt, Rinehart, & Winston

Course Overview

This course provides a review and extension of Algebra 1; algebra of real and complex numbers, with technology-reinforced emphasis on functions; evaluating, simplifying, and factoring polynomial, rational, radical, exponential, and logarithmic expressions; solving and graphing related equations, inequalities, and systems of equations; solving related story problems.

Skills Taught

The student will be able to: • Analyze and represent mathematical situations using algebraic

symbols. • Communicate using proper mathematical terms to logically explain

a step by step process. • Compare transformations, symmetry and describe relationships

between functions using coordinate geometry • Formulate strategies in problem solving processes. • Understand numbers, types of numbers, number systems,

representing numbers, operations. • Create mathematical models to understand quantitative

relationships. • Cooperate with other students to facilitate learning and problem-

solving. • Listen carefully in order to follow directions completely and to

identify relevant information for well-defining and solving problems. • Participate actively in the learning process so as “to own” the

learning. • Persevere in the learning process, despite whatever difficulties are

encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. • Prove deductively and inductively, as appropriate, the mathematical

results studied in the course. • Synthesize mathematical concepts and problem-solving strategies

together to create strategies to solve unfamiliar problems. Assessments Unit test and quizzes. Sample Activities

Find examples of conic structures in the environment and in man-made materials. Projects relating linear systems in real life situations. Theoretical vs. Experimental probability with M&M packages

Technology

Graphing Calculator (TI-84 Plus Silver Edition) Mathematica and www.WolframAlpha.com .

EHS Student and Faculty Portals Interactive assignment calendars Bulletins announcing major events All class materials posted in Resources Links to useful websites and videos

Classroom Technology Document Camera with Wireless Projector SmartBoard with Epson Easy Interactive Tools TI-84 Emulator Software

Algebra 2 Honors Mathematics Texts

College Algebra, 5th edition; Blitzer, Robert; Pearson/Prentice Hall, 2010.

Course Overview

Accelerated and deeper study of regular Algebra 2 topics, with emphasis on applications, derivation, and proof, including: Review and extension of Algebra 1. Algebra of real and complex numbers. Technology-reinforced emphasis on functions. Evaluating, simplifying, and factoring polynomial, rational, radical, exponential, and logarithmic expressions. Solving and graphing related equations, inequalities, and systems of equations. Basic matrix algebra. Sequences, series, combinatorics. Solving related story problems.

Skills Taught

The student will be able to: • Analyze how and why the mathematics they study works. • Appreciate the beauty, simplicity, and power of mathematics as a

language to communicate succinctly, accurately, and persuasively about realities, particularly complex and subtle ones.

• Articulate their reasoning in the problem-solving process. • Compare and contrast problems and their solutions for

reasonableness and accuracy, that is, check answers. • Connect current learning with skills and knowledge acquired during

all previous studies of mathematics. • Cooperate with other students to facilitate learning and problem-

solving. • Create mathematical models to describe quantitative phenomena

that are encountered theoretically and in students’ everyday life. • Evaluate mathematical expressions, particularly polynomial,

rational, exponential, and logarithmic expressions in one variable. • Express cause and effect relationships between quantities in the

language of mathematics. • Imagine the geometry of algebraic expressions as an aid to

understanding those expressions and their mathematical implications. • Initiate on their own whatever action is necessary to master the

skills and knowledge that are the subject matter of this course and to refresh material from previous math courses.

• Listen carefully in order to follow directions completely and to identify relevant information for well-defining and solving problems.

• Organize course materials for easy retrieval, use, and reuse, as in using a 3-ring binder effectively.

• Participate actively in the learning process so as “to own” the learning.

• Perform mathematical computations efficiently and accurately by hand and, when appropriate, using technology.

• Persevere in the learning process, despite whatever difficulties are encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. • Prove inductively or deductively, as appropriate, the mathematical

results (properties, formulae, theorem conclusions, etc.) studied in the course.

• Question all assumptions in the problem-solving process. • Solve relational expressions (equations and inequalities) • Synthesize disparate mathematical concepts and problem-solving

strategies together to create strategies to solve unfamiliar problems. • Understand mathematics as the language for understanding and

communicating about the quantitative reality of which students are a part.

Assessments Unit test and quizzes. The Cognitive Tutor.

Sample Activities

View The Proof of Fermat’s Last Theorem video & complete note sheet. Prove . Prove is irrational. Program calculators with the quadratic formula and use it to solve quadratic equations. Derive the quadratic formula using completing the square. Compute curves of best fit using TI-84 graphing calculator and MS Excel. Build a Synthetic Division Machine in MS Excel, applying the Remainder, Factor, and Rational Roots Theorems, to factor polynomials. Derive the laws of exponents. Derive the laws of logarithms from the properties of exponents. Use Geometer’s Sketchpad to investigate affect of coefficients in exponential and logarithmic functions. Derive equations of conic sections; emphasize function vs relation. Use Mathematica and WolframAlpha to factor, multiply, and graph polynomials.

Technology

The Cognitive Tutor, www.CarnegieLearning.com Graphing Calculator (TI-84 Plus Silver Edition) Microsoft Excel Geometer’s Sketchpad Mathematica and www.WolframAlpha.com

Precalculus Mathematics

Texts Precalculus, Larson Course Overview

Trigonometry, elementary analysis, and discrete mathematics, with technology-reinforced emphasis on functions; prepares students for college-entrance exams, Calculus, and college mathematics

Skills Taught

The student will be able to: Review of Algebra 2 • Analyze and represent mathematical situations using algebraic

symbols. • Communicate using proper mathematical terms to logically explain

a step by step process. • Compare transformations, symmetry and describe relationships

between functions using coordinate geometry • Formulate strategies in problem solving processes. • Understand numbers, types of numbers, number systems,

representing numbers, operations. Trigonometry, Discrete, Elem Analysis • Strategize using concepts and application of Trigonometry. • Express ideas coherently verbally and in writing using

Trigonometric terminology. • Develop further critical thinking and problem solving skills. • Create mathematical models to understand quantitative

relationships. • Cooperate with other students to facilitate learning and problem-

solving. • Listen carefully in order to follow directions completely and to

identify relevant information for well-defining and solving problems. • Participate actively in the learning process so as “to own” the

learning. • Persevere in the learning process, despite whatever difficulties are

encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. • Prove deductively and inductively, as appropriate, the mathematical

results studied in the course. • Synthesize mathematical concepts and problem-solving strategies

together to create strategies to solve unfamiliar problems.

Assessments Unit test and quizzes.

Sample Activities

Unit Circle project to visualize and use hands on activity to create a unit circle. Find examples of conic structures in the environment and in man made materials. Projects relating linear systems in real life situations. Theoretical vs. Experimental probability with M&M packages

Technology

Graphing Calculator (TI-84 Plus Silver Edition) Mathematica and www.WolframAlpha.com .

EHS Student and Faculty Portals Interactive assignment calendars Bulletins announcing major events All class materials posted in Resources Links to useful websites and videos

Classroom Technology Document Camera with Wireless Projector SmartBoard with Epson Easy Interactive Tools TI-84 Emulator Software

Precalculus Honors Mathematics

Texts

Precalculus with Limits: A Graphing Approach, 5th Edition by Larson, Hostetler, and Edwards; Houghton Mifflin, 2008.

Course Overview

Precalculus Honors prepares students for the study of calculus through understanding the verbal, numerical, graphical, and symbolic representations of functions and using them to model real-life problems. These types of functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise. Analytic trigonometry, analytic geometry, sequences, series, probability, and basic statistics are also covered.

Skills Taught

The student will be able to: • Demonstrate the understanding of concepts from multiple perspectives –

algebraically, graphically, and numerically. • Analyze and connect mathematical concepts to real-life data and applications. • Discover and appreciate that problems may be solved in more than one way

or that different methods yield the same result. • Acquire and demonstrate strong note-taking and test-taking skills. • Aspire to and persevere in developing the abilities to visualize, analyze, and

describe accurately and coherently the theoretical and practical aspects of mathematics.

• Listen attentively to, evaluate thoroughly, and challenge appropriately the mathematical thinking and strategies of others.

• Understand the need and develop the confidence to become more reflective and independent while maintaining the collaborative skills useful for success beyond the school years.

• Explore the use of technology and other resources in developing critical thinking skills, problem-solving strategies, and greater mastery of the material.

Assessments Class Discussion Homework Quizzes Exams Unit Tests

Sample Activities

Use Excel for loan payment and other types of financial analysis. Use patty papers to explore conic sections. Use a graphing calculator and parametric equations to simulate a free throw for basketball and examine the effects of the angle of launch, initial height, and initial velocity.

Technology

Geometer’s Sketchpad Graphing Calculator (TI-84 Plus Silver Edition) Microsoft Excel

Calculus Mathematics

Texts

Calculus of a Single Variable, Larson, Ron and Edwards, Bruce; Brooks/Cole Cengage Learning, 9th Edition, 2010.

Course Overview

This course extends students’ previous study of basic functions through an understanding of limits, derivatives, and integrals. Students should be able to apply calculus concepts in order to analyze various functions and interpret models of dynamic situations. The course employs a multi-representational approach (graphical, numerical, analytical, and verbal). This course aims to prepare students for a college level calculus course, to develop problems solving skills, and to develop an appreciation for how calculus can be used to describe the world.

Skills Taught

The student will be able to: • Interpret functions represented in a variety of ways: graphically,

numerically, analytically, and verbally and analyze the connections among those representations.

• Understand the meaning of the derivative in terms of a rate of change and local linear approximations, and solve a variety of problems using derivatives.

• Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and solve a variety of problems using integrals.

• Express the relationship between the derivative and the definite integral using both parts of the Fundamental Theorem of Calculus.

• Communicate mathematics and explain solutions to problems both verbally and in written sentences.

• Persevere in the learning process, despite whatever difficulties are encountered, to master the skills and knowledge that are the subject matter of the course.

• Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

• Synthesize mathematical concepts and problem-solving strategies together to create strategies to solve unfamiliar problems.

• Appreciate calculus as a coherent body of knowledge and as a human accomplishment.

Assessments Daily Homework Quizzes Tests Mid-year and Final comprehensive exams

Sample Activities

Investigating theorems using Calculus in Motion on Geometer’s Sketchpad Differentiability activity to explore the differentiability of different piecewise functions

Learning the relationship between a function and its derivative using a card matching game (f and f ’) Partner competitions Jeopardy Running activity to find the average rate of change and compare it to the instantaneous rate of change Derivative flashcard matching activity Using integrals to find the volume of a plastic cup

Technology

TI-84 Plus Graphing Calculator Online eTextbook and assignments (www.webassign.com) Online Student Solutions (www.calcchat.com) EHS Student and Faculty Portals

Assignment calendars All class materials posted in Resources

Classroom Technology Document Camera with Wireless Projector Eno Board with Epson Easy Interactive Tools TI-84 Emulator Software

AB Calculus AP Mathematics

Texts

Calculus of a Single Variable, Larson, Ron and Edwards, Bruce; Brooks/Cole Cengage Learning, 9th Edition, 2010.

Course Overview

Course is comparable to a college-level, first-semester course in differential and integral calculus with applications; prepares students for the Advanced Placement Calculus AB exam.

Skills Taught

The student will be able to: • Interpret functions represented in a variety of ways: graphically,

numerically, analytically, and verbally and understand the connections among those representations.

• Understand the meaning of the derivative in terms of a rate of change and local linear approximations, and solve a variety of problems using derivatives.

• Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and solve a variety of problems using integrals.

• Express the relationship between the derivative and the definite integral using both parts of the Fundamental Theorem of Calculus.

• Communicate mathematics and explain solutions to problems both verbally and in written sentences.

• Describe a physical situation with a function, a differential equation, or an integral.

• Solve problems, experiment, interpret results, and support conclusions using technology.

• Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

• Appreciate calculus as a coherent body of knowledge and as a human accomplishment.

Assessments Graded homework and assignments Quizzes Tests Mid-year comprehensive exam Practice AP Exam

Sample Activities

Working practice AP free-response questions Investigating theorems using Calculus in Motion on Geometer’s Sketchpad Learning the relationship between slope fields and differential equations using a card matching game Critiquing student responses to homework questions using the document cameraUsing programs in the TI-84 graphing calculator to investigate Riemann sums and area under a curve

Technology

TI-84 Plus Graphing Calculator Online eTextbook (www.webassign.com) Online Student Solutions (www.calcchat.com) Online multiple-choice question practice (www.webassign.com) EHS Student and Faculty Portals

Interactive assignment calendars Bulletins announcing major events All class materials posted in Resources Links to useful websites and videos WOWmath.org math videos YouTube channel: RobbWorld (http://www.youtube.com/user/RobbWorld#g/p) MacTutor History of Mathematics website (http://turnbull.mcs.st-and.ac.uk/~history/index.html) Women Mathematicians (http://www.agnesscott.edu/lriddle/women/ women.htm) Visual Calculus website (http://archives.math.utk.edu/visual.calculus/index.html) Paul’s Online Calculus Notes (http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx)

Classroom Technology Document Camera with Wireless Projector SmartBoard with Epson Easy Interactive Tools TI-84 Emulator Software

AP Calculus BC Mathematics

Texts

Calculus of a Single Variable AP* Edition, Larson, Edwards, Brooks/Cole, Cengage Learning, 9e, 2010.

Course Overview

The course addresses all topics that are listed in the Topic Outline for Calculus BC, which is contained in the AP® Calculus Course Description, and aims to prepare students to place out of two semesters of comparable college calculus courses. The course capstones and extends students’ previous study of basic functions, their properties, algebra, and graphs, through a careful development and interweaving of the core themes of limits, derivatives, integrals, and calculus-based approximations into a coherent whole that equips students to apply calculus concepts to model dynamic behavior and to analyze functions, including those expressed in parametric, polar, or vector form. The course employs a multi-representational and interconnected approach (graphical, numerical, analytical, and verbal) and emphasizes the use of technology, student collaboration, and articulate communication about mathematics. The course aims to help students develop an appreciation for the beauty of mathematics, in general, and for the utility of calculus, in particular, for solving problems and for acquiring a deeper understanding of the universe of which the students are a part. The course helps students lay a solid mathematical foundation upon which to pursue appropriate, subsequent college studies in mathematics and related disciplines.

Skills Taught

The student will be able to: • Understand (1) functions represented in a variety of ways -

graphical, numerical, analytical, or verbal – and the connections among these representations; (2) the meaning of the derivative in terms of a rate of change and local linear approximation; (3) the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change; and (4) the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

• Solve a variety of pure and applied mathematical problems using derivatives and integrals.

• Explain solutions to problems both verbally and in written sentences.

• Create a mathematical model from a written description of a physical situation using a function, a differential equation, or an integral.

• Use technology to help solve problems, experiment, interpret results, and support conclusions.

• Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

• Appreciate calculus as a coherent body of knowledge and as a human accomplishment.

• Cooperate with other students to facilitate learning and problem-solving.

• Listen carefully in order to follow directions completely and to identify relevant information for well-defining and solving problems.

• Participate actively in the learning process so as “to own” the learning.

• Persevere in the learning process, despite whatever difficulties are encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. Assessments Chapter tests.

Formula quizzes. Mid-year exam. An optional end-of-year Practice AP® Calculus BC exam.

Sample Activities

Prove Properties of Derivatives Theorems. Prove Properties of Integrals Theorems. In-class and homework practice problems from past AP® Calculus AB and BC Exams.

Technology Graphing Calculator (TI-84 Plus Silver Edition). On-line eTextbook (www.WebAssign.com). On-line Student Solution Manual (www.CalcChat.com ). On-line lecture videos: www.HoustonACT.org, www.KhanAcademy.com http://ocw.mit.edu/high-school/courses/highlights-of-calculus Mathematica and www.WolframAlpha.com . Calculus in Motion (Geometer’s Sketchpad).

Statistics AP Mathematics

Texts

The Practice of Statistics, Starnes, Daren; Yates, Daniel, and Moore, David; W.H. Freeman, 4th edition, 2010. 5 Steps to a 5, AP Statistics, Hinders, Duane, McGraw-Hill, 2011

Course Overview

Introductory college-level course in statistics, with emphasis on experimental design, collecting data, addressing assumptions, selecting appropriate statistical tests, explaining conclusions drawn, and using technology; course requires use of writing and critical- thinking skills; prepares students for the Advanced Placement Statistics exam.

Skills Taught

The student will be able to: • Analyze collected data with appropriate graphical and numerical

techniques to study patterns and departures from patterns. • Determine important characteristics of a sampling distribution such

as shape, center, and variability. • Create a plan for collecting data for a survey or well-designed

experiment to avoid sources of bias, placebo effect, and confounding variables.

• Critique a statistical study in the real world for its design, implementation, and conclusions.

• Perform the appropriate statistical inference procedures using tables, a calculator, or Fathom software to construct a confidence interval or complete a hypothesis test.

• Communicate statistical results in the appropriate context and explain conclusions both verbally and in written sentences.

• Understand the difference between association and causation. • Analyze statistical results and conclusions for experimental designs,

in addition to ways in which statistics can be improperly used to mislead, confuse, or distort the truth.

• Understand the role of random behavior and the applications of probability in statistical inference.

• Solve problems, experiment, interpret results, and support conclusions using technology.

• Appreciate the role of statistics in real life and in a wide variety of disciplines such as medicine, business, engineering, psychology, and mathematics.

Assessments Graded homework assignments Quizzes, Tests, Midyear Exam Practice AP / Final exam

Sample Activities

Online Fathom class survey to collect data Hiring Discrimination Simulation Random Rectangles Activity to explore sampling techniques Practice with AP Free Response questions Guessing Correlation Website

Penny Lab for Sampling Distributions M&M Lab for Chi-Square Procedures Written review of published statistical study

Technology

TI-84 Plus Calculator Fathom Dynamic Data Software YMS4e Companion Website - online quizzes, videos, statistical applets Optional online eTextbook YouTube videos Rice Virtual Lab in Statistics Applets from various websites, such as the Reese’s Pieces Applet

Finite Mathematics Mathematics

Text Finite Mathematics, Lial, Greenwell, and Ritchey; Pearson, 9th edition Course Overview

Review an extension of algebra topics, with emphasis on applications and using technology; topics include matrices, linear programming, and mathematics of finance; prepares students for introductory college mathematics.

Skills Taught

The student will be able to: • Analyze and solve linear, quadratic, exponential, proportional,

inequality, absolute value, systems of equations and radical word problems.

• Understand and explain linear, inequality, and quadratic graphs. • Evaluate matrices and understand the many uses of matrices in real

world problems. • Evaluate and research simple and compound interest, future and

present value of annuity, and amortization, then create a financial plan for buying a first home after college.

• Cooperate with other students to facilitate learning and problem-solving.

Assessments Graded homework and assignments Quizzes Tests Mid-year comprehensive exam

Sample Activities

Matho Jeopardy Partner Competitions Working problems posted around the room Collecting real world data to analyze ratios, proportions, and percents Exponents Magic Square White Board Races

Technology TI-84 Plus Graphing Calculator EHS Student and Faculty Portals

Interactive assignment calendars Bulletins announcing major events All class materials posted in Resources

Classroom Technology Document Camera with Wireless Projector SmartBoard with Epson Easy Interactive Tools TI-84 Emulator Software

Plane Trigonometry Mathematics

Texts Trigonometry, Larson and Hostetler; Houghton Mifflin, 7th edition

Course Overview

Introduction to the basic concepts of trigonometry, with emphasis on applications.

Skills Taught

The student will be able to: • Describe angles and use angles to model and solve real life problems. • Understand the unit circle, describe its relationship to real numbers,

and evaluate trigonometric functions using the unit circle and a calculator.

• Evaluate and graph all trigonometric functions and their inverses • Participate actively in the learning process so as “to own” the

learning. • Solve real life problems involving right triangles, directional

bearings, and harmonic motion. • Plan ahead properly for assessments.

Assessments Graded homework and assignments Quizzes Tests Final comprehensive exam

Sample Activities

Matho Jeopardy Partner Competitions Working problems posted around the room Creating Unit circles with paper plates

Technology

TI-84 Plus Graphing Calculator EHS Student and Faculty Portals

Interactive assignment calendars Bulletins announcing major events All class materials posted in Resources

Classroom Technology Document Camera with Wireless Projector SmartBoard with Epson Easy Interactive Tools TI-84 Emulator Software

Computer Science 1 & 2 Mathematics

Texts

How to Design Programs: An Introduction to Computing and Programming by Matthias Felleisen, Robert Bruce Findler, Matthew Flatt, Shriram Krishnamurthi published by at http://www.htdp.org.

Course Overview

This course is designed to allow students to practice solving problems and to understand related fundamental control structures, data and their common implementations.

Skills Taught

The student will be able to: • Analyze how and why geometric theorems work. • Articulate their reasoning in the problem-solving process. • Compare and contrast problems and their solutions for

reasonableness and accuracy. • Connect the structure of a mathematical system, connecting

definitions, postulates, logical reasoning, and theorems. • Cooperate with other students to facilitate learning and problem-

solving. • Describe geometric relationships using correct vocabulary and

standard symbols • Listen carefully in order to follow directions completely and to

identify relevant information for well-defining and solving problems.

• Participate actively in the learning process so as “to own” the learning.

• Persevere in the learning process, despite whatever difficulties are encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. • Prove inductively or deductively, as appropriate, the mathematical

results (properties, formulae, theorem conclusions, etc.) studied in the course.

• Synthesize mathematical concepts and problem-solving strategies together to create strategies to solve unfamiliar problems.

• Describe the role of major hardware and software components of a computer system, and their relationship to one another

• Respect the ethical and social implications of computer use • Understand a problem, analyze the problem, design a solution,

manage and implement your solution and evaluate the effectiveness of your solution

• Perform simple calculations on the binary number system and demonstrate an understanding of its relevance to the relationship

between electronics and computing • Appreciate the widespread implications of technological advances

in our everyday lives • Share ideas/projects in a classroom setting and in competitive

arenas • Design and implement simple computer-based solutions to

problems by writing, running, and debugging computer programs. • Understand simple data structures • Create algorithms to solve problems

Assessments Unit test and quizzes. Develop new programs in a timed setting Modify provided programs and documentation to create new program solutions

Sample Activities

Write programs to solve algebraic problems and expressions Calculate area and volume of common geometric shapes and objects Draw geometric shapes and patterns (ie, Sierpinski’s Triangle) Sort data using insertion sort algorithm Use recursive programs to generate sequences and series of numbers Program a solution to the popular Hangman game Create programs that read data from files, common data structures and the user Traverse a tree data structure using three different algorithms

Technology

Java Standard Development Kit Student laptop computers ENO Smartboard Integrated Development Environment (DrJava or BlueJ)

Computer Science AP Mathematics

Text Exposure Java 2012, Leon Schram

Course Overview

This course is designed to allow students to practice solving problems by using an Object-Oriented Design in program development and to understand related fundamental data structures and their common implementations. The course includes a variety of projects involving interactive classes integrated throughout the course, including a project where students design and implement simple card games and an interactive grid based game.

Skills Taught

The student will be able to: • Analyze how and why programmatic solutions work. • Articulate their reasoning in the problem-solving process. • Compare and contrast problems and their solutions for

reasonableness and accuracy. • Connect the structure of a mathematical system, connecting

definitions, postulates, logical reasoning, and theorems. • Cooperate with other students to facilitate learning and problem-

solving. • Describe relationships between program objects using correct

vocabulary and standard symbols • Listen carefully in order to follow directions completely and to

identify relevant information for well-defining and solving problems. • Participate actively in the learning process so as “to own” the

learning. • Persevere in the learning process, despite whatever difficulties are

encountered, to master the skills and knowledge that are the subject matter of the course.

• Plan ahead properly for assessments. • Prioritize activities in order to devote sufficient time to master the

subject matter of the course. • Synthesize mathematical concepts and problem-solving strategies

together to create strategies to solve unfamiliar problems. • Create computer-based solutions to problems by writing, running,

and debugging computer programs. • Evaluate commonly-used algorithms and data structures • Create and evaluate algorithms and data structures to solve

problems • Write structured program code fluently in an object-oriented

paradigm using the programming language Java. • Understand the standard Java library classes from the AP Java

subset • Understand a large program consisting of several classes and

interacting objects. • Interpret a description of the design and development process

leading to such a program. (An example of such a program is the AP Computer Science Case Study.)

• Explain the roles of the major hardware and software components of a computer system, their relationship to one another, and the roles of these components within the system

• Respect the ethical and social implications of computer use Assessments Unit test and quizzes.

Develop new programs in a timed setting Modify provided programs and documentation to create new program solutions

Sample Activities

Write Java programs to create overflow and demonstrate the limitations of a computing device Use logarithms and quadratics to explain the performance of a program Use provided classes of Card objects to develop a simple interactive card game Create programs that read data from files, common data structures and the user Traverse a tree data structure using three different algorithms Implement, analyze and test common sort routines (Insertion, Selection, Merge, Heap) Develop an interactive Java application based on the AP GridWorld distribution

Technology

Java Standard Development Kit Student laptop computers ENO Smartboard Integrated Development Environment (DrJava or BlueJ)