**The Math Teacher**

*In taking a moment to consider the amazing
multitude of careers that humans endeavor in, certainly one of the most stereotyped,
misunderstood and critical-to-mankind professions is that of the math teacher.
Today, with the information revolution completely rewriting the way we live
our lives, the math teacher must be at the forefront of knowing what
the latest tools and resources exist for her to utilize. The longest section
of this website by a huge margin, and arguably the most important, the following
resources are intended for the modern-day math teacher to enhance her lessons
and engage her students.*

*NOTE: Unlike the rest of the site, since
this particular resource list is so lengthy I refrained from including icons
with direct links and instead provided the URL for your perusal. Also thanks
to my classmates in the course "Computers in Math Education" for helping
build this great list! *

__MATHEMATICAL TOPIC: “Calculus/Integrals”__

1) Site: Karl’s Calculus Tutor – Section 11: “Methods of Integration”

URL: http://www.karlscalculus.org/calc11_1.html

Content: The above URL will take the user to a page called “Methods of
Integration.” From there, the user can use the table of contents link
at the bottom of the page to link to pages covering various calculus topics.
This site contains step-by-step examples of how to calculate an integral. The
author adds a fun style of teaching the subject matter by using examples like
the “Death Star.”

Uses: This site is good as both a reference and a learning aid for finding the
indefinite integral. The site begins with an easy to follow example and builds
on it. The site explains the integration techniques for functions involving
the number “e”, logarithms, fractions, functions with constants,
and trigonometric functions. Throughout the site, there are links to click on
if a refresher is needed for a specific topic. There are also problems to work
out with links to the solutions which is a helpful practice tool.

2) Site: Antiderivative

URL: http://en.wikipedia.org/wiki/Indefinite_integral

Content: This site defines the antiderivative, shows the uses and properties,
gives techniques for solving, and lists several examples. Throughout the site,
the key words or concepts are highlighted and provide a link to other pages
that give an explanation of the word or concept.

Uses: This site provided a good general understanding of how to calculate the
antiderivative and how it can be used to compute the definite integral using
the “fundamental theorem of calculus.” The links on this page provide
an extensive knowledge-base of integration. Teachers and students can benefit
from this site and it can be used either as a refresher or to study integration
in more depth.

3) Site: Definite Integral

URL: http://mathworld.wolfram.com/DefiniteIntegral.html

Content: This site defines the definite integral and shows its relation to the
indefinite integral. The “fundamental theorem of calculus” is used
to explain the definite integral. There is much reference to history of math
and many famous mathematicians are noted. The “Leibniz integration rule”,
“Newton-Cotes formulas”, the “Euler-Mascheroni constant”
are a few of the famous names that appear.

Uses: This site explores some of the more complex integrals. The student interested
in advancing their understanding of integral calculus and its origins will find
this site useful. The site is a bit advanced for the student that wants to learn
about integration for the first time.

4) Site: The Wolfram Integrator

URL: http://integrals.wolfram.com/index.jsp

Content: This is a small site that is very powerful. The site contains an integral
calculator. Along with the “integrator” are links to the history
of integration, the functionality of the integrator, and frequently asked questions.
When the answer is displayed, links appear to give a further understanding.
There are random examples that can be solved or the user can enter a function
and the integrator will solve for the integral and display it.

Uses: This site is excellent for solving integration problems. A user is prompted
to enter any function and the integrator will display the answer with a link
for further discovery. This can be used to check an integration problem worked
out by hand, or to simply explore different integration techniques. The links
that explain the integration rules are helpful learning aids.

5) Site: Riemann Sums

URL: http://science.kennesaw.edu/~plaval/applets/Riemann.html

Content: This site contains an applet that shows how Riemann Sums can be used
to calculate the area between the x-axis, the graph of y=f(x), and the vertical
lines x=a, and x=b. The applet contains areas to enter the required information
and a display area that shows a graphing window to view the results. Along with
the applet is extensive information on how to use the applet. The site contains
a link to pages that help the user with the proper syntax for the java applet.

Uses: This site is both an excellent teaching aid as well as a learning aid.
The user of this site enters a function along with an interval, the number of
sub- intervals to use, and one of five methods of calculating Riemann Sums.
The calculated area is then displayed. This site is an excellent way to show
the link between the definite integral and the Riemann Sum.

__MATHEMATICAL TOPIC: “Symbols used in Mathematics”__

1) Site: The History of zero

URL: http://www.yaleglobal.yale.edu/about/zero.jsp

Content: Zero is perhaps the most pervasive symbol known. A complete history
of the number zero is presented. The site explains how zero was discovered in
the East and how it took centuries for it to make its way to the West. Included
is the idea of zero being used as a placeholder long before it was used in any
mathematical calculations. The dilemma of division by zero is presented as well
as the crucial role it played in the development of calculus.

Uses: This site provides a valuable history lesson about just how important
the number zero is and how it helped to shape our present-day mathematics. The
site is a good source for getting the student interested in other areas of mathematics
history.

2) Site: Compounding Interest and e

URL: http://mathforum.org/library/drmath/view/52559.html

Content: Included is a brief history of how the number ‘e’ was discovered
and who discovered it. The steps involved in discovering this number are also
presented. Also included is the most popular use of the number ‘e’
in calculating compound interest.

Uses: This site will educate the student on how the number e was discovered
and who discovered it. The steps listed in determining ‘e’ are relatively
easy to follow. The student will learn how to derive this number by using the
binomial theorem and expanding a series until it converges on the number ‘e.’

3) Site: Talking about Pi

URL: http://www.cecm.sfu.ca/~jborwein/pi_cover.html

Content: This site contains a comprehensive repository of information on .

Included is the life and history of pi, lectures on pi, papers on pi, and many
links to fun facts about pi including a formula for calculating 1.24 trillion
digits of pi.

Uses: This site can be used by students and instructors to either introduce
the number pi, or to study some of its more advanced uses. The fun facts and
history, along with a chronology make it a great source for anyone doing research
or writing a paper on the subject.

4) Site: Dianne’s Guide to Complex Numbers

URL: http://people.bath.ac.uk/ma3dcp/complexhome.html

Content: This site contains a history of the square root of minus one, definitions
of imaginary and complex numbers, properties of complex numbers, as well as
theorems and formulas like DeMoivre’s Theorem and Euler’s Formula.

Uses: This site can be used by students and teachers to either introduce the
concept of complex numbers, or to study some of their more advanced uses. The
site is an excellent reference for writing a paper on the subject. It is also
very useful in learning how to compute complex numbers and how they are used
in some formulas and theorems.

5) Site: You can’t get there from here.

URL: http://www.mathacademy.com/pr/minitext/infinity/

Content: This site introduces the concept of infinity in a manner similar to
the way most of us were probably introduced to it as children. Included is the
idea of infinity getting smaller and smaller and how artists like M.C. Escher
depicted this. This history of infinity is presented with mention of some of
the great mathematicians like Aristotle, Cantor, Galileo, Gauss, and Wallis.
“Cantors Set Theory” is explained using a depiction of two hands
placed together. There is a link at the bottom of the page that takes you to
the “Link Library.” There are other useful sites that cover various
mathematics topics in this library.

Uses: This site is useful for students and teachers of math that want to understand
the origin and uses of infinity and for “non-math” people that are
just curious. It is a valuable reference for writing papers as well as introducing
some concepts on set theory. “Do all infinite sets have the same cardinality?”
This interesting question posed by Cantor is answered.

__Topic: Complex Numbers__

1. Dave’s Short Course on Complex Numbers

• URL: http://www.clarku.edu/~djoyce/complex/

• Content: This site contains much information about complex numbers in
a text book fashion. It has an outline on links that explain this concept and
where/why it is used in absolute values, powers & roots, angles/polar coordinates,
etc.

• Uses: This is a good site to find additional information about complex
numbers that the student’s textbook might not have. There are plenty of
diagrams that are good visuals in case the student is not understanding the
text. Also, having all the information in one place is an advantage because
it can give the student the idea that complex numbers are not going to be in
one particular unit. These numbers are used all throughout math.

2. WolframMathWorld

• URL: http://mathworld.wolfram.com/ComplexNumber.html

• Content: The contents on this site begin on one page. There are links
on specific words that go into further explanations when clicked. It starts
with the definition moving to history and then how complex numbers are used.

• Uses: Searching for information on this site is made easy by the links
associated with each short description. Clicking on Complex Multiplication shortcuts
to a page contains the step-by-step instructions. This page also contains many
other links that relate to this particular topic.

3. College Algebra Tutorial 12: Complex Numbers

• URL: http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut12_complexnum.htm

• Content: This site is a scaled down version of teaching complex numbers.
It is explained simply with more examples than descriptions. It walks the student
through from the standard form to addition/subtraction to square roots. There
are links to definitions of key terms.

• Uses: This sequential listing of the use of complex numbers is wonderful
tool for those beginning. There are sample problems at the end of the page that
give the answer and walk through the solution. These problems make for a more
interesting interactive site.

4. The Math Forum @ Drexel

• URL: http://mathforum.org/dr.math/faq/faq.imag.num.html

• Content: The site contains introductions to specific math disciplines
and then has a Questions and Answers section from students. The questions and
information are organized by levels such as middle school, high school, or college.

• Uses: This is a good site for students to research for problems similar
to what they are experiencing in class. Students can browse or search archives
and they can ask question that will be answer by Dr. Math. This site also provides
math puzzles for those who like to be challenged.

5. John & Betty’s Journey into Complex Numbers

• URL: http://mathforum.org/johnandbetty/

• Content: This is a fun site that wrote a children’s book around
complex numbers. It walks the student through in a child’s world to explain
how the come about imaginary numbers and what you can do with them.

• Uses: This would be a great book for students to read and write a report
on. It uses imagination with math that may appeal to more students. These students
may even learn quicker from this format then lecture and textbooks.

__Topic: Cartesian Coordinate Systems__

1. Drawing Plane and Coordinate Systems

• URL: http://www.univie.ac.at/future.media/moe/galerie/zeich/zeich.html

• Content: This site has applets that are interactive. It has them for
the Cartesian coordinates, coordinate systems, polar coordinates, and oblique
coordinates. It goes into a bit of explanation but not in depth.

• Uses: Students could use this as and introduction to systems. It would
help them to get the gist of the coordinate world. They would need tasks assigned
to use these applets properly.

2. Coordinate Systems Overview

• URL: http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys.html

• Content: There are many coordinate systems on this page and the Cartesian
is one of them under the title “Basic Coordinate Systems”. It has
links to graphs of common terms. These graphs contain explanations and equations
used in these systems.

• Uses: This is another introductory site but goes another step. It contains
geographic systems so the student can see that these coordinate systems actually
have a real world use. The Global Systems would be an excellent example for
students to peruse.

3. Cartesian Coordinate System

• URL: http://en.wikipedia.org/wiki/Cartesian_coordinate_system

• Content: The page for this is full of information to teach the coordinate
system. It moves from the definition to history and captures the two & three-dimensional
systems. It also goes into the quadrants.

• Uses: For a formal definition, this is a good site to introduce some
higher key concepts. Albeit non-interactive, it has the correct information
for a student to learn from. It also has many links to key terms and relevant
subjects.

4. Maths – Cartesian Coordinate Systems – Martin Baker

• URL: http://www.euclideanspace.com/maths/geometry/coordinatesystems/cartesian/index.htm

• Content: This site gets more into the 3-D aspect of the Cartesian coordinate.
It uses pictures to get the point across for teaching right/left hand coordinate
systems.

• Uses: Teaching 3-D planes is made easier by this site because the pictures
of the hands. Students could imitate these pictures instead of the teacher doing
this at the front of the class. Sometimes it is hard to get this concept across
and this page may be the solution for some students.

5. Cartesian Coordinates

• URL: http://www.warnercnr.colostate.edu/class_info/nr502/lg1/glossary/cartesian.html

• Content: This site contains a graphic that shows how a Cartesian coordinate
system would work on a map of the United States. It puts a graph in the middle
of the US and graphs major cities.

• Uses: As a short introduction, this would be a good way to show real
world examples to the students. There is a link to a page called “Identifying
Locations” which is more real world examples.

__Topic: Logarithms__

1. Logarithms – Topic in Pre-Calculus

• URL: http://www.themathpage.com/aPreCalc/logarithms.htm#common

• Content: This contains simple definitions of logarithms including natural
& common logs and the laws. It has examples that when finished, rolling
the mouse pointer over the pink squares will reveal the answers.

• Uses: It is a good introductory page to logs and this could be used
as a homework assignment. It has enough background and examples to be used in
such a way.

2. Math Skills Review - Logarithms

• URL: http://www.chem.tamu.edu/class/fyp/mathrev/mr-log.html

• Content: This is a nice summary site of logarithm facts. It also teaches
how to find the logs on a calculator. There are sample problems that deal with
the natural/common logs.

• Uses: This is another site that would be a good assignment for students.
It has the descriptions for higher level thinking so this would be better suited
for high school/college age.

3. Properties of Logarithms

• URL: http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/calctopic1/logs.html

• Content: This site contains instruction on logarithms and has interactive
questions examples. It allows guessing for the answers and then eventually if
it is not solved, there is a “peek” button to obtain the answer.

• Uses: This would be something the students could do in class with the
help of a teacher. The interactive examples would appeal to some students and
help them learn more in the process.

4. Properties of Logarithms

• URL: http://campus.northpark.edu/math/PreCalculus/Transcendental/Logarithmic/Properties/index.html

• Content: For a higher level college class, this is a site that would
be appropriate to visit because of its use of interactive graphs. It also has
links to key terms and examples to follow.

• Uses: Graphing logs is important to understanding some of the concepts
of logarithms. This site provide the interactive tool to accomplish small assignments.

5. What the Heck are Logarithms

• URL: http://www.ces.clemson.edu/ge/staff/park/Class/ENGR120/Handouts/Logarithms.html

• Content: This not a well formatted site but the information is really
good. It walks through logs in a logical way without the calculator. It stresses
understanding the concept instead of memorizing.

• Uses: This would be a good structure for teaching a class. There is
so much here to use but not using the site. The examples are good as well as
how it is written.

__PROBABILITY__

Site: Mrs. Glosser’s Math Goodies

URL: http://www.mathgoodies.com/lessons/vol6/intro_probability.html

Content: This site contains examples and key terms related to probability. It
also links to interactive puzzles and worksheets. Each example is accompanied
by an experiment findings probability using a spinner, a dice, and marbles in
a jar.

Uses: Students, parents, and teachers could use this site to review key terms
of probability (outcomes, events, etc). Elementary teachers could use this site
as an introduction to probability. Students could use the site for review and
reinforcement. Simple and straight forward site.

Site: Statistics Glossary

URL: http://www.cas.lancs.ac.uk/glossary_v1.1/prob.html - outcome

Content: This site contains rules for multiplying probability, explaining simple
events, possible outcomes. Bayes Theorem. The site list several areas of probability
each area is linked to an explanation and example.

Uses: teachers could use this site to research areas probability.

Site: Probability Games

URL: http://www.rsscse.org.uk/pose/level1/book7/notes.htm

Content: Games to help students build a foundation about the concept of probability.
The site includes instructions for games, examples of templates of game pieces,
post-test questions and answers.

Uses: Teachers could use this site to create get ideas for game that could be
use to enhance and enrich teaching probability.

Site: Figures from the History of Probability and Statistics

URL: http://www.economics.soton.ac.uk/staff/aldrich/Figures.htm

Content: This site contains a list of mathematicians who contributes to the
study of probability and statistics. The list is also in chronological order
so that the storied that impacted probability are in order. There are links
to math theories about probability, ideas for using probability in the classroom.

Uses: Students could use this sight to conduct intense research on those who
contributed and impacted to evolution of probability. Teachers could use this
site to gain background knowledge on Bayes, Fisher, Gauss, and many more.

Site: Wolfram Math World

URL: http://mathworld.wolfram.com/Probability.html

Content: This site contains links to vocabulary terms and symbols related to
probability, explanations for each term and other resources related to probability.

Uses: Teachers could use the site as a reference because it links sites like
the Introduction of Probability models.

__PYTHAGOREAN THEOREM__

Site: Pythagorean Theorem and Its Many Proofs

URL: http://www.cut-the-knot.org/pythagoras/index.shtml

Content: This site includes the laws of cosine, general formula for the Pythagorean
theorem, and 72 Proofs for the Pythagorean theorem.

Uses: Teachers could use this site a research tool. They could also use the
proofs and examples of how the Pythagorean theorem works.

Site: The Pythagorean theorem

URL: http://www.geom.uiuc.edu/~demo5337/Group3/promenu.html

Content: This site contains pre-Pythagorean theorem information. It also introduces
the Pythagorean. Also include on this site is the Square Root Spiral and hands-on
activities.

Uses: Students could use this site to review lines, angles and other information
necessary to developing and understanding about the Pythagorean theorem.

Site: Pythagorean theorem

URL: http://mathematica.ludibunda.ch/pythagoras6.html

Content: This site has a history of the Pythagorean theorem, interactive proofs
and other resources to be used.

Uses: Students could use this site for visual proof and better understanding
of the Pythagorean theorem.

Site: The Pythagorean theorem

URL: http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html

Content: This site includes a brief history of the Pythagorean theorem, Pythagorean
triplets, suggestions for hands-on activities students could do.

Uses: Students could benefit from the visual proofs on the site. Students could
also this site for in depth explanations of the Pythagorean.

Site: The Pythagorean theorem

URL: http://www.ms.uky.edu/~lee/ma502/pythag/pythag.htm

Content: Law of Cosines, brief history

Uses: Students could use this site to student early uses of the Pythagorean
theorem.

__POLYGONS__

Site: The World of Math Online

URL: http://www.math.com/tables/geometry/polygons.htm - types

Content: This site includes definitions, visual examples, formulas for calculating
area of a regular polygon and the sum of the interior angles, and names of polygons,
parts of polygon

Uses: Teachers and students could use to begin investigating polygons and terms
related to polygons.

Site: Math is Fun

URL: http://www.mathsisfun.com/geometry/plane.html

Content: This site includes a list of two dimensional shapes, formulas for two-dimensional
shapes, description of acute, right, obtuse, straight and reflex angles, geometric
symbols such as perpendicular and parallel.

Uses: Teachers could use this site as a resource or as a teaching aide.

Site: Open Math Reference

URL: http://www.mathopenref.com/tocs/polygontoc.html

Content: An interactive example of regular and irregular polygon. Properties
of polygons and links related to the topic of polygons.

Uses: Teachers could this site to teach children how the interior angles of
polygons change as the sides increase. Students could use the site to independently
investigate diagonals and more.

Site: The Math Forum @ Drexel

URL: http://mathforum.org/dr.math/faq/faq.polygon.names.html

Content: This site includes the names of polygons, the origins of polygon names.

Uses: This site provides students with fun interesting information about polygons.

Site: Figures and polygons

URL: http://www.mathleague.com/help/geometry/polygons.htm

Content: Several images of polygons

Uses: Teachers can use this site as a resource and teaching tool.

__TOPIC: The History of Pi__

Site: Pi History

URL: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html

Contents: This site provides a chronology history of the number pi. This site
provides references to how pi was used through out history and how pi was used
in different math formulas.

Uses: Teachers and students could use this website when getting ready for pi
day. Teacher could find interesting facts about pi through history and possibly
create web quest for students for a pi day activity. Students could use this
website when answering the questions posed in the web quest.

Site: History of Pi

URL: http://www.exploratorium.edu/pi/history_of_pi/index.html

Content: This site gives a brief history of the number pi. This history starts
with the use of pi by the ancient Babylonians to the uses of pi in the 18th
century.

Uses: This site would provide great background information for creating a web
quest for pi day. This site could also be used as a quick reference guide for
both students and teachers for pi day.

Site: History of Pi

URL: http://library.thinkquest.org/C0110195/history/history.html

Content: This site provides a definition of pi, a history of pi, uses for pi,
and some fun activities associated with pi.

Uses: This site could be used by both teachers and students for the background
information. Teachers could use this site to create a web quest on pi for pi
day. Teachers could also explore the activities with their students to further
their understanding of the number pi. Students could use this site to help them
answer the questions from the teacher created web quest.

Site: Pi Day

URL: http://www.mathwithmrherte.com/pi_day.htm

Content: This site provides many different activities for pi day.

Uses: Teachers can use this site for the activities for pi day. Teachers could
use these activities to explore the uses of pi with their students on pi day.

Site: Interesting numbers - pi

URL: http://gwydir.demon.co.uk/jo/numbers/interest/pi.htm

Content: This site provides a definition of pi, how to calculate the number
pi, a history of pi, and a table of various formulas that use pi.

Uses: This site is a great resource for teachers when teaching pi. The site
provides very detailed explanations as well as useful graphic for further understanding
of the concept of pi.

__Numbers, Number Systems and Number Relationships__

Site: Count Us In

URL: http://www.abc.net.au/countusin/default.htm

Content: Games that are designed to help students

see relationships between numbers.

Uses: This site contains 15 games that target various math concepts such as:
counting, sorting, ordering numbers, and matching.

Site: Internet 4 Classrooms

URL: http://www.internet4classrooms.com/skills_1st.htm

Content: This is a comprehensive site featuring numerous math games. Games are
organized in groups according to the math skill(s) they reinforce.

Uses: Check out the section on counting to practice counting by 1s, 2s, and
10s. There are also sections devoted to place value, numeration, and ordinal
numbers, a great way to enhance some difficult concepts.

Site: Jenny Eather’s Rainforest Math

URL: http://www.rainforestmaths.com/

Content: This is a comprehensive site featuring numerous math games. These games
will target skills found within the standard: Number, Number Systems and Number
Relationships.

Uses: Click on a level/grade to play various math games. Each game can be played
in Level A (Kindergarten) through Level G (6th grade) which allows you to challenge
or remediate. Tons of great games that will practice: patterns, place value,
odd/even, and number patterns. This site also contains great activities that
help to maintain other math standards (ex. measurement and computation). NOTE:
This is site from Queensland, Australia. Therefore, the money practice will
not suit your child’s needs.

Site: Learning Planet

URL: http://members.learningplanet.com/act/count/free.asp

Content: This is a wonderful site for skip counting.

Uses: First, choose what number you want to count by (1-9). Then the game board
sets up a few numbers in order, randomly arranging the rest. You must sequence
the remaining numbers in order to move on to the next board.

__Computation and Estimation__

Site: Funbrain

URL: http://www.funbrain.com/brain/MathBrain/MathBrain.html

Note: If at first this link does not work, hit REFRESH on your browser

Content: Games designed to practice addition and subtraction.

Uses: This site contains the Math Arcade. Choose male/female, skill level (grade)
and your game piece and then proceed to the arcade. In order to get to the next
level/game, you must win the preceding game. After each win, you move on to
a new level. Neat thing about this site, it provides you with a password at
the end of each level. Therefore, if you need to leave the game for whatever
reason, you can return to the last level achieved. Games center around both
timed and un-timed addition and subtraction practice,

Site: Aplus Math

URL: http://www.aplusmath.com/

Content: Addition and Subtraction Practice

Uses: Practice your addition and subtraction via timed flashcards. This site
also pairs the practice of addition and subtraction facts with fun games such
as: MATHO (similar to Bingo), Uncover the Hidden Picture, Concentration, and
Space Blasters. Some games are timed, while others are not. Options range from
one digit to two digit addition/subtraction, as well as multiplication and division.

Site: Play Kids Games

URL: http://www.playkidsgames.com/mathGames.htm

Content: Addition and Subtraction Practice

Uses: Games such as Save the Math Apples, Space Shuttle Launch, and Robot Calculator,
allow you to set a level (easy, medium, hard) and practice addition and subtraction
facts. Also reinforces place value in that you need to click on individual numbers
in order to create 2 digit numbers. Math Fact Practice allows you to set the
time, skill level, and mathematical operation. At the end of the timed set,
it generates a summary of your work.

Site: Ed By Design

URL: http://www.edbydesign.com/maths/number_cruncher_add.html

Content: Addition Practice

Uses: This site contains The Number Cruncher. Set your level of difficulty (junior,
expert, genius) and solve addition problems until you get to the reward screen.
You must use your keyboard to enter in the answers. Once you have mastered addition
number cruncher, challenge yourself to the subtraction, multiplication and division
versions.

__Measurement and Estimation__

Site: The United States Mint: h.i.p. Pocket Change

URL: http://www.usmint.gov/kids/

Content: A fun, educational site that is maintained by the United States Mint
It provides information on coins, the U.S. Mint, and U.S. History, as well as
interactive games.

Uses: This site contains neat games as well as informational links. Be sure
to play Coin Memory, a great way to practice identification of the heads and
tails of various coins. Cents of Color allows you to view quarters from each
of the fifty states. You can also hit the INFO button to learn what the significance
is of the tail side. The painting option allows you to paint the quarter and
print it out. Pinky’s Create a Card allows the user to create and print
a card. In order to do this, you must first choose your graphics/words from
the gallery and then pay for the designs with money from your virtual bank.
If you give too much, it asks how much change you should receive. Once your
card is complete, print it out!

Site: National Library of Virtual Manipulatives

URL: http://nlvm.usu.edu/en/nav/category_g_1_t_4.html

Content: This link will take you to the NLVM homepage of K-2 Measurement. In
addition to money and time practice, you can work with virtual manipulatives
that are similar to those used in class (ex. geoboards, attribute blocks, pattern
blocks, etc).

Uses: Time – Analog and Digital Clocks allows the user to set a given
time on one clock and see what it will look like on the other clock. Click the
Time- Match Clocks option in order to practice setting the digital clock to
match the wall clock time given by the computer. The Money option, allows you
to count and name money, pay exact amounts, and make a dollar. Click New Problem
in order to pass on problems that may be too difficult.

NOTE: This site is also a great resource for many other math concepts.

Here are a few ideas:

? Use the virtual base-10 blocks in order to reinforce place value.

? Kids love using the Geoboards in class in order to create designs and recreate
a given shape

? Use Attribute Blocks to learn color and shape concepts through sorting.

? Use Pattern Blocks to create/continue patterns

Site: Arcytech: Educational Java Programs

URL: http://arcytech.org/java/money/

Content: This site allows the user to practice counting money.

Uses: Click on Start the Money Program. The computer will tell you what you
are buying and how much you will need. You must move coins/bills into the cart
in order to buy the item. Hit DONE and it will tell you if you are right. Hit
NEXT for another question.

__Mathematical Problem Solving and Communication__

Site: PBS Kids Cyberchase

URL: http://pbskids.org/cyberchase/

Content: This site requires users to think outside the box

in order to work their way through various tasks.

Uses: Suggestion: click Popular Games to see what other kids

have picked as their favorites. This site if full of great problem solving tasks.
For example, Railroad Repair needs you to fix the tracks so the train can get
through. It will tell you the size of the missing piece, either use that exact
size or add two together to create a new piece. Try Can You Fill It to see if
you can fill the container without the liquid pouring over. You have a few choices,
so see what combinations work. In Poodle Weigh In you have to figure out what
combinations of weights will balance the poodle. Try them all!

Site: Math Playground

URL: http://www.mathplayground.com/SolveIt_main.html

Content: Word Problems

Uses: First, click on your grade level. Then, decide what you would like your
word problem to look like (choices include: addition/subtraction, pictures/no
pictures, etc.) and how many questions you would like. The site creates a virtual
worksheet. Read the problem, enter an answer and click check to see if you correct.

Site: KidsCom

URL: http://www.kidscom.com/games/tangram/tangram.html

Content: Problem solving via tangrams

Uses: First, choose a puzzle. Next, complete the puzzle by clicking and dragging
the pieces into the picture. Hold shift and click your mouse in order to rotate
the shapes. Hold alt and click your mouse to flip shapes.

Note: We studied tangrams when we learned about China in Social Studies.

Site: National Council of Teachers of Mathematics

URL: http://www.figurethis.org/index.html

Content: This site was created by the National Council of Teachers of Mathematics
to provide parents and teachers with tools to facilitate problem solving and
reasoning in mathematics.

Uses: Click on Family Corner for information and various resources. Challenge
Index allows you to download and print each challenge. Math Index allows you
to see which tasks reinforce/utilize which mathematical concept. This site also
contains an informational powerpoint presentation.

__ Mathematical Topic: Women in the History of Mathematics__

1) Site: Biographies of Mathematical Women

URL: www.scottlan.edu/lriddle/women/women.htm

Content: The website above provides a directory of women who are acknowledged

for their individual achievements in Mathematics before the 18th century thru
the 20th century. Three search options exist; alphabetical order, chronological
order and place of birth. A link is provided for additional research.

Uses: The above website gives students access to women whom were/are actively

involved in the Development of Mathematical Concepts. Students can investigate
the

purpose of the women’s contributions.

2) Site: Association for Women in Mathematics

URL: www.awm-math.org/noetherbrochure/TOC.html

Content: This site primarily focuses on women whom have contributed to the field
of mathematics during the 20th & 21st centuries. Obstacles many of the featured
women were faced with are discussed.

Uses: Students research women who have made essential and continuous involvement
in the development of Mathematics.

3) Site: The Mac Tutor History of Mathematics Archive

URL: www-groups.dcs.st-and.ac.uk/~history/Indexes/Women.htm

Content: Included in the above website is a list of renowned women which identify

their association to the field of Mathematics. By clicking the appropriate link,
a brief

biography is provided along with additional resources to pursue.

Uses: The above website allows students to view a collection of Women

Mathematician. Access to each woman’s biography can be obtained by selected
the

alphabetical hyperlink. Once access to the hyperlink is achieved pictures and
a list

of further resources are supplied.

4) Site: Distinguished Women of Past and Present

URL: www.distinguishedwomen.com

Content: This website is devoted to Distinguished Women of Past & Future
in a

variety of fields. Information pertaining to these women can be sorted by subject
or

name. The developer of the site, Danuta Bois, provides insight for her reasoning
for

developing this website.

Uses: Students can use the site to search women in the history of mathematics.

5) Site: About.com

URL: http://womenshistory.about.com/cs/sciencemath1/tp/aatpmathwomen.htm

Content: About.com provides a list of the top 10 Women in Mathematics History.

Uses: The above website can be used to identify early pioneers in the field
of

Mathematics. Additional websites can be accessed through this site.

__NUMBER SENSE-RATIONAL NUMBERS__

Site: Education Place; Math Steps

URL: http://www.eduplace.com/math/mathsteps/7/a/

Content: Education place in conjunction with Houghton Mifflin offers a website
referred to as math steps including lesson plans for teachers, helpful tips
and other pertinent information. Just click on the grade you are currently teaching.
The only setback is that it ranges from Kindergarten to seventh grade.

Uses: When a level is clicked listed on the page are helpful guides to refresh
a teacher’s memory, lesson ideas, tips and tricks for the subject and
a question guide if students happen to have questions pertaining to the topic.

Site: Shelley Walsh’s math article guide

URL: http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/rationals.htm

Content: Shelley Walsh provides a website concerning rational numbers. She explains
the meaning of fractions, equivalent fractions, adding and subtracting fractions,
mixed numbers, multiplication of fractions, and division. Examples are provided
for some concepts, pictures are also provided for visual learners.

Uses: Reference guide or learning page for students. Students can understand
the concepts of rational numbers and what makes up rational numbers, shows students
how to cross multiply, determine which fraction is bigger and reciprocals.

Site: Purple math number types

URL: http://www.purplemath.com/modules/numtypes.htm

Content: Offers the classification of numbers and where they are placed, such
as rational, irrational, natural, whole, integers and complex integers.

Uses: Teacher can use this site to teach students the difference and what classifications
numbers fall under. List several types of numbers and the classification of
each number. List numbers according to types.

Site: Home School Site

URL: http://www.homeschoolmath.net/teaching/irrational_numbers.php

Content: A guideline that gives you more and a lesson on the insight to irrational
numbers. Uses examples like Pi and sq root of 2 and the sine of an angle to
teach the concept of irrational numbers.

Uses: Teachers can explore irrational numbers, which sometimes are ignored or
not recognized.

Site: Encyclopedia

URL: http://www.ebroadcast.com.au/lookup/encyclopedia/ra/Rational_number.html

Content: Web encyclopedia that offers an explanation on rational numbers. Properties
of rational numbers are included ranging from their characteristics to a densely
ordered set. Egyptian fractions are also briefly introduced.

Uses: The first website I’ve noticed involving history of mathematics
by including Egyptian mathematics. Teachers can incorporate the history of mathematics
within their lessons.

__MATHEMATICAL TOPIC: “Trigonometric Identities”__

1) Site: Interactive Mathematics

URL: http://www.intmath.com/Analytic-trigonometry/Analytic-trigo-intro.php

Content: The above URL will take the user to a page called “Analytic Trigonometry.”
From there, the user can link to pages covering various trigonometry topics
or click on the home link to learn other mathematics topics. Some of the trigonometry
topics include “Uses of Trigonometry”, “Proving Trigonometric
Identities”, “Solving Trigonometric Equations”, and “Graphs
of Inverse Trigonometric Functions.”

Uses: This site is one of the better sites for learning how to prove trigonometric
identities. This site is useful for students of mathematics at the secondary,
undergraduate, and graduate levels. It is also a good source for teachers and
anyone interested in trigonometry.

2) Site: List of Trigonometric Identities

URL: http://en.wikipedia.org/wiki/Trigonometric_identity

Content: This site includes many trigonometry topics from notation and definitions,
to identities and proofs. The site contains many easy-to-read tables and pictures
that help the student understand the topic.

Uses: This site is ideal or learning how to prove some of the more advanced
trigonometric identities. Students and teachers can use this site as a complete
reference for their trigonometry needs. The site does not teach trigonometry,
but it is a great reference to either refresh your understanding of the subject
or to take your study to the next level. Although the site is easy to understand
and well organized for the novice, it covers concepts in great detail and can
be used by the more advanced user.

3) Site: Summary of trigonometric identities

URL: http://www.clarku.edu/~djoyce/trig/identities.html

Content: This site list a summary of the trigonometric identities in an easy-to-
read manner. It lists the more important identities first and then mentions
the identities that are less common.

Uses: This site is valuable for anyone needing a quick reference to the trigonometric
identities. The identities are organized in a way that makes it easy to use
as a quick reference. An interesting fact is listed under the “Product
Identities” section stating that these identities were used prior to logarithms
to perform multiplication. It is explained in a few sentences and it is relatively
easy to understand. The site also has a drop down menu on the bottom of the
page to link you to other important trigonometry topics.

4) Site: Verifying trigonometric identities

URL: http://www.math.uconn.edu/~stein/math109/Slides/math109-06.pdf

Content: This site list strategies and hints for verifying the trigonometric
identities. The site explains what an identity is and it takes the “Pythagorean
Identity” and manipulates it using division and subtraction techniques
to derive other identities.

Uses: This site is helpful in learning how to verify trigonometric identities.
It allows the user to see step-by-step, how certain identities are derived from
other identities. It states that every trigonometric identity is of the form:
“left hand side = right hand side.” The site is in a PDF format
and enables the user to simply click on the down arrow in the right margin to
see a line-by-line display of the information.

5) Site: Finding your way around the TI-83+/84+ Graphing Calculator –
“Verifying Trig Identities”

URL: http://mathbits.com/MathBits/TISection/trig/trigidentity.htm

Content: This is a short page, but the information is valuable. The site contains
steps on how to verify a trigonometric identity using your TI graphing calculator.
The site contains easy to view displays of the calculator window to guide you
along.

Uses: The site lists step-by-step instructions for verifying that a trigonometric
function is an identity with your TI 83 or 84 calculator. The site shows the
user how to enter two functions that are believed to be identities of each other.
By graphing them both in the same screen, the user is asked to set the bubble
animation for the second graph to observe if the bubble runs over the first
graph. If it does, the equation is a trig identity. The page also shows how
to verify the y- values of each function corresponding to the same set of x-
values. The site also has a link at the bottom to take you to the table of contents
for more valuable mathematics topics using the graphing calculator.