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Math Resources (Page
2 of 4): Middle, Secondary, Post-Secondary Levels Subject Specific
Resources

Algebra
Algebasics.com contains 16 sections of
step-by-step worked out problems on algebraic concepts. Use this site with middle school students and above to introduce concepts or for test review,
including SAT review. Macromedia Flash is used accompanied with audio
explanations from a math teacher. Select from hundreds of problems
beginning with order of operations, rules for working with signed numbers,
equations, ratio/proportion, inequalities, absolute value, exponents,
polynomials, factoring, rational expressions/equations, linear equations and
their systems, functions, radicals, quadratics, and applications.
AlgebraLab.org focuses on topics and
skills from high school mathematics that students need for introductory science
courses. You'll find topics in algebra I and II, geometry, trigonometry,
statistics. There are lessons, hands-on activities, an interactive
glossary, study aids with interactive practice problems, technical reading
passages, word problems, connections between math and science to various
careers, and more. The project was developed in conjunction with a Florida
Department of Education Enhancing Education Through Technology Competitive
Grant, a National Council of Teachers of Mathematics' Edward G. Begle Grant for
classroom-based research in precollege mathematics, and Florida's Volusia County
Schools.
Elementary Algebra with
Applications (3rd edition) is a free online text from GetMath.com and
Bernard Klein Publishing for students who have not had a formal course in
algebra. The entire document can be downloaded. Quizzes, tests, and
answers are included. Written by experienced math teachers.
The
Math Dude, available from Montgomery Public Schools (MD), is an award
winning video series for helping middle and high school learners of Algebra I.
Shows can be viewed on the Web, via podcasts through iTunes or RSS feeds, or
downloaded to your computer. These are a must see!
Purplemath
is a "not to miss" Algebra resource with lessons on preliminary,
beginning, intermediate, advanced topics, and word problems. An extensive
list of Internet resources related to Algebra is also provided, including a link
to online calculators. This site, developed by E. Stapel of Western
International University, is award winning.
Virtual Math Lab
from West Texas A&M University concentrates on Beginning Algebra,
Intermediate Algebra, and College Algebra. Each course has complete
tutorials (many with video explanations), practice problems with answers, and resources for
extra help.
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Geometry
Geometry.net is a comprehensive math
search engine for middle school math and above. Additional topics include
computers and the Internet, technology, physics, biology, biographers, and
sports. There is a math help desk with 28 sub-categories, and resources
for standardized test preparation.
Geometry from the Land
of the Incas, by Antonio Gutierrez, is an award-winning site that provides
an eclectic mix of sound, science, and Incan history intended to interest
students in Euclidean geometry. The site includes geometry problems, proofs,
quizzes, puzzles, quotations, scientific speculation, and more. Best used
with high school students and above.
Mathematics Open Reference
is a free plane geometry textbook for high school learners. Its focus is
on using interactive materials and animations to develop concepts.
Sections on constructions are excellent.
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Trigonometry and Pre-Calculus
Dave's Short Trig
Course, by Dave Joyce of Clark University in Massachusetts, contains
explanations, practice problems and answers. Best of all is that images
are virtual manipulatives developed in Java so that learners can explore the
properties presented. A brief background of the Pythagorean Theorem and
similar triangles is included. See also
Dave's Short Course on Complex
Numbers
Demos with Positive Impact connects
instructors of pre-calculus, calculus, and post-calculus courses with effective
teaching tools to help them get important ideas across to students during their
lectures. This project focuses on demonstrations that use some form of
instructional technology (e.g., physical equipment or examples, graphical
displays, simulations, computations, interactive modules, calculators, computers
and computer software, the Web). Really first-rate!
Exploring
Precalculus, by Dr. William Mueller, provides an introduction to precalculus
using Mathcad or StudyWorks as a calculation and visualization tool. Many
interactive examples let you explore the concepts and practice the skills
necessary for understanding calculus. Central themes (functions, rates of
change, and accumulation) are developed intuitively, from several perspectives
(algebraic, numeric, and graphic). Materials suitable for use in grades
9-12, and post-secondary.
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Calculus
Calc101 provides automatic solutions,
powered by webMathematica, to derivative and integral problems found in
beginning calculus. The site's goal is to help you to raise your grade by 10%.
Get all the steps including the final answer. Step-by-step matrix operations and
determinants are coming soon; linear equations will come later. Derivatives and
polynomial multiplication and division are free. There is a small fee for
integral solutions and linear algebra, but you can always see the first and last
step.
Calculus by
International Education Software helps students to learn about limits,
derivatives, and integrals visually through precise definitions and a series of
interactive applets.
Calculus is among math projects at the secondary education level
posted at Curriki and the
Global Education and Learning Community. Java is used for complete courses
in AP Calculus at both the AB (Introductory Calculus 1 and 2) and BC
(General Calculus 1 and 2) levels. Audio explanations accompany text
equivalent and multimedia demonstrations of concepts are presented.
Interactive practice problems are presented to test understanding.
Feedback shows how answers are derived. This is truly worth using.
Note Java modules might take a while to download.
Calculus: Graphics for
the Calculus Classroom by Douglas Arnold of the University of
Minnesota. This site contains a series of graphical demonstrations
suitable for first year calculus: a differentials and differences animation,
computing the volume of water in a tipped glass, Archimedes' calculation of pi,
animation of a bouncing ball, secants and tangents, zooming in on a tangent
line, a trig limit, graphs for a discussion on limits, a nowhere differentiable
function, introduction to the number e, and computing the volume of the
region formed by two intersecting cylinders.
Calculus on the Web is
partially supported by the National Science Foundation and is a project of G.
Mendoza and D. Reich at Temple University. This site has interactive
exercises with feedback and help sections that explain concepts. There are
seven books online: Precalculus; Calculus 1, 2, and 3; Linear Algebra, Number
Theory, and Abstract Algebra.
Calculus-help.com by M.
Kelley has been recognized by The National Council of Teachers of Mathematics
and The College Board. Don't miss Tutorials
for the Calculus Phobe, an ongoing project to present topics from this
subject in an easily understood audio-visual format. Flash animation is
incorporated. Topics include limits, continuity, differentiation, with
more to come.
Calculus: The Integrator from Wolfram
Research is powered by webMathematica. Enter any expression and the
integration is performed for you. Also read about the history and
applications of integration.
Calculus Tutor --
Karl's Calculus Tutor includes number systems, limits, continuity, derivatives
and applications, exponentials and logs, trig functions, and sections on
integration and applications. Some interactive features are included.
Demos with Positive Impact connects
instructors of pre-calculus, calculus, and post-calculus courses with effective
teaching tools to help them get important ideas across to students during their
lectures. This project focuses on demonstrations that use some form of
instructional technology (e.g., physical equipment or examples, graphical
displays, simulations, computations, interactive modules, calculators, computers
and computer software, the Web). Really first-rate!
Visual Calculus
from the University of Tennessee Math Department at Knoxville is an excellent
resource that includes tutorials, drills and programs for pre-calculus and
calculus. Animations, interactive pages, step-by-step solutions and
illustrations are included for topics ranging from functions, graphing with
technology, solving equations, and conic sections to limits and continuity,
derivatives and applications, integration and applications, sequences and
series. As a veteran calculus teacher, P. Deubel highly recommends this
site.
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Statistics and Probability
DIG Stats is an excellent
resource for integrating statistics and data visualization into mathematics and
science courses in grades 9-14. Modules with student activities cover concepts
from descriptive statistics, inferential statistics, two dimensional graphical
analysis and three dimensional data visualization. Using Microsoft Excel
and graphing calculators, students analyze real world data sets from a variety
of scientific disciplines. Data were derived from WWW databases,
university and government researchers, and student projects. Guides,
quizzes, and answers are provided. This site is associated with the
Central Virginia Governor's School for Science and Technology.
Exploring Data provides
curriculum support materials for teachers of high school and up introductory
statistics. These include activities, worksheets, overhead
transparency masters, datasets and assessment to support data exploration, and a
collection of articles to learn about statistics. Explore concepts like stem
plots, dot plots, histograms, measures of location, box plots, normal plots,
scatter plots, assessment, linear regression, probability, hypothesis testing,
curve fitting, and much more. A resource list of additional support materials
includes texts, web sites, datasets, java applets and mailing lists. Most
of the resources of the site are the property of Education Queensland in
Australia.
Statistics:
Power from Data, a product of Statistics Canada, is a complete online
text with exercises, answers, and lesson plans. Although intended for use
with secondary students, the text could be used with middle school or
post-secondary audiences. Chapters address data collection, data
processing, problems with using information, organizing data, graph types,
analytical graphing, measures of central tendency and spread, sampling methods,
and more. There is a glossary.
What are the Odds? The Ins and Outs of Probability (by graduate students at
University of Virginia) if primarily for secondary students. It contains
lesson plans, an interactive quiz, an extensive data bank of questions relating
to probability concepts sorted by topic, history, and additional resources on
probability.
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Multiple
Subjects
Analyze Math by A. Dendane (United
Arab Emirates University) contains math tutorials and problems (with
applets) for a various topics in algebra, trig, geometry, calculus, and more.
Excellent explanations.
Argyll Centre of Edmonton Public Schools in Canada hosts Jim
Reed's Math and Science Resources. His resources address elementary and secondary
topics in numbers/operations, patterns and relations, shape and space,
probability and statistics, algebra, geometry, and trigonometry. Students can
engage with interactive learning activities, see movies, and manipulate
excellent Java math applets to study concepts. The site is also an
excellent resource for the home-schooled student. Highly recommended.
FlashyApps.com uses Flash accompanied by audio to illustrate some basic
principles of mathematics (multiplication and division), algebra (quadratic
function) and an introduction to trigonometry. The flash animations for
illustrating the development of the six trig graphs are particularly useful for
classroom demonstration.
GeoGebra is free,
multiplatform, dynamic mathematics software for secondary schools that
joins geometry, algebra and calculus. You can do constructions with
points, vectors, segments, lines, conic sections as well as functions
and change them dynamically afterwards. You can enter equations
and coordinates directly. GeoGebra has the ability to deal with
variables for numbers, vectors and points, finds derivatives and
integrals of functions and offers commands like Root or
Extremum. It received several international awards, including
the European and German educational software awards. In
Dynamic
Mathematics with GeoGebra, authors Markus Hohenwarter, principle
developer of the software, and Judith Preiner (2007) illustrate the
basic ideas of the software and some of its versatile possibilities by
discussing several interactive examples.
HippoCampus,
a project of the Monterey Institute for Technology and Education, is a "free,
public website for high school and college students that offers NROC multimedia
correlated to most major textbooks." NROC is the National
Repository of Online Courses for students and faculty in higher education, high
school, and advanced placement. Among the full math textbooks online are
Algebra (IA, IB, and Elementary) and Calculus (Introductory I and II,
General I and II, AB and BC levels for advanced placement). Multimedia
includes audio explanations, visuals, interactivity. Individual
instructors can customize the Hippo website to better meet the needs for groups
of students. Highly recommended.
MathBits.com "is devoted to offering fun, yet challenging, lessons and
activities in high school (and college level) mathematics and computer
programming for students and teachers." Subjects include algebra 1,
geometry (including materials for using Geometer Sketchpad), and algebra 2,
principally.
Mathematics
Across the Curriculum Electronic Bookshelf developed at Dartmouth
College features materials with an interdisciplinary approach to mathematics
topics. The bookshelf topics include algebra, calculus and differential
equations, physical science, art, computer sciences, pre-algebra, history and
geography, literature, biology/medicine/psychology, data analysis, statistics,
business/economics, math and music, discrete math, and trigonometry.
National
Curve Bank, maintained at the Department of Mathematics at California State
University, Los Angeles, contains highly relevant visual content and
explanations for upper level mathematics--calculus, pre-calculus, trigonometry,
geometry, fractals, and so on. JAVA applets are included. Some
content includes practice problems on various topics. The developers
"strive to provide features - for example, animation and
interaction - that a printed page cannot offer." Geometrical, algebraic, and
historical aspects of curves, "the kinds of attributes that make the mathematics
special and enrich classroom learning" are included.
Participants are encouraged to submit your best web
animation as a "deposit" in the National Curve Bank. Highly
recommended!
Science
and Mathematics Initiative for Learning Enhancement (SMILE) at the Illinois
Institute of Technology contains over 900 individual lessons in Biology,
Chemistry, Mathematics, and Physics written by teachers and for teachers.
"The SMILE program is designed to enhance the elementary and high school
learning of Science and Mathematics through the use of the phenomenological
approach." The section on mathematics contains almost 200 single
concept lessons on geometry and measurement, patterns and logic, probability and
statistics, recreational and creative math, practical and applied math,
arithmetic, graphs and visuals, algebra and trigonometry, and miscellaneous.
S.O.S. MATHematics by Math
Medics, L.L.C., in Texas contains over 2500 pages of short and easily understood
explanations from simplifying fractions to algebra, trigonometry, calculus,
differential equations, complex variables, matrix algebra. Tables are
included and a link to CyberExams to practice for tests and quizzes. Site
is for high school, college, and adult learners.
The Math Page is by
Lawrence Spector of the Borough of Manhattan Community College, The City
University of New York. This site has four major sections. Practice
problems illustrating concepts are presented throughout with
answers.
- Skills in Arithmetic is a complete course, which includes addition,
subtraction, multiplication, division; mental arithmetic, powers of 10,
regrouping, decimals, parts of natural numbers, fractions, and percents.
- Topics in Trigonometry addresses ratio and proportion, definitions of the
trig functions, solving right triangles, the 30-60-90 degree right triangle,
the law of sines, the law of cosines, the unit circle, radian measure, and
arc length.
- Topics in Pre-calculus include formal rules of algebra, rational and
irrational numbers, functions and graphs, logarithms, the binomial theorem,
and mathematical induction.
- The Evolution of Real Numbers.
Zona Land's More
Mathematics than Science is devoted to helping students understand algebra,
geometry (including conic sections), trigonometry, and curve fitting.
Don't miss the interactive manipulatives and virtual reality demonstrations of
concepts.

 Spice
up the first five minutes of your high school and lower-division college math
classes with Mudd Math Fun Facts.
Fun Facts are designed for, and work best in courses where the typical student
needs that boost to generate interest and arouse curiosity in math. The
Fun Facts will cause students who are studying algebra, geometry, probability,
calculus, number theory, and topology, for example, to look at mathematics
differently!
Taken from the quick activity on multiplication by 11, can you figure out
what's going on here?
253 x 11 = 2783
117 x 11 = 1287
532 x 11 = 5852
267 x 11 = 2937
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References:
Hohenwarter, M., &
Preiner, J. (2007, Mar.) Dynamic mathematics with GeoGebra [online].
Journal of Online Mathematics and Its Applications, 7, article
#1448. Available:
http://www.maa.org/joma/Volume7/Hohenwarter/index.html
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See
other pages of the section on Math Web Resources and Standardized Test
Preparation: Math Manipulatives and Standardized
Test Preparation.
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