COURSE
DESCRIPTION for GRADES 9 - 12
MATHEMATICS
Integrated
Math I (Pre-Algebra I) 2
Semesters, 36 Lessons
In this course, students connect physical, verbal,
and symbolic representations of the real number system.
They investigate the properties of real numbers and
estimate, compute, solve, and judge reasonableness
of problems with real numbers including ratio, proportion,
percent, integers, rational numbers, numbers expressed
in scientific notation, and square roots of perfect
and non-perfect squares. Students generalize patterns
and sequences and apply formulas to real-world problem
situations. Students examine basic geometric properties
of two-dimensional and three-dimensional shapes. They
graph solutions to equations; use coordinate geometry
to analyze properties of two-dimensional figures and
perform translations, reflections, rotations, and
dilations; define basic trigonometric ratios in right
triangles; and apply proportions to solve problems
involving right triangle trigonometry. Students apply
direct and indirect measurement techniques and tools,
and derive formulas to determine perimeter, area,
volume, and various attributes of plane and solid
geometric figures. They use measures of center and
spread to analyze data; evaluate the change of data
and display it appropriately in graphs; make predictions
based on samples representative of a larger population;
use permutations and combinations to calculate the
number of possible outcomes recognizing repetition
and order; and compute the probability of compound
events, independent events, and simple dependent events.
Students solve and graph linear equations, absolute
value equations, and inequalities; compute with polynomials;
define functions; determine slope and intercepts;
draw graphs of linear equations & inequalities;
solve systems of equations, & explore simple nonlinear
equations.
College
Preparatory Algebra I 2
Semesters, 36 Lessons
In this course, students connect physical, verbal,
and symbolic representations of the real number system;
investigate properties including closure; demonstrate
fluency in computations with real numbers; solve and
graph linear equations and inequalities. They use
formulas to solve problems including exponential growth
and decay; add, subtract, multiply, and divide monomials
and polynomials; and solve quadratic equations with
real roots by graphing, formula, and factoring. Students
define functions, determine slope, calculate distance,
and draw graphs of linear equations using slope, y-intercept,
parallel, and perpendicular lines; determine the characteristics
of linear, quadratic, and exponential functions; solve
systems of linear equations involving two variables
graphically and symbolically; simplify and compute
with rational and radical expressions; model and solve
problem situations involving direct and indirect variation.
They describe and interpret rates of change from graphical
and numerical data; find, use, and interpret measures
of center and spread to compare and draw conclusions
about data; evaluate the appropriateness of data collection
and analysis; and identify possible misuses of statistical
data. They use counting techniques and the Fundamental
Counting Principal to determine possible outcomes,
compute probabilities of compound events, independent
events, and simple dependent events; and make predictions
based on theoretical probabilities and experimental
results. Students define basic trigonometric ratios
in right triangles and apply proportions to solve
problems involving right triangle trigonometry.
Integrated
Math II (Integrated Geometry) 2
Semesters, 36 Lessons
In this course, students study the topics presented
in geometry but in a modified format. On occasion,
students find that problems and/or explanations have
been adapted to a simpler format. Students are given
extra guidance with more difficult problems. Students
formally define geometric figures; describe and apply
the properties of similar and congruent figures; and
justify conjectures involving similarity and congruence.
They recognize and apply angle relationships in situations
involving intersecting lines, perpendicular lines,
and parallel lines; use coordinate geometry to represent
and examine the properties of geometric figures including
slope, midpoint, distance, parallel, and perpendicular
lines; draw and construct representations of two-
and three-dimensional geometric objects using a variety
of tools such as straightedge, compass, and technology.
Students represent and model transformations in a
coordinate plane and describe the results; prove or
disprove conjectures and establish the validity of
conjectures about geometric objects, their properties
and relationships by counterexample, inductive and
deductive reasoning, and critiquing arguments made
by others. Students use right triangle trigonometric
relationships to determine lengths and angle measures;
use algebraic representations to model and solve problem
situations and to describe and generalize geometric
properties and relationships. Students will connect
physical, verbal, and symbolic representations of
irrational numbers. They will calculate and explain
the difference between absolute error and relative
error; interpret the relationship between two variables
using multiple graphical displays and statistical
measures; model problems dealing with uncertainty;
differentiate and explain the relationship between
the probability of an event and the odds of an event.
College
Preparatory Geometry 2
Semesters, 36 Lessons
In this course, students formally define geometric
figures; describe and apply the properties of similar
and congruent figures; and justify conjectures involving
similarity and congruence. They recognize and apply
angle relationships in situations involving intersecting
lines, perpendicular lines, and parallel lines; use
coordinate geometry to represent and examine the properties
of geometric figures including slope, midpoint, distance,
parallel, and perpendicular lines; draw and construct
representations of two- and three-dimensional geometric
objects using a variety of tools such as straightedge,
compass, and technology. Students represent and model
transformations in a coordinate plane and describe
results; prove or disprove conjectures and establish
the validity of conjectures about geometric objects,
their properties and relationships by counterexample,
inductive and deductive reasoning, and critiquing
arguments made by others. Students use right triangle
trigonometric relationships to determine lengths and
angle measures; use algebraic representations to model
and solve problem situations and to describe and generalize
geometric properties and relationships; connect physical,
verbal, and symbolic representations of irrational
numbers; calculate and explain the difference between
absolute error and relative error; interpret the relationship
between two variables using multiple graphical displays
and statistical measures; model problems dealing with
uncertainty with area models; differentiate and explain
the relationship between the probability of an event
and the odds of an event.
Integrated
Math III (Integrated Algebra II) 2
Semesters, 36 Lessons
In this course, students study the topics presented
in algebra but in a modified format. On occasion,
students find that problems and/or explanations have
been adapted to a simpler format. Students are given
extra guidance with more difficult problems. In this
course, students review basic algebra and geometry
topics. They demonstrate fluency in operations with
real numbers, vectors and matrices; represent and
compute with complex numbers; use fractional and negative
exponents to find solutions for problem situations;
describe and compare the characteristics of the families
of quadratics with complex roots, polynomials of any
degree, logarithms, and rational functions. They investigate
rates of change, intercepts, zeros and asymptotes
of polynomial, rational, and trigonometric functions
graphically and with technology; identify families
of functions with graphs that have rotation symmetry
or reflection symmetry about the y-axis, x-axis, or
y =x. They solve problems with matrices and vectors,
solve equations involving radical expressions and
complex roots, solve 3 by 3 systems of linear equations,
and solve systems of linear inequalities; solve quadratic
expressions, investigate curve fitting, and determine
solutions for quadratic inequalities; investigate
exponential growth and decay and use recursive functions
to model and solve problems. They compute with polynomials
and solve polynomial equations using a variety of
methods including synthetic division and the rational
root theorem; solve inverse, joint, and combined variation
problems; solve rational and radical equations and
inequalities; and describe the characteristics of
the graphs of conic sections. Students use permutations
and combinations to calculate the number of possible
outcomes recognizing repetition and order; and compute
the probability of compound events, independent events,
& dependent events.
College
Preparatory Algebra II 2
Semesters, 36 Lessons
In this course, students review basic algebra and
geometry topics. They demonstrate fluency in operations
with real numbers, vectors and matrices; represent
and compute with complex numbers; use fractional and
negative exponents to find solutions for problem situations;
describe and compare the characteristics of the families
of quadratics with complex roots, polynomials of any
degree, logarithms, and rational functions. They investigate
rates of change, intercepts, zeros and asymptotes
of polynomial, rational, and trigonometric functions
graphically and with technology; identify families
of functions with graphs that have rotation symmetry
or reflection symmetry about the y-axis, x-axis, or
y =x. They solve problems with matrices and vectors,
solve equations involving radical expressions and
complex roots, solve 3 by 3 systems of linear equations,
and solve systems of linear inequalities; solve quadratic
expressions, investigate curve fitting, and determine
solutions for quadratic inequalities. They investigate
exponential growth and decay and use recursive functions
to model and solve problems; compute with polynomials
and solve polynomial equations using a variety of
methods including synthetic division and the rational
root theorem; solve inverse, joint, and combined variation
problems; solve rational and radical equations and
inequalities; and describe the characteristics of
the graphs of conic sections. Students use permutations
and combinations to calculate the number of possible
outcomes recognizing repetition and order; compute
the probability of compound events, independent events,
and dependent events.
Advanced
Math (Pre-Calculus) 2
Semesters, 36 Lessons
In this course, students determine what properties
hold for operations with complex numbers. They apply
combinations as a method to create coefficients for
the Binomial Theorem; solve problems involving derived
measurements; use radian measures to solve problems
involving angular velocity and acceleration; apply
informal concepts of successive approximation, upper
and lower bounds, and limits in measurement situations.
Students use matrices to represent translations, reflections,
rotations, dilations, and their compositions; derive
and apply the basic trigonometric identities; relate
graphical and algebraic representations of lines,
simple curves, and conic sections. Students recognize
and compare specific shapes and properties in multiple
geometries; analyze the behavior of arithmetic and
geometric sequences and series as the number of terms
increases; translate between the numeric and symbolic
form of a sequence or series. They describe and compare
the characteristics of transcendental and periodic
functions and represent the inverse of a transcendental
function symbolically; solve systems of equations
using matrices and graphs, with and without technology.
They use mathematical induction and explore the concepts
of limit; compare estimates of the area under a curve
over a bounded interval by partitioning the region
with rectangles; translate freely between polar and
Cartesian coordinate systems; use the concept of limit
to find instantaneous rate of change for a point on
a graph as the slope of a tangent at a point. They
use descriptive statistics to analyze and summarize
data, including measures of center, dispersion, correlation,
and variability; and use theoretical or experimental
probability to determine probabilities in real-world
situations involving uncertainty.
Business
Math 1 Semester,
18 Lessons
This course is a semester course designed with lots
of practical applications of mathematics. Students
compute work wages, commission, piecework pay, tips,
and net pay for an earnings statement. They record
checkbook progress, reconcile checking account statements
and examine various types of savings accounts; and
use recursive functions such as determining compound
interest for a financial investment. Students create
and analyze tabular and graphical displays of data
such as making and adjusting budgets and displaying
results in circle graphs; determine measures of central
tendency and create and interpret frequency tables,
stem-and-leaf plots, and bar graphs. Students compute
sales tax, use installment plans, and investigate
finance charges associated with credit cards; examine
comparative shopping techniques including best buys,
discount prices, catalog orders, and the consumer
price index. Students use scale drawings and estimate
and compute perimeter, area, and volume in real-world
problem situations; examine permutations and combinations
and their applications in consumer situations; compute
the probability of compound events, independent events,
and dependent events. Students compute with matrices,
representing and generalizing real-world problem situations;
examine purchasing and owning a car including gas
mileage, depreciation, insurance coverage and financing;
determine the costs of financing a home including
house payment, property taxes, insurance, maintenance,
and improvements; estimate total costs for a trip
by determining distance on a map, calculating gas
mileage, finding best buy for lodging, and exchanging
currency; and connect statistical techniques to consumer
situations by evaluating health, sports and advertising
data.
OGT
Mathematics Preparation 2
Semesters, 36 Lessons
This course is designed to assist students in preparation
for the Ohio Graduation Test in mathematics. Students
investigate properties and order of operations, evaluate
expressions, identify subsets of the real number system,
and determine equivalent forms of real numbers; estimate,
compute, and solve problems with real numbers including
ratio, proportion, percent, integers, rational numbers,
scientific notation, and square roots; generalize
patterns and sequences and apply formulas to real-world
problem situations. Students determine length, area,
and volume and the appropriate use of linear, square
and cubic unit measurements; generalize patterns and
sequences using tables, graphs, and symbolic algebra;
define functions; determine slope and intercepts;
draw graphs of linear equations and inequalities;
and explore simple quadratic and exponential functions.
Students solve linear equations, inequalities, systems
of equations, quadratic equations, and direct and
inverse variation problem situations. They define
geometric figures and apply the properties of similar
and congruent figures; recognize and apply angle relationships
involving intersecting lines, perpendicular lines,
and parallel lines; use coordinate geometry to examine
the properties of geometric figures including slope,
midpoint, distance, parallel, and perpendicular lines.
They perform translations, reflections, rotations,
and dilations; define basic trigonometric ratios in
right triangles and apply proportions to solve problems
involving right triangle trigonometry. They use measures
of center and spread to analyze data; use permutations
and combinations to calculate the number of possible
outcomes recognizing repetition and order; and compute
the probability of compound events, independent events,
and simple dependent events.
Intervention
Math 2
Semesters, 36 Lessons
Intervention Math is a course designed to review the
student in basic concepts necessary for success in
applying mathematics involved in everyday life. The
subject matter studied is familiar and motivational,
integrating problem solving and focusing on real applications
of mathematical skills. This course is designed primarily
for the student who seeks to improve his or her knowledge
of basic mathematics. Topics studied include computations
and applications of whole numbers, decimals, fractions,
ratios, and percent; measurement in metric and customary
units; geometric figures, finding volume and surface
area; statistics, graphs, and probability; and integers,
the coordinate plane, and algebraic equations.
Transition
to College Math 1
Semester, 18 Lessons
Transition to College Math is a course intended to
cover traditional topics in college algebra and trigonometry
at the freshman level. This course was written in
accordance with the Ohio Academic Content Standards
for grades 11 and 12 and includes such topics as:
Systems of Linear Equations, Complex Numbers, Quadratic
Functions, Logarithms, Trigonometry, Matrices, Vectors,
and the Conic Sections.
Rev. 09-23-06
