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.



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