MATHEMATICSMATHEMATICS
The Illinois Learning Standards for Mathematics were developed
by Illinois teachers for Illinois schools. These goals, standards
and benchmarks are an outgrowth of the 1985 Illinois State Goals
for Learning influenced by the latest thinking in school mathematics.
This includes the National Council of Teachers of Mathematics;
Curriculum and Evaluation Standards for School Mathematics; ideas
underlying recent local and national curriculum projects; results
of state, national, and international assessment findings; and
the work and experiences of Illinois school districts and teachers.
Mathematics is a language we use to identify, describe and investigate
the patterns and challenges of everyday living. It helps us to
understand the events that have occurred and to predict and prepare
for events to come so that we can more fully understand our world
and more successfully live in it.
Mathematics encompasses arithmetic, measurement, algebra, geometry,
trigonometry, statistics, probability and other fields. It deals
with numbers, quantities, shapes and data, as well as numerical
relationships and operations. Confronting, understanding and solving
problems is at the heart of mathematics. Mathematics is much more
than a collection of concepts and skills; it is a way of approaching
new challenges through investigating, reasoning, visualizing and
problem solving with the goal of communicating the relationships
observed and problems solved to others.
All students in Illinois schools need to have the opportunity
to engage in learning experiences that foster mastery of these
goals and standards. Knowledge of mathematics and the ability
to apply math skills to solve problems can be an empowering force
for all students-both while in school and later in their lives.
Students reaching these goals and standards will have an understanding
of how numbers are used and represented. They will be able to
use basic operations (addition, subtraction, multiplication, division)
to both solve everyday problems and confront more involved calculations
in algebraic and statistical settings. They will be able to read,
write, visualize and talk about ways in which mathematical problems
can be solved in both theoretical and practical situations. They
will be able to communicate relationships in geometric and statistical
settings through drawings and graphs. These skills will provide
all Illinois students with a solid foundation for success in the
workplace, a basis for continued learning about mathematics, and
a foundation for confronting problem situations arising throughout
their lives.
APPLICATIONS OF LEARNING
Through Applications of Learning, students demonstrate and deepen
their understanding of basic knowledge and skills. These applied
learning skills cross academic disciplines and reinforce the important
learning of the disciplines. The ability to use these skills will
greatly influence students' success in school, in the workplace
and in the community.
SOLVING PROBLEMS
Recognize and investigate problems; formulate and propose solutions
supported by reason and evidence. The solving of problems is at
the heart of "doing mathematics." When people are called
on to apply their knowledge of numbers, symbols, operations, measurement,
algebraic approaches, geometric concepts and relationships, and
data analysis, mathematics' power emerges. Sometimes problems
appear well structured, almost like textbook exercises, and simply
require the application of an algorithm or the interpretation
of a relationship. Other times, particularly in occupational settings,
the problems are non-routine and require some imagination and
careful reasoning to solve. Students must have experience with
a wide variety of problem-solving methods and opportunities for
solving a wide range of problems. The ability to link the problem-solving
methods learned in mathematics with a knowledge of objects and
concepts from other academic areas is a fundamental survival skill
for life.
COMMUNICATING
Express and interpret information and ideas. Everyone must be
able to read and write technical material to be competitive in
the modern workplace. Mathematics provides students with opportunities
to grow in the ability to read, write and talk about situations
involving numbers, variables, equations, figures and graphs. The
ability to shift between verbal, graphical, numerical and symbolic
modes of representing a problem helps people formulate, understand,
solve and communicate technical information. Students must have
opportunities in mathematics classes to confront problems requiring
them to translate between representations, both within mathematics
and between mathematics and other areas; to communicate findings
both orally and in writing; and to develop displays illustrating
the relationships they have observed or constructed.
USING TECHNOLOGY
Use appropriate instruments, electronic equipment, computers and
networks to access information, process ideas and communicate
results. Technology provides a means to carry out operations with
speed and accuracy; to display, store and retrieve information
and results; and to explore and extend knowledge. The technology
of paper and pencil is appropriate in many mathematical situations.
In many other situations, calculators or computers are required
to find answers or create images. Specialized technology may be
required to make measurements, determine results or create images.
Students must be able to use the technology of calculators and
computers including spreadsheets, dynamical geometry systems,
computer algebra systems, and data analysis and graphing software
to represent information, form conjectures, solve problems and
communicate results.
WORKING ON TEAMS
Learn and contribute productively as individuals and as members
of groups. The use of mathematics outside the classroom requires
sharing expertise as well as applying individual knowledge and
skills. Working in teams allows students to share ideas, to develop
and coordinate group approaches to problems, and to share and
learn from each other in communicating findings. Students must
have opportunities to develop the skills and processes provided
by team problem-solving experiences to be prepared to function
as members of society and productive participants in the workforce.
MAKING CONNECTIONS
Recognize and apply connections of important information and ideas
within and among learning areas. Mathematics is used extensively
in business; the life, natural and physical sciences; the social
sciences; and in the fine arts. Medicine, architecture, engineering,
the industrial arts and a multitude of occupations are also dependent
on mathematics. Mathematics offers necessary tools and ways of
thinking to unite the concepts, relationships and procedures common
to these areas. Mathematics provides a language for expressing
ideas across disciplines, while, at the same time, providing connections
linking number and operation, measurement, geometry, data and
algebra within mathematics itself. Students must have experiences
which require them to make such connections among mathematics
and other disciplines. They will then see the power and utility
that mathematics brings to expressing, understanding and solving
problems in diverse settings beyond the classroom.
STATE GOAL 6: Demonstrate and apply a knowledge and sense
of numbers, including numeration and operations (addition, subtraction,
multiplication, division), patterns, ratios and proportions.
STATE GOAL 7: Estimate, make and use measurements of objects,
quantities and relationships and determine acceptable levels of
accuracy.
STATE GOAL 8: Use algebraic and analytical methods to identify
and describe patterns and relationships in data, solve problems
and predict results.
STATE GOAL 9: Use geometric methods to analyze, categorize
and draw conclusions about points, lines, planes and space.
STATE GOAL 10: Collect, organize and analyze data using
statistical methods; predict results; and interpret uncertainty
using concepts of probability.
BEGINNING ALGEBRA
MAT120
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: none
Beginning Algebra is the study of the real number system and its properties. Methods of solving various kinds of equations and inequalities with variables, characteristics of ratios and proportions, solving proportions and applying proportions to real-world situations, functions with tables and graphs, and characteristics of linear equations are among the topics studied.
INTERMEDIATE ALGEBRA
MAT130
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Successful completion of Beginning Algebra
Intermediate Algebra is a continuation of the study of the real number system and it properties studied in Beginning Algebra. Methods of solving systems of two equations with two variables, properties of exponents and scientific notation, evaluation exponential equations, factoring polynomials, solving quadratic equations, simplifying expressions containing radicals, and solving and graphing equations involving rational expressions are among the topics studied.
BUSINESS MATH
MAT200
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Algebra I or Beginning Algebra
This course is to prepare students to be competent consumers and business persons in tomorrow's marketplace. It reviews basic math skills, and gives the student practice in applying math to personal business and business situations. The personal business topics include net and gross income, pricing and sales tax, checking and savings accounts, credit cards, loans, automobile purchase and operation, housing costs, insurance, investments, and record keeping.
TECHNICAL MATH
MAT210
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Algebra I or Intermediate Algebra or permission
of instructor
This course is designed to develop and refine job- related mathematical skills.
GEOMETRY
MAT220
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Algebra I or Intermediate Algebra
Geometry is the study of plane and solid figures and logic. Students will learn how to use deductive and inductive reasoning techniques to solve problems. These problems will include topics involving triangle relationships, ratio and proportion, parallel and perpendicular lines and circles. In addition, plane figures will be constructed with compass and straight edge, formulas for areas and volumes of plane and solid figures will be derived and applied, and transformations will be studied. Students complete a major project every quarter.
ALGEBRA II
MAT321 (This course receives an honor point of 1.00 plus the points
for the grade)
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Algebra I and Geometry
Algebra II reviews some topics of Algebra I and emphasizes the study of non-linear equations and trigonometry.
ADVANCED MATH
MAT410
Length of Course: 2 semesters
Credit: 1 unit
Prerequisite: Algebra II
This class is intended for students who desire to take four years of math in high school but do not wish to take PreCalculus or Calculus immediately. The focus is on problem solving skills, group problem solving, problem presentation, and on consolidating previously learned math skills.
PRECALCULUS
MAT421 (This course receives an honor point of 1.00 plus the points
for the grade)
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Algebra II
The course enables students to display, describe, transform, and interpret numerical information represented as data, graphs, or equations. It integrates statistical, algebraic, and trigonometric concepts, and also previews calculus in its work with functions and in its development of intuitive notions of limit.
AP CALCULUS
MAT431 (This course receives an honor point of 1.00 plus the points
for the grade)
Length of course: 2 semesters
Credit: 1 unit
Prerequisite: Precalculus
This course prepares students for the Advanced Placement Calculus Exam which qualifies them for credit and advanced placement at most colleges and universities.