Download mathematics - Three Village Central School District

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Thhrreeee V
Viillllaaggee C
Ceennttrraall SScchhooooll D
Diissttrriicctt
ESSENTIALS OF LEARNING
MATHEMATICS
Math 7
Math A
MATH B
Pre-Calculus
Math 12X
Visual Basic
The mission of the Three Village Central School District, in
concert with its families and community, is to provide an
educational environment, which will enable each student to
achieve a high level of academic proficiency and to become a
well-rounded individual who is an involved, responsible
citizen.
Math 7-12
All students are required to complete the Math A Regents assessment as a minimum graduation
requirement. Students are grouped in one of three courses in the 7th grade, based on their 6th
grade performance. Our 7-12 sequence challenges all students to attain a high level of
competency in mathematics. Students are expected to complete math B, the new and more
rigorous requirement of the advanced regents diploma.
Advanced
7th Grade
8th Grade
9th Grade
10th Grade
Math 7th Advanced
(Algebra)
Local Exam
Math 8 Advanced
(Math A)
Local Exam
8th grade assessment
Math 9 Advanced
(Math A/B)
Jan. Math A Regents
Math 10 Advanced
(Math B)
June Math B Regents
PreCalc I & II
11th Grade
12th Grade
Regents
Honors
Math 7th Regents
(Algebra)
Local Exam
Math 8 Regents
(Math A)
Local Exam
8th grade
assessment
Math 9 Regents
(Math A)
Math 7th Honors
(Math A)
Local Exam
Math 8 Honors
(Math A)
June Math A Reg.
8th grade
assessment
Math 9 Honors
(Math B)
Local Exam
June Math A
Regents
Math 10 Regents
(Math B)
Local Exam
Math 11 Regents
(Math B)
June Math B
Regents
Calculus or
AP Calc A/B and/or
Statistics and/or
AP Computer Science
PreCalc I & II
and/ or
Statistics and/or
Visual Basic*
Math 10 Honors
(Math B)
June Math B
Regents
Math 12X or
PreCalc I & II
and/or
AP Computer
Science
AP Calc A/B or
B/C
and/or
AP Computer
Science
* Intro to Visual Basic and Visual Basic can be taken by 10th, 11th, or 12th graders.
MATH 7
Mathematical Reasoning:
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Develop various problem solving
skills/strategies
Express solutions clearly and logically,
using appropriate mathematical notation,
terms, and language
Explain and show solution processes in a
variety of ways (words, numbers, symbols,
pictures, charts, graphs, tables, diagrams,
and models)
Apply strategies and results from simpler
problems to more complex situations.
Numbers and Numeration:
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Understand, represent, and use numbers in a variety
of equivalent forms (integer, fraction, decimal,
percent, exponential, expanded, and scientific
notation)
Develop an understanding of number theory
Recognize and understand order relations for
decimals, integers, and rational numbers
Understand and apply ratios, proportions, and
percents
Modeling/Multiple Representation:
Operations:
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Understand and use order of operation rules and procedures
Understand and apply the associative, commutative,
distributive, inverse, and identity properties
Consistently and accurately perform all operations (add,
subtract, multiply, and divide) on integers and rational
numbers
Evaluate algebraic expressions
Apply concepts of ratio and proportion to solve problems
Measurement:
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Develop knowledge and understanding of standard units of measurement
and metric units of measurement
Use a protractor to find the measure of an angle
Know and apply formulas for perimeter and area of polygons, and
circumference and area of circles
Identify three-dimensional figures and calculate the volume and surface area
of these figures
Classify polygons by their properties (measure of angles and length of sides)
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Develop and explore models of chance
Interpret, demonstrate understanding,
and use variables in expressions,
formulas, equations, and properties
Use variables to represent
relationships
Develop procedures for geometric
relationships
Organize and display collected data
using appropriate tables, charts, and
graphs
Uncertainty:
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Use estimation to check
reasonableness of results
Develop and explore
basic probability
concepts
Understand how to
express probability as a
fraction, decimal, and
percent
Patterns and Functions:
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Describe and represent numerical and geometric patterns and functions, using equations, graphs, and tables
Organize and analyze data using graphs and tables
Use pre-algebra variable expressions to solve problems
Translating words to symbols
Develop methods to solve basic linear equations – 1 and 2 step equations including fractions, decimals, and integers
Use properties of polygons to classify them
Solve proportions for the missing value – unit price, better buy, and scale drawings
Explore relationships involving points, lines, angles, and planes
Use patterns and functions to represent and solve problems
Understand the difference between similarity and congruence
MATH A
Mathematical Reasoning:
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Number and Numeration:
Construct valid arguments
Determine the truth value of simple compound
sentences
Operations:
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Use addition, subtraction, multiplication, division, and
exponentiation with real numbers and algebraic
expressions
Understand and use scientific notation
Evaluate algebraic expressions and formulas
Understand and apply all operations with radicals
Use addition, subtraction, and multiplication with
polynomials
Understand and use factoring or polynomials to solve
problems
Use integral exponents on integers and algebraic
expressions
Recognize and identify symmetry and transformations
of figures
Measurement:
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Apply formulas to find measures such as length, area,
volume, weight, time, and angle in real-world contexts
Choose and apply appropriate units and tools in
measurement situations
Use statistical methods including the measures of central
tendency to describe and compare data
Apply proportions to scale drawings and direct variation
Use right triangle trigonometry
Relate absolute value, distance between two points, and the
slope of a line to the coordinate plane
Understand and explain the role of error in measurement
Use geometric relationships in relevant measurement
problems involving geometric concepts – similar
polygons/comparison of volumes of similar solids
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Apply and understand the properties of real
numbers
Understand and use rational and irrational
Modeling/Multiple Representation:
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Represent problem situations
symbolically by using algebraic
expressions, sequences, tree
diagrams, geometric figures, and
graphs
Understand and use properties of
triangles and quadrilaterals to solve
problems
Understand angle relationships in
polygons – interior/exterior
Understand and perform basic
geometric constructions
Use transformations in the
coordinate plane
Understand and apply the concepts
of basic loci and compound loci
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Uncertainty:
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Understand theoretical and
empirical probability
Use theoretical and empirical
probability to represent and solve
problems involving uncertainty
Determine probabilities, using
permutations and combinations
Understand the concepts of
counting principle, sample space,
complement, mutually exclusive
and independent events
Patterns and Functions:
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Represent and analyze functions, using verbal descriptions, tables, equations, and graphs
Solve and graph linear equations (inequalities) with integral, fraction, or decimal coefficients
Solve algebraically and graphically systems of linear equations (inequalities) and quadratic-linear pairs
Graph circles and parabolas
Apply linear and quadratic functions in the solution of real-world problems
Develop techniques for solving factorable quadratic equations
MATH B
Mathematical Reasoning:
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Construct Euclidean and analytic mathematical
proofs using mathematical reasoning and the laws
of logic
Construct indirect Euclidean proofs
Numbers and Numeration:
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Understand and use rational, irrational, and
complex number systems
Modeling:
Operations:
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Use addition, subtraction, multiplication, division, and
exponentiation on real numbers, complex numbers and
algebraic expressions
Use transformations to investigate geometry and
functions to include slope and midpoint formulas
Measurement:
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Use unit circle to define trigonometric functions
Use sum and difference, double and half angle
trigonometric identities in the solution of real world
problems
Use law of sines and law of cosines in a variety of
problems including resolution of forces
Use statistical methods, including variance and standard
deviation to describe and compare data
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Patterns and Functions:
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Uncertainty:
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Investigate Bernulli experiments, including the
binomial theorem
Analyze and synthesize the following statistical
concepts: measures of central tendency, sigma
notation, measures of dispersion, mean absolute
deviation, scatter plots, lines of best fit, bias/random
sample, variance and standard deviation, and normal
approximation for the binomial distribution.
Model quadratic inequalities both
algebraically and graphically
Model composition of transformations
Recognize the following functions:
polynomial, exponential, and
logarithmic
Recognize conic sections: circle,
parabola, hyperbola, and ellipse
Solve real world problems using
linear, quadratic, trigonometric, and
exponential functions
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Represent functions and their inverses
in a variety of ways including: models,
verbal explanations, tables, equations,
and graphs
Analyze parametric change on graphs
of functions
Apply functions in solutions of real
world problems
Solve the following types of
equations: fractional, radical,
quadratic, trigonometric, logarithmic,
and exponential
Analyze inequalities and absolute vale
both algebraically and graphically
PRE-CALCULUS
Numbers and Numeration:
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Introduce the number e
Understand logarithms, including the natural
log
Evaluate expressions and solve equations
involving trigonometric functions
Functions:
• Find an inverse of a function
• Work with composition of functions
• Determine domain and range of a real valued
function
• Classify functions and understanding their
properties
Technology:
• Use the TI-89 to find intercepts and
extrema for cures
• Use CAS (Computer Algebraic System)
for purpose of solving more algebraically
involved problems
Modeling:
• Develop a linear function from
data for purposes of making
estimates
• Use exponential functions to
model compound interest,
population growth, and
radioactive decay
• Use law of sines and cosines for
design or engineering
• Use quadratic equations to
model rectilinear motion
• Introduce optimization
Calculus:
• Understand the idea of a limit
• Evaluate limits
• Appreciate and comprehend the
concept of the derivative
• Differentiate elementary functions
MATH 12X
** See pre-calculus for topics covered. Additional topics listed below**
Mathematical Reasoning:
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Write a proof by induction for various
situations including series and divisibility
Define a limit with delta and epsilon and then
apply it in proofs
Examine differentiability and continuity of
elementary functions
Patterns:
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Decide whether a sequence diverges or
converges
Infinite series with divergence and
convergence
Use formulas to determine infinite and
finite sums