North East Independent School District, San Antonio, Texas

Curriculum & Instruction Mathematics

Philosophy	Guiding Principles	Indicators of Excellence	Course Sequence K-9
Course Sequence 9-12	Course of Study - K	Course of Study 1-2	Course of Study 3-4
Course of Study 5-6	Course of Study 7-8	Course of Study Algebra 1	Course of Study Geometry
Course of Study Algebra II	Course of Study Precalculus	Course of Study Mathematical Models	Course of Study AP Statistics
Course of Study AP Calculus A/B	Course of Study AP Calculus B/C	Elementary Program	Secondary Program

Mathematics Program Coordinator - Lori Murach - 804-7165 ext. 360

North East ISD Mathematics Philosophy

"Knowing mathematics means being able to use it in purposeful ways.

Mathematical ability comes from being taught math so that understanding is emphasized, ideas are explored, alternate methods are encouraged and the purpose for what is being done is always evident." ( M. Burns) Core Values:

Depth of Understanding
Reasoning
Purpose
Communication

Core Purpose:

Mathematics is something to be deeply understood so that it can be used effectively.

Deep understanding of mathematics content includes:

a knowledge of relative size of numbers and how numbers are put together;

a proficiency with basic skills;

the ability to use patterns, relationships, and algebraic thinking to analyze situations;

the use of visual and spatial skills developed through the study of geometry;

a competence with a variety of techniques, tools and formulas for determining measurement; and

the ability to make sense out of data.

Effective use of mathematics includes the ability to:

solve problems arising from real-life and mathematical situations;

use computers, especially for application of tools like spreadsheets and databases, to solve time-consuming problems;

use models, known facts, properties, and relationships to explain thinking and justify answers and solution strategies; and

use patterns and relationships to analyze mathematical situations.

"Each NEISD teacher of mathematics will create a classroom environment in which students will make sense of mathematics and acquire confidence in using it. Through the NEISD Mathematics Program, students will know mathematics and be able to use it in purposeful ways."

(Dr. Richard A. Middleton)

BACK TO THE TOP OF MATHEMATICS North East Guiding Principles

Mathematics

Guiding Principles	Bibliography Source
Equity and Excellence -- It is necessary for citizens to have a more sophisticated knowledge of mathematics. Therefore, all students must become fluent and flexible in dealing with quantitative information. School mathematics programs need to nurture the development of mathematical proficiency in students who are exceptionally talented as well as those who have adequate talent.	NCTM. (2000). Principles and standards for school mathematics. Reston, VA: Author.NSF. (1996). Infusing equity in systemic reform: An implementation scheme.Carnegie Council. (1990). Turning points: preparing American youth for the 21st centuryHouse, Peggy A. (Ed.). (1987). Providing opportunities for the mathematically gifted, K-12. Reston, VA: National Council of Teachers of Mathematics.
Mathematics Curriculum -- The curriculum must be coherently structured so that all students have the opportunity to build knowledge, skills and confidence with significant mathematical ideas in the strands of number, geometry, measurement, probability, statistics, and algebraic thinking.	Mokros, J., Russell, S.J., & Economopoulos, K. (1995). Beyond arithmetic. Palo Alto: Dale Seymour Publications.Bennett, W., Finn, C. & Cribb, J. (1999). The educated child. New York: The Free Press.NCTM. (2000). Principles and standards for school mathematics. Reston, VA: Author.Slowinski, Joseph, Laine, Sabrina, & van der Ploeg, Arie. (1999, June). "Benchmarking against the TIMSS: lessons from first in the world." Policy Issues. Oak Brook, IL: NCREL
Teaching for Understanding -- Students develop understanding as they engage in experiences which allow them to draw on prior knowledge to construct new and deeper meaning of the mathematical relationships that exist. The ability to reason clearly, communicate mathematical ideas effectively, draw connections within mathematics and between mathematics and other fields, and solve real problems contribute to understanding and provide evidence of understanding.	Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olievier, A., & Human, P. (1997). Making sense. New Hampshire: Heinemann.Perkins, D. & Blythe, T. (1994, February). "Putting understanding up front." Educational Leadership, pp. 4 - 7.Zemelman, S., Daniels, H. & Hyde, A. (1993). Best practice: New standards for teaching and learning in America’s schools. New Hampshire: Heinemann. Whitin, David J., Mills, Heidi, & O’Keefe, Timothy. (1990). Living and learning mathematics. New Hampshire: Heinemann Educational Books, Inc.
Learning Environment -- To channel and focus student achievement, a stable and supportive learning environment must be provided. Teachers must vary the setting for learning to include a mix of whole class, small group and individual work. Learning environments must feel emotionally safe for learning to take place.	Caine, Renate Nummela & Caine, Geoffrey. (1990, October). "Understanding a brain-based approach to learning and teaching." Educational Leadership, pp. 66 - 70.Tomlinson, Carol Ann & Kalbfleisch, M. Layne. ( 1998, November). "Teach me, teach my brain: a call for differentiated classrooms." Educational Leadership, pp. 52 - 55.

Student-Centered Learning -- Classroom activities must be in the form of real-world applications. They include the incorporation of manipulatives or technology when appropriate and adequate time for summarization and reflection. These activities enable students to transfer information from short-term memory to long-term memory by constructing their knowledge so that they can automate skills.	Kamii, Constance & Devries, Rheta. (1978). Piaget, children, and number. Chicago, IL: Urban Education Research Program, College of Education, University of Illinois at Chicago Circle.Bastista, Michael T. (1999, February). "The mathematical miseducation of America’s youth." Phi Delta Kappan, pp. 425 - 433.Smith, Stephanie Z., Smith, Marvin E., & Romberg, Thomas A. (1993, May). "What the NCTM standards look like in one classroom." Educational Leadership, pp. 4 - 7.
Authentic Learning and Real-World Problems Appropriately challenging applications need not be delayed until after paper-and pencil skills or after theory. Each enriches the other. Applications provide rich opportunities to teach both pure and applied mathematics.	Whitin, David J., Mills, Heidi, & O’Keefe, Timothy. (1990). Living and learning mathematics. New Hampshire: Heinemann Educational Books, Inc.Usiskin, Zalman. (1993, May). "Lessons from the Chicago math project." Educational Leadership, pp. 14 - 18.
Mathematical Tools -- Appropriate use of calculators and computers is a way of increasing the amount and quality of learning afforded students during the course of their mathematics education. Students use technology to gather and interpret information, perform descriptive and graphical analysis, make statistical predictions and inferences, and create and use simulations.	Drier, Hollylynne Stohl, Dawson, Kara, & Garofalo, Joe. (1999. February). "Not your typical math class." Association for Supervision and Curriculum Development, pp. 21 - 25.Wenglinsky, Harold. (1998, September). "Does it compute? The relationship between educational technology and student achievement in mathematics." Policy Information Reports (online), Princeton, NJ: Educational Testing Service.Bright, George W., Waxman, Hersholt C., & Williams, Susan E. (Eds.). (1994). "Impact of calculators on mathematics instruction." Lanham, MD: University Press of America, Inc.Usiskin, Zalman. (1993, May). "Lessons from the Chicago math project." Educational Leadership, pp. 14 - 18.

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NORTH EAST MATHEMATICS PROGRAM:

INDICATORS OF EXCELLENCE

Teachers will:

Students Will:

Environment Reflects:

create a classroom in which all students can reflect on mathematics and communicate their thoughts and actions

pose thought-provoking questions that challenge students’ thinking and contribute to understanding

select and pose coherent sequences of activities, experiences and problems that increase students’ opportunities to forge understanding

provide balance between allowing students to pursue their own ways of thinking and providing important information that supports the development of significant mathematics analyze and reflect on student learning for planning, assessment of student learning, and communication of progress to parents consider the relationship of a task to broader mathematical goals to determine which materials/technologies/ manipulatives will enhance student understanding

communicate and justify mathematical ideas and solutions in written and oral forms develop a disposition to formulate, represent, abstract, and generalize in situations within and outside mathematics actively engage with mathematics through real/meaningful problems that are motivating and challenging develop understanding through the connection of concrete experiences to abstract representations as part of a comprehensive, coherent plan develop a repertoire of mathematical representations that can be used purposefully, flexibly, and appropriately

engage in self assessment of mathematical learning

use mathematical tools, including manipulatives and technology, appropriately to understand important mathematical ideas and to delve into content more deeply

Learning that all students can learn to communicate mathematical ideas and to participate actively in mathematical inquiry encouragement of students to question and understand mathematical relationships real-world applications of mathematics using technological tools such as calculators, data bases, spreadsheets and Internetopportunities for students to work in a variety of settings, including alone, small group, and whole class acceptance of a wide variety of strategies to solve problems and the ability to adapt them to new situations opportunities for students who work at different paces to demonstrate their abilities, thus testing learning rather than speed

Physical access to a multitude of instructional tools including technology (calculators, computers, probeware, and accompanying software) and manipulatives sufficient time for students to solve problems ample space allotment to allow for activity-based learning

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MATHEMATICS COURSE SEQUENCE

GRADES K - 9

BACK TO THE TOP OF MATHEMATICS

MATHEMATICS COURSE SEQUENCE

GRADES 9 - 12

BACK TO THE TOP OF MATHEMATICS

North East ISD

Mathematics Course of Study K - 12

Kindergarten Through hands-on experiences, games and working with concrete materials, children in kindergarten develop beginning number concepts, use patterns, describe shapes and solids and collect, organize and display data.	Number, Operations and Quantitative Reasoning Use numbers to describe objects in a set (through 20) Use language such as "more than", "same number as", and "less than" Write numerals from 0 to 10 Tell "one more than" and "one less than" a given number Identify ordinal position in a sequence Identify 1/2 of a whole and explains why it is 1/2 Model addition and subtraction problems with concrete objects Patterns, Relations and Algebraic Thinking Identify, extend, and create simple patterns of sound, physical movement and concrete objects Use patterns to predict what comes next Use number word patterns to count to 100 Geometry Use terms of position such as over/under, inside/outside, in front of/behind, top/bottom, etc. Describe, identify and compare circles, triangles and rectangles including squares Measurement Compare and order concrete objects according to length, capacity, or weight Compare situations or objects according to temperature Compare events according to duration Sequence events Read a calendar using days, weeks, and months Probability and Statistics Construct and use graphs of real objects or pictures to answer questions
First Grade First graders use numbers to express quantities and relationships to solve problems and translateinformal language into mathematical symbols.They learn to recognize and solve problems in addition and subtraction situations using addition and subtraction facts. First graders recognize patterns in numbers and operations. Students use informal language and observation of geometric properties to describe shapes and solids. They develop measurement concepts as they identifyand compare attributes of objects and situations.Students collect and display data and use information from graphs to answer questions. Children use drawings, models, and manipulatives as they learn. They identify mathematics in everyday situations and are asked to communicate their observations usingobjects, words, pictures, and numbers.	Number, Operations and Quantitative Reasoning Create sets of tens and ones using concrete objects to compare and order whole numbers up to 99 Describe the relative values of pennies, nickels, dimes and quarters Read and write numbers to 99 to describe sets of objects Identify ordinal positions, first through tenth Learn what simple fractions represent Learn and apply basic addition and subtraction facts using concrete materials Model and create addition and subtraction situations with concrete objects and write corresponding number sentences Patterns, Relations, and Algebraic Thinking Use patterns to make predictions Skip count by twos, fives, and tens Find patterns in numbers, including even and odd Identify the inverse relation between addition and subtraction Geometry Describe and identify objects in order to sort them according to a given attribute Identify and name circles, triangles, and rectangles including squares Describe the shape of balls, boxes, cans, and cones Measurement Estimate and measure length, capacity and weight of objects using non-standard units Tell time using hours and half hours Recognize reasonable temperatures such as a hot day or a cold day Order three or more events by how much time they take Probability and Statistics Display data in a real-object graph, pictograph or bar graph Use information from graphs to draw conclusions and answer questions Identify events as certain or impossible
Second Grade Second graders usenumerical relationships to compare and order whole numbers. They continue to work on addition and subtraction focusing on applying those skills to problem situations. They also begin to develop an understanding of the concept of multiplication and division. Second grade students usepatterns to expressrelationships, makepredictions and solveproblems. Second graders continue to use attributes to identify, compare, and contrast shapes and solids and to measure length, capacity, time and weight. Second graders continue to organize data to construct graphs, answer questions and draw conclusions. Asbefore, students usehands-on tools and drawings. They decide on the best approach to solving a problem and are asked to explain and support their thinking both orally and in writing using pictures, words and symbols.	Numbers, Operations and Quantitative Reasoning Represent, compare and order whole numbers through 999 using concrete models Read numbers (through 999) and record the comparison using numbers and <, >, or = Round two digit numbers to the nearest ten Identify the place value of a digit in a three digit number Name fractional parts of a whole object or a set of objects when given a concrete representation Recall and apply addition facts to 18 and related subtraction facts Add and subtract two digit numbers to solve problems Determine the value of a collection of coins less than one dollar Model, create and describe multiplication or division situations Pattern, Relations, and Algebraic Thinking Use patterns to describe relationships and make predictions Use patterns in numbers and operations Geometry Identify attributes of two-dimensional shapes and three-dimensional solids Use whole numbers to locate and name points on a line Measurement Measure length, capacity and weight using concrete models that approximate standard units (metric and customary) Read a thermometer Describe time on a clock using hours and minutes Probability and Statistics Construct pictographs and bar graphs Use graphed data to answer questions and draw conclusions Describe events as "more likely" or "less likely" to occur Use objects or pictures to show all possible combinations with a given set of objects
Third Grade Students in grade 3 use algorithms for addition and subtraction to solve problems involving whole numbers. During the year they learn to recognize and solve problems in multiplication and division situations.They concretely develop basic concepts of fractions and decimals. Third graders use appropriate language and organizational structures to represent and communicate relationships, make predictions and solve problems. They continue learning about geometric shapes, measuring things using standard units and measurement tools, gathering data, and working with graphs in order to make decisions and predictions and solve problems.	Number, Operations and Quantitative Reasoning Read, write, and describe value of whole numbers up to 999,999 Compare and order whole numbers through 9,999 Determine the value of a given collection of coins and bills Use fraction names and symbols to describe fractional parts of whole objects or sets of objects with denominators of 12 or less Compare fractional parts of whole objects or sets of objects in a problem situation using concrete models Construct concrete models of equivalent fractions for fractional parts of whole objects Add and subtract to solve word problems involving whole numbers through 999 Learn and apply multiplication facts through the tens using concrete materials Solve and record multiplication problems (one digit multiplier) Use models to solve division problems and use number sentences to record the solution Round two digit numbers to the nearest ten and three digit numbers to the nearest hundred Estimate sums and differences to determine reasonable results Pattern, Relations, and Algebraic Thinking Use patterns to solve problems Use lists, tables, and charts to express patterns and relationships Geometry Name, describe and compare shapes and solids Identify congruent shapes Create shapes with lines of symmetry Locate and name points on a line using whole numbers and fractions such as halves Measurement Estimate and measure lengths using standard units Determine the perimeter of a shape Use concrete models to determine the area of shapes Tell and write time to the minute and solve problems involving time Probability and Statistics Collect, organize, record and display data in pictographs and bar graphs where each picture or cell might represent more than one piece of data Interpret information from pictographs and bar graphs Use data to describe events as "more likely", "less likely", or "equally likely"
Fourth Grade Fourth grade students continue to deepen their understanding of multiplication and division and sharpen their skills as they apply their knowledge in problem situations. They grow more familiar wit fractions and decimals as they describe and compare parts of whole objects or sets of objects. Fourth grade students use appropriate language and organizational structures to analyze, describe and represent relationships. In geometry, they take a closer look at lines, shapes, and solids. Students continue to select and use appropriate units and procedure as they apply measurement concepts.	Number, Operations and Quantitative Reasoning Read, write, compare and order whole number through the millions place Read, write, compare and order decimals, involving tenths and hundredths using concrete materials Generate equivalent fractions using concrete and pictorial models Represent fractional quantities greater than one using concrete models and pictures Relate decimals to fractions that name tenths and hundredths using models Add and subtract to solve meaningful problems involving whole numbers and decimals Represent multiplication and division situations using objects, pictures, words and numbers Recall and apply multiplication facts through 12 x 12 Use multiplication (two digit numbers) and division (1 digit divisors) to solve meaningful problems involving whole numbers Use rounding to approximate reasonable results in problem situations Estimate a product or quotient beyond basic facts Patterns, Relations and Algebraic Thinking Use the inverse relationship between multiplication and division to solve division problems related to multiplication facts Use patterns to multiply by 10 and 100 Describe the relationship between two sets of related data Geometry Identify angles as obtuse, acute, or right Identify and construct models of parallel, intersecting, and perpendicular lines Identify and describe shapes and solids using formal geometric language Connect transformations to congruency and symmetry Locate and name points on a number line Measurement Select and use appropriate units and procedures to measure weight and capacity (metric and customary) Measure to solve problems involving length (including perimeter), time, temperature, and area Probability and Statistics List all possible outcomes of a probability experiment Use a pair of number to compare favorable outcomes to all possible outcomes Interpret bar graphs, line graphs, and double bar graphs

Fifth Grade Fifth grade students use algorithms for addition, subtraction, multiplication, and division to solve meaningful problems. They continue to develop an understanding of equivalent fractions and decimal representations. They refine their problem solving strategies as they solve problems that arise from everyday experiences and activities in and outside of school. Fifth graders continue to communicate observations and strategies using mathematical language and symbols. Students in fifth grade select and use formal language to describe their reasoning as they identify, compare , and classify shapes and solids; and they use numbers, standards units, and measurement tools to describe and compare objects, make estimates and solve application problems.	Number, Operations and Quantitative Reasoning Read, write, compare and order whole number through the billions place Read, write, compare and order decimals through the thousandths place Generate equivalent fractions Compare two fractional quantities in problem-solving situations Use models to relate decimals to fractions that name tenths, hundredths, and thousandths Use addition and subtraction to solve problems involving whole numbers and decimals Use multiplication and division to solve problems involving whole numbers Identify prime factors and common factors Model addition and subtraction of fractions with like denominators Estimate to determine reasonable results in problem situations Patterns, Relations and Algebraic Thinking Make generalizations based on observed patterns and relationships Identify prime and composite numbers Use diagrams and number sentences to represent real-life situations Geometry Identify critical attributes (i.e., parallel, perpendicular, and congruent parts) of geometric shapes and solids Uses critical attributes to define geometric shapes and solids Classify polygons according to critical attributes (i.e., number of sides, angles) Construct circles and identify the radius, diameter, chord, center, and circumference Sketch the results of translations, rotations, and reflections Locate and name points on a coordinate grid (using ordered pairs of whole numbers) Measurement Select and use appropriate units and procedures to measure volume Measure to solve problems involving length, weight, capacity, time, temperature, and area Describe numerical relationships between units of measure within the same measurement system (customary and metric) Probability and Statistics Describe and predict the results of a probability experiment Make line graphs Describe the range and median of a set of data presented in tables or graphs
Sixth Grade Within a well-balanced mathematics curriculum, the primary focal points at Grade 6 are using ratios to describe proportional relationships involving number, geometry, measurement, and probability and adding and subtracting fractions. Sixth graders learn about integers and exponents. In sixth grade, students solve application problems involving estimation and measurement of length, area, time, temperature, capacity, weight, and angles. They get more experience working with statistical representations of data and using probability to make predictions. Students apply Grade 6 mathematics to solve problems connected to everyday experiences and activities inside and outside of school. They communicate about Grade 6 mathematics through informal and mathematical language, representations, and models.	Number, Operations, and Quantitative Reasoning Compare and order non-negative rational numbers Use integers to represent real-life situations Write prime factorizations using exponents Identify factors and multiples Use addition and subtraction to solve problems involving fractions and decimals Use multiplication and division of whole numbers to solve problems Solve problems involving proportional relationships Patterns, Relations, and Algebraic Thinking Use tables and symbols to represent and describe proportional and other relationships Generate formulas to represent relationships involving perimeter area, and volume from a table of data Formulate equations from problem situations Geometry Use angle measurements to classify angles as acute, obtuse, and right Identify relationships involving angles in triangles and quadrilaterals Describe the relationship between radius, diameter, and circumference of a circle Locate and name points on a coordinate plane using ordered pairs of non-negative rational numbers Measurement Estimate measurements and evaluate their reasonableness Select and use appropriate units, tools, or formulas to measure and to solve problems involving length, area, time, temperature, capacity, and weight Measure angles Convert measures with the same measurement system Probability and Statistics Use experimental and theoretical probability to make predictions Use mean, median, mode, and range to describe data Sketch circle graphs to display data Solve problems by collecting, organizing, displaying, and interpreting data
Seventh Grade Students in Grade 7 apply addition, subtraction, multiplication, and division of decimals, fractions, and integers. They use proportional relationships in number, geometry, measurement, and probability. Seventh graders use statistical measures to describe data. They prepare for the systematic study of algebra by using tables and symbols to represent relationships and formulating equations from problem situations.	Number, Operations, and Quantitative Reasoning Compare and order integers and rational numbers Convert between fractions, decimals, whole numbers and percents Represent squares and square roots Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals Use models to add, subtract, multiply, and divide integers Simplify numerical expressions Patterns, Relationships, and Algebraic Thinking Solve problems involving proportional relationships Represent a mathematical relationship in numerical, geometric, verbal, and symbolic form Use equations to solve problems Geometry Classify pairs of angles as complementary or supplementary Use properties to classify shapes and solids Locate and name points on a coordinate plane using ordered pairs of integers Graph translations on a coordinate plane Sketch a solid when given the top, side, and front view Make a two-dimensional model of the surface area of a solid Use geometric concepts and properties to solve problems Measurement Estimate measurement and solve application problems involving length, area, and volume Probability and Statistics Construct sample spaces for compound events Find the approximate probability of a compound event using data Select and use an appropriate representation for presenting collected data and justify the selection Make inferences and convincing arguments based on an analysis of data Choose among measures of central tendency (mean, median or mode) and range to describe a set of data and justify the choice for a particular situations
Eighth Grade Eighth grade students use concepts, algorithms, and properties of rational numbers to explore mathematical relationships and to describe increasingly complex situations. A primary focal points at Grade 8 is using basic principles of algebra to analyze and represent proportional and non- proportional relationships. Eighth graders use probability to describe data and make predictions. They continue to use geometric properties and relationships, spatial reasoning, and measurement principles and procedures to model and analyze situations and solve problems.	Number, Operations, and Quantitative Reasoning Compare and order rational numbers in various forms Approximate the value of irrational numbers Express numbers in scientific notation Select and use appropriate operations to solve problems and justify solutions Patterns, Relationships, and Algebraic Thinking Estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates Make connections among various representations of a numerical relationships Use graphs, tables and algebraic representations to make predictions and solve problems Geometry Generate similar shapes Graph dilations, reflections and translations on a coordinate plane Draw solids from different perspectives Demonstrate the Pythagorean Theorem using pictures and models Locate and name points on a coordinate plane Measurement Estimate answers and use formulas to solve application problems involving surface area and volume Use indirect measurement to solve problems Describe how changes in dimensions affect linear, area, and volume measurements Probability and Statistics Find the probability of compound events Use probability to make predictions and decisions Use statistical procedures to describe data Evaluate predictions and conclusions based on statistical data
Algebra I In Algebra I, students use symbols in a variety of ways to study relationships among quantities. They use functions to represent and model problem situations and to analyze and interpret relationships. Algebra I students work in many situations to set up equations and use a variety of methods to solve these equations. In Algebra I, students use a variety of representations, tools, and technology to model mathematical situations and to solve meaningful problems. As they do algebra, students continually use problem- solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling and justification and proof.	Foundation of Functions Describe independent and dependent quantities in a functional relationship Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations and inequalities Identify and sketch linear and quadratic parent functions Identify mathematical domains and ranges Make and interpret scatterplots Use symbols to represent unknowns and variables Manipulate symbols in order to solve problems and use the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations Translate among and use algebraic, tabular, graphical, or verbal descriptions of linear functions Linear Functions Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs Investigate, describe, and predict the effects of changes in "m" and "b" on the graph of y=mx+b Graph and write equations of lines Determine the intercepts of linear functions Solve problems involving direct variation Formulate equations and inequalities, solve them and analyze the solutions in terms of the situation Formulate systems of linear equations from problem situations, solve them using a variety of methods, and analyze the solutions in terms of the situation Quadratic and Other Nonlinear Functions Analyze graphs of quadratic functions and draw conclusions for given problem situations Investigate, describe and predict the effects of changes in "a" and "c" on the graph of y=ax2+c Analyze graphs of quadratic functions and draw conclusions for given problem situations Solve quadratic equations Generate the laws of exponents and applies them in problem-solving situations Analyze data and represent situations involving inverse variation Analyze data and represent situations involving exponential growth and decay
Geometry In Geometry, students use geometric thinking to understand mathematical concepts and the relationships among them. They study properties and relationships having to do with size, shape, location, direction, and orientation of figures. Geometry students solve meaningful problems using geometric ideas, relationships, and properties. As they do geometry, students continually use problem- solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling and justification and proof.	Geometric Structure Understand the structure of, and relationships within, an axiomatic system Use constructions to explore attributes of figures and to make conjectures Construct and justify statements about geometric figures and their properties Use inductive reasoning to formulate a conjecture Use deductive reasoning to prove a statement Use a variety of representations (concrete, pictorial, graphical, verbal, or symbolic) to describe geometric relationships and solve problems Geometric Patterns Make generalizations about geometric properties including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles Use properties of transformations and their compositions to make connections between mathematics and the real world Identify and apply patterns from right triangles to solve problems Dimensionality and the Geometry of Location Describe and draw slices of three-dimensional objects Use nets to represent and construct three-dimensional objects Use top, front, side and corner views of 3-D objects to create accurate representations and solve problems Use one- and two-dimensional coordinate systems to represent points, lines, line segments, and figures Use slopes and equations of lines to investigate parallel and perpendicular lines and special segments of triangles and other polygons Develop and use distance and midpoint formulas Congruence and the Geometry of Size Find area of polygons, circles, and sectors of circles Develop, extend, and use the Pythagorean Theorem Find surface areas and volumes in problem situations Analyze properties and describe relationships in geometric figures Apply the concept of congruence to justify properties of figures and solve problems Similarity and the Geometry of Shape Use similarity properties and transformations Use ratios to solve problems involving similar figures Apply the concepts of similarity to justify properties of figures and solve problems
Algebra II In Algebra II, student s study algebraic concepts and the relationships among them to better understand the structure of algebra. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations. Students in Algebra II learn that equations and functions are algebraic tools that can be used to represent geometric curves and figures and they perceive the connections between algebra and geometry and use the tools of one to help solve problems in the other.	Foundations for Functions Collect and organize data, make scatterplots, fit curves to the appropriate parent function, interpret the results and proceed to model, predict and make decisions and critical judgments Use tools including matrices, factoring, radicals, and properties of exponents to simplify expressions and transform and solve equations Use complex numbers to describe the solutions of quadratic equations Formulate systems of equation and inequalities from problem situations, use a variety of methods to solve them and analyze the solutions in terms of the situations Algebra and Geometry Identify and sketch graphs of various parent functions (linear, quadratic, square root, inverse, exponential, absolute value, polynomial, and logarithmic) Describe conic sections Relate simple parameter changes in the equation to corresponding changes in the graph Identify the conic sections form a given equation Connect algebraic and geometric representations of sequences and series Quadratic Functions Represent quadratic functions in different ways and translate among their various representations Interpret and describe the effect of parametric changes in quadratic functions Formulate equations and inequalities based on quadratic functions, solve them and analyze the solutions in terms of the situation Other Functions Formulate equations and inequalities based on square root functions, solve them and analyze the solutions in terms of the situation Formulate equations and inequalities based on rational functions, solve them and analyze the solutions in terms of the situation Formulate equations and inequalities based on exponential and logarithmic functions, solve them and analyze the solutions in terms of the situation Define trigonometric functions and describe characteristics of them
Precalculus In Precalculus, students continue to build on their Algebra I, Algebra II, and Geometry foundations as they expand their understanding through other mathematical experiences. Students use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study mathematical concepts and the relationships among them. Students use functions, equations, and limits as useful tools for expressing generalizations and as means for analyzing and understanding a broad variety of mathematical relationships. Students also use functions as well as symbolic reasoning to represent and connect ideas in geometry, probability, statistics, trigonometry, and calculus and to model physical situations. Students use a variety of representations, tools, and technology to model functions and equations and solve problems.	Define polynomial, rational, radical, exponential, logarithmic, trigonometric and piecewise-defined functions and translate among verbal, numerical, graphical, and symbolic representations of them Investigate continuity, end behavior, vertical and horizontal asymptotes, and limits and connect them to the graph of a function Interpret the meaning of the symbolic representations of functions and operations on functions within a context Investigate identities (logarithmic properties, trigonometric identities, and exponential properties) graphically and verify them symbolically Use functions and their properties to model and solve real-life problems Use regression to determine a function to model real-life data Represent patterns using arithmetic and geometric sequences and series Investigate divergent and convergent series Apply sequences and series to solve problems Use conic sections, their properties, and parametric representations to model physical situations Use concept of vectors to model situations defined by magnitude and direction Analyze and solve vector problems generated by real-life situations
Mathematical Models with Applications In this course students use algebraic, graphical, and geometric reasoning to recognize patterns and structure, to model information, and to solve problems from various disciplines. Students use mathematical methods to model and solve real-life applied problems involving money, data, chance, patterns, music, design, and science. Students use mathematical models from algebra, geometry, probability, and statistics and connections among these to solve problems from a wide variety of advance applications.	Use a variety of strategies and approaches to solve both routine and non-routine problems Use graphical and numerical techniques to study patterns and analyze data Develop and implement a plan for collecting and analyzing data in order to make decisions Use probability models to describe everyday situations involving chance Use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting Solve problems involving personal taxes Analyze data to make decisions about banking Analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option Use amortization models to investigate automobile and home financing and compare buying and renting/leasing Analyze types of savings options involving simple and compound interest and compare relative advantages of these options Analyze and compare coverage options and rates in insurance Investigate and compare investment options including stocks, bonds, annuities, and retirement plans Use algebraic and geometric models to describe situations and solve problems Use algebraic and geometric models to represent patterns and structures
AP Statistics This non-calculus based course introduces the student to the management, interpretation and analysis of data within today’s society.	Exploring Data Interpret graphical displays (dotplot, stemplot, histogram) Summarize distributions of univariate data Compare distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) Explore bivariate data Explore categorical data (frequency tables) Planning a Study Overview methods of data collection Plan and conduct surveys Plan and conduct experiments Producing Models Using Probability and Simulation Understand probability as relative frequency Combine independent random variables Understand the normal distribution Simulate sampling distribution Statistical Inference Understand confidence intervals Perform tests of significance Examine special case of normally distributed data
AP Calculus A/B This course includes differential and integral calculus with applications of previous math courses. Topics include: limits of a function, continuity, maxima and minima, area, volume, center of mass and other applications.	Functions, Graphs, and Limits Analysis of graphs Limits of functions Asymptotic and unbounded behavior Continuity as a property of functions Derivatives Concept of derivative Derivatives at a point Derivatives as a function Second derivatives Application of derivatives Computation of derivatives Integrals Riemann sums Interpretations and properties of definite integrals Applications of integrals Use of Fundamental Theorem of Calculus to evaluate definite integrals Use of Fundamental Theorem of Calculus to represent a particular antiderivative Techniques of antidifferentiation Application of differentiation Numerical approximations to definite integrals
AP Calculus B/C Calculus B/C is primarily concerned with providing students experience with calculus’ methods and applications. The course emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally.	Functions, Graphs, and Limits Parametric, polar, and vector functions Derivatives Analysis of planar curves given in parametric form, polar form, and vector form, including velocity and acceleration vectors Geometric interpretation of differential equations vial slope fields Relationship between slope fields and derivatives of implicitly defined functions Numerical solution of differential equations using Euler’s method L’Hôpital’s Rule Derivatives of parametric, polar, and vector functions Integrals Applications of integrals Antiderivatives by substitution of variables, parts, and simple partial fractions Improper integrals Solving logistic differential equations and using them in modeling Polynomial Approximations and Series Concept of series Series of constants Taylor series

The mathematics page was last updated on October 02, 2006. If you have any questions about this program, please contact the program coordinator or the webpage coordinator .