A Few Things I've Created

       Online Math Games, Demonstration/Exploration Tools, & Puzzles, organized by grade, K through 12.

Online Mathematics Practice Worksheets/Quizzes and Review Resources - Most of the online practice is in the form of games which can be found at Online Math Games, Demonstration/Exploration Tools, and Puzzles (above). This page has links to worksheets and quizzes for practicing math skills. More quizzes can be found on this Teaching Resources page below. Also, there are links to Review Resources, which are tutorials to review mathematical topics from arithmetic through calculus.

Top Ten Lists for Using Technology to Help Elementary/MS Students Learn Mathematics
Top Ten Lists for Using Technology to Help HS Students Learn Mathematics

Games and PowerPoint Games for Math Practice - We've made a number of PowerPoint files that can be used in the classroom to review math topics and skills in a game environment. This files can be edited with your own questions.

TI Graphics Calculator Tips - Including the TI Connect cable and Cabri Jr.

Computer Hints, Tips, and Shortcuts - on Windows, Word, Internet Explorer, Power Point, etc. I don't have much yet, but hope to add to it. This is a place I look if I've forgotten how to do something (e.g., making a sticky space in Word).

• Basic Computer Hints, Tips, and Shortcuts
• Intermediate Computer Hints, Tips, and Shortcuts
• Online Needs - This is a page of needed plug-ins for Internet use and online courses.
• Web Page Summary - This make help if you are making web pages.

Analytic Scoring Scale for Scoring Student Work on Problem-solving Tasks (by Jim Olsen) This is a rubric I designed (with initial help in a class) and have used with teachers for a number of years. The primary purpose of this scale is to award credit to students for following the 4-step problem-solving process. A student can get the wrong answer and still score quite well using this rubric. Conversely, a student with the right answer (alone) may not get all the points. If you wish to actually evaluate student knowledge of a specific math topic, I'd recommend using a different scale. This is a generalizable, analytic rubric. It does break up the student's work into parts (gives three sub-scores), but it is generalizable, in that it can be used with about any problem-solving problem.

Systematic Guess and Check Problem-Solving Strategy - The basics of trouble-shooting.

Amounts From Rates Worksheet - Primarily a graph interpretation activity. One of a number of, what I call, "early calculus topics." Real-world applications. Rates vary over time and the student must find the total amount accumulated. Appropriate for Algebra II or Pre-Calculus.

Solids of Revolution - Students rotate a triangular or rectangular region about an axis to create a solid. Students identify the solid and find its volume. Second "early calculus topic." Appropriate for Algebra II or Pre-Calculus. First 5 are straightforward cones and cylinders. Second 5 are a bit more challenging. No calculus required. Basic volume formulas used.

List of Objectives Involving Change, Rates, and Rate of Change - School districts need to decide where (when) students will be introduced to these ideas, and when the ideas will be developed, mastered, and reviewed.

Graphing Rational Functions by Hand - While generally I highly favor use of graphing technology, and favor real-world application, here's an activity that is only in a math context, and we get the answers just using our heads. It is strong in building number sense and function sense.

• Overview
• How to with examples

My Mastery Quiz system:

Overview

ICTM Handout from the presentation titled, "Using Problem Solving to Teach the Illinois Standards." Sarah Dalpiaz gave this talk (as I was out of town for a wedding).  In MSWord format.

Teaching Mathematics via problem solving: Here are some example problems.

Function Handouts

Here is a series of handouts related to the function concept. Each is given as a Word document and as a rich text format document. These handouts assume that students have been exposed to the function concept minimally. That is, they know that "there in an input, some thing happens, and there is an output," and that "inputs and outputs can be put into ordered pairs."

The Definition(s) of a Function ~ Is Yours in Here? Different books use different definitions for function. It's all the same concept. This handout helps make connections between different-sounding definitions. function-defs.doc function-defs.rtf

The Representation and Synonym Games - The fact that functions have many representations and that there are many synonyms for terms (such as "y-value") make it tough for students. This handout can help. REPS_SYN.doc REPS_SYN.rtf

Basic Function Objectives - Some of these basic objectives can be learned in middle school. basic_objectives.doc basic_objectives.rtf (For more advanced objectives see the Misconceptions and Difficulties handout below and reword the "difficulties" into things the student can do.)

Function Notation ~ "OK, so f(x) doesn't mean f times x, what does it mean?" FUN_NOTATON.doc FUN_NOTATON.rtf

Levels of Graph Comprehension - Although literal reading of data presented in graphical form is an important component of graph-reading ability, the maximum potential of the graph is realized when the reader is capable of interpreting and generalizing from the data. Just like reading text, there is difference between reading the words and comprehending the ideas. graphcomprehension.doc graphcomprehension.rtf (rich text format may not have all the graphics in the example)

Misconceptions and Difficulties in the Understanding the Function Concept - The function concept is central and key to mathematics, but it is also complex, due to its many related concepts and multiple representations. Miscon_difficulties.doc Miscon_difficulties.rtf

My Top 10 Reasons for Using Computers and Calculators to Help Students Learn Mathematics - PowerPoint.

Why it is important for W.I.U. to make a commitment to the preparation of teachers - three documents

• The Illinois Board of Higher Education hereby adopted The Illinois Commitment: Partnerships, Opportunities, and Excellence as the goals for higher education for the first decade of the 21st century. Goal #2 states, "Higher education will join elementary and secondary education to improve teaching and
  learning at all levels."
• W.I.U. is a member institution in the Renaissance Group, a national consortium of colleges and universities with a major commitment to the preparation of educational professionals. The Group holds the principle that the importance of the education of teachers is an all-campus responsibility.
• W.I.U.'s Strategic Plan Higher Values in Higher Education. Our values state that we are committed to an academic environment that encourages lifelong development of our students as teachers and that we will serve as a resource for and stimulus to economic, educational, cultural, environmental, and community development in our region and well beyond it.
  

Problem Solving Databases

= Featured Links

I am highly interested is using problem solving to teach the standard school mathematics curriculum. (I think we can have our cake and eat it too - involve students in problem solving and have them learn the mathematics curriculum at the same time.) To this end I am interested in problem databases that are organized by the mathematical content. Below are a few.

MPAAC K-12 Problem-Solving Database - Search for problems by Illinois Learning Standard.  These problem write-ups written by teachers in the MPAAC grant project at W.I.U.

TIPS - Tipping the Scales In Problem Solving. Open-response items for early elementary through junior high. Student work included. From another grant project at W.I.U.

Problems With a Point - Problems "with a Point" help students in grades 6-12 learn new mathematical ideas by building on old ones. In a searchable database format.  While each problem or sequence has its focus on one mathematical idea, many show how it connects with another.  New from the Education Development Center.

Best of the MathNerds - A few really nice problems. I like the The Magnificent Seven.

MATHmodels.org - Mathmodels is COMAP’s new modeling forum.

ProblemCorner.org - Searchable datebase of "20,000 problems from 38 journals and 21 contests, all published before 1990." Many are college level.

NRICH - Lots of problems for various levels (from the UK, "stages 4-5" are grades 9-12). See also Maths Finder ("Maths" in the UK = "Math" in the USA).

Mathematics Problem-Solving Model - helps educators meet the challenges of teaching and assessing open-ended problem solving. See also, SMARD, the Secondary Mathematics Assessment and Resource Database.

Math in the Workplace - Good real-world word problems from various professions. Keyed to the Idaho Mathematics Achievement Standards, which are similar to the NCTM Standards and standards from Illinois and other states. Part of K-12 Resources for Teachers from Micron.

Mathschallenge.net - A web site dedicated to the puzzling world of mathematics.

Secondary Mathematics Problems (I'm working on these now - I hope to add to these often).

1. Pythagorean Theorem Problems

New E-Labs site - This is one of the best sites on the Internet for grades 3-6. A few I really like are Division with Remainders, Equivalent Fractions, and Transformations. This is a new (shockwave based) version of the popular E-labs (java based) we've used for years. Part of the Learning Site, from Harcourt School Publishers. Math Jingles are new. (E-Labs is the older site is being phased out and being replaced by the New E-Labs site.)

CyberChase Games - From PBSKIDS. Click here for my descriptions and my evaluation of the games. For K-7 students. Part of Cyberchase.

Project Interactivate - For me, right now, this is the Number One Free Math Site on the Internet for interactive applets! (Otherwise known as the "Shodor Applets.") The goals of this project are the creation, collection, evaluation, and dissemination of interactive Java-based courseware for exploration in science and mathematics. They have Tools, Activities, Teacher Page, Student Page, a Newsletter, and more. The Function Flyer is one of the best applets on the web. A couple more I really like are Equivalent Fractions Pointer and forest fire simulation (Chaos Discussion), Arithmetic Practice Game that is Connect 4, and Fraction 4 - click a tree to start the burn! (Other ways to access this applets and activities is use us Curriculum Materials. From the Shodor Educational Foundation, Inc.

Huge Virtual Manipulatives Site - Click in the body of the table for the standard and grade level band. I especially like Platonic Solids, Platonic Solid Duals, Space Blocks (like Multi-Link cubes), Algebra Balance Scales, Coin Problem (use logic to find the lighter coin!), Transformations-Reflection (dynamically interact with and see the result of a reflection transformation).

More Virtual Manipulatives - From Archytech.org. The links below may be slightly different explore to find you favorites.
    Pattern Blocks on-line - You can play with Pattern Blocks on-line.  Activities available as well.
    Base 10 Blocks  on-line - Make sure to check out the hammer and glue options.

Wolfram (Mathematica) Demonstrations Project - This is a web collection of freely available, interactive demonstrations in math, science, and many other areas, at all levels from elementary education to front-line research. You do have to download the Mathematica Player, which is free, and runs all demonstrations. A few of my early favorites are Piecewise functions, Splitting a Cube, Buckyball in Icosahedron, Color (Rubic's) Cube, 3D Dissection Puzzle, Polygonal Numbers, and Fractal Tetrahedron.

Mr. Beneli's Website - Flash applets on modeling addition, integers, percents, lines, slope, and more. Ido Beneli is a high school math teacher in Arizona

Protractor applet - Very nice. Has an intro (which can be skipped). Various interactive activities with and without a virtual protractor.

Math Playground - educational site for elementary and middle school students. Math Games, Word Problems, and Logic Games.

Journal of Online Mathematics and its Applications (JOMA) - New from the Mathematical Association of America. Includes higher mathematical thinking. See the Mathlets in each issue (these are Java applets).

Math Investigations and Games ("Maths Stuff") - by Duncan Keith (a math teacher in England). Mostly for high school and middle school. Pretty nice site. I especially like the Broken Calculator Game , Rush Hour, Function Machines, Ball-Dropping applet.

Funbrain.com - Games (see MathBrain) for practicing math. Grades 1 to 8. See also the Quiz Lab.  Teachers can post quizzes for their students to do online.

iKnowthat.com - K-6 Games. Bucky's Blueprints and MathBlox practice. Might be fun for indoor recess on rainy days. Decipher Word Problems ("pick-an-operation" word problems).

Academic Skill Builders - Meteor Multiplication, Alien Addition, and Minus Mission. Gives very nice diagnostic reports.

Arithmetic Practice Games - Interactive games to practice addition, subtraction, multiplication, and division. Online worksheets too that correct themselves. Part of APlusMath.com.

Virtual Algebra Tiles - A good exercise.  Not a lot of variety.  Does not show all you can do with Algebra Tiles, but a good activity none the less.

Explorelearning - (formerly ExploreMath.com) This is probably the best site on the web for interactive math applets--however it is no longer free. These applets (they call them "Gizmos") are excellent! I believe you do get to use one applet free per day. There is a 30-day demo as well. Many of the Gizmos also have an online assessment built in.

Ron Blond's Page - Good applets for secondary teachers.  Check out slope comparison and quadratic function applet and wrapping function (note: for the wrapping function applet, I prefer to click APPROXIMATE in the lower right).

Cayley Quilt Maker - Algebra and Geometry come together. Interactive applet. The user creates 4, 6, or 8 elements of a set (think of it as a mathematical group, if you wish). The applet creates the "multiplication" table (there are five different operations to chose from--depending on the number of elements and the operation selected, it may not actually be a group). Then the applet creates a "quilt" using one of seven geometric transformations. Fairly easy to use. I nice representation that bring modern algebra and geometry together. See about, for a listing of the operations and transformations. Also has a nice Clock Arithmetic Demonstration.

Cross Section of the Cube - Toni's Tiara Game - (May take a while to load, but worth the wait.) Rotate and turn the cube by grabbing it or turning the surrounding circle. Move the plane by using the slider. Part of Bright Sparks Interactive games. From New Zealand Maths.

VisualFractions.com - That's it.  Learn about fractions visually.  Includes equivalent fractions, mixed fractions, addition, subtraction, multiplication, and division of fractions.  Learning games included.

Math Java applets (or use Manipula Math with Java) has great animated graphics for Geometry through Calculus.  My favorite is Surfing (Derivatives). I like the section on the Pythagorean Theorem under Geometry 2. These are from Japan.  New stuff all the time on the updates page. See also the neat applet on linear transformation. or Linear Transformation(dog 2).

Java Applets by Daniel J. (deej) Heath - Calculus, algebra, trig, geometry, abstract algebra, and more. Featured: Real & Complex Roots of a Polynomial and The d - e Definition of a Limit,

Building Houses - Applet for building a building and seeing the three (top, front, and right) views. Helps students with spatial visualization.

Contig for Windows - This is free software that you will load (and run) to (from) your hard drive. Contig is a very good strategy game (and you practice arithmetic and order of operations at the same time!). The site has the rules. I would play Contig first on a physical game board (with markers), to learn the game. Then learn how to do it on the computer (vs. the computer). There are different levels of difficulty and "computer strategy." This is timed (which can be adjusted). I believe the default settings are challenging and fast, so you probably want to change these the first time, or it will be frustrating.

Online - Interactive Mathematics - Online Practice (computer graded). Multiple levels.

Tangents Applet - This applet draws the graph of a function and its derivative. A tangent line is drawn on the function, and a crosshair marks the corresponding point on the graph of the tangent. You can move the tangent line by clicking-and-dragging on either graph.

Visual Multiplication Table - Self-explanatory (or read the Quick Instructions). Hints and tricks for learning multiplication facts.

Make Your Own Kaleidoscope! - Use your own graphic (from the Internet) to make an interactive kaleidoscope.

Tangrams - Online. Part of fwend.com.
Tangram House - online puzzles.
Cyberchase Tangrams - PBS.

Interactive Mathematics Miscellany and Puzzles - Lots of puzzles with Java applets.  The site has won many awards.  Try Flipping Pancakes or Farmer and Wife To Catch Rooster and Hen or the Three Glass (water pouring) problem (or the water pouring variation).  Then move on to the more advanced.  Lots of explanations and theory provided. See Tower of Hanoi and the Tower of Hanoi Explanation and the Sierpinski Gasket and Tower of Hanoi. All from cut-the-knot.com.

Puzzles - Such as Tower of Hanoi.  Part of math.com.  The Hex-7 page is very interesting and includes a great example of a "non-constructive" proof of a winning strategy for player one.  The games can also be found at mazeworks.com.

Online Interactive Puzzle Hall of Fame - Fun online and you have to think. See also Clickmazes.

Tower of Hanoi on the Web - more Tower of Hanoi information, history, and variations.

§» Problem Solving (Including Puzzles & Games)

Freepuzzles.com - Good problem of the week possibilities. Rated by difficulty.

Sudoku - This is the hot puzzle game. Can play online at this site. (You can google for more Sudoku sites, as you wish.)

Puzzles from MentalWorkout.com - Good problem of the week possibilities. (To print some of these out you'll want a color printer.) From MentalWorkout.com which also has games.

Mathematical Games from Fife, Scotland - Arithmetic practice to geometrical visualization to strategy games and more. See also these mathematical games.

The Problem Site - Educational Games, Puzzles, and Problem Solving. Math games, math problems, word games, word puzzles, mystery quests.

PROBLEMS for Math Problem Solving - from Nine Quick Learning Strategies for Success. PROBLEMS is an eight step process for solving math word problems.

Word Problems For Kids - Grades 5 through 12.

Mathematische Basteleien - Interesting things on paper folding, tetrahedrons, soma cube (click here to go straight to the soma cube applet, do read the directions), Rubic's cube, and more. (Don't worry that you can't pronounce the title!)

Puzzle solvers at Cryptic Manor - Try your hand at the spy game as you tour the NSA's Cryptic Manor. Many of the puzzles to be solved here involve making and breaking code. Grades: 3 - Post-secondary.

 Problems of the Week -- Students can submit their solutions. (Not all of these are continually active, but most have a nice archive of problems available.)

• Math Fundamentals (elementary) Problem of the Week
• AIMS Puzzle Corner
• Mathcounts Problem of the Week (middle school)
• Middle School Problem of the Week
• Education Place Brain Teasers weekly problems for grades 3-4, 5-6, 7-8
• Discrete Math Problem of the Week
• Geometry Problem of the Week
• Algebra Problem of the Week
• Trig/Calculus Problem of the Week (from the Math Forum)
• Calculus Problem of the Week (from Kentridge H.S.)
• College Problem of the Week
• Lists of more problem of the week sites.

Math Contests and Competitions (for K-12)

• Online Math League - Grades 3-12.
• Math Olympiads - Grades 4-6 and 7-8.
• Mathcounts - Grades 6-8.
• American Mathematics Competitions - Grades 6-12. AMC 8, AMC 10, AMC 12, AIME, USAMO, andIMO. Mathematical Association of America.
• Math League - Lots of quickie problems and exercises. "The Math League is dedicated to bringing challenging mathematics materials to students. The Math League specializes in math contests, books, and computer software designed to stimulate interest and confidence in mathematics for students from the 4th grade through high school." Click here for some (printable) free samples and to order problem books.
• USA Mathematical Talent Search (USAMTS) - Has a great Proofs Without Words page. From NSA.
• American Regions Math League - "the World Series of mathematics competitions."
• Mu Alpha Theta - Mu Alpha Theta is a National Mathematics Honor Society (HS and 2-year college students).
• National Assessment & Testing - Seattle, WA. Administers high quality, affordable mathematics competitions for high school math teams and honor societies.
• Mandelbrot - high school.
• See also this list.

Internet Center for Mathematics Problems - This is just a page of links (lots of links).

MATHCOUNTS - A coaching and competition program for middle school students nationwide. Even if you don't participate, the handbook (available online) they provide are a great source of math problems. Comprehensive discussion of problem solving strategies is included.

Shack's Math Problems - Great problems (mathproblems.info).

Interactive NIM sites:

• NIM Skulls - Remove from one group. Remove 1, 2, or 3 (then REST). Make him take the last.
• Fruit Game - Remove fruit from rows. Goal is to try to eat the last. (Take/eat those to the right of your click.)
• Game of NIM - Three rows - just checkmarks. Same goal as fruit game.

21st Century Problem Solving - Problem solving site.  Includes "exercises in problem solving" which guide students through the understanding the problem phase and through the steps of the problem.

Rubik's Cube On-line - Part of Room 108 Educational Games.

The Burr Puzzles Site - Great for spatial visualization.  From IBM Research site.

Boredom Buster Sites (sites with games and puzzles for kids):

• Counton.org - Games, poems, Virtual Mathematics Museum, and more. From the U.K.
• Funology.com - Not just math. Jokes, tricks, Brain Drains, and more. "For ages 1 to 10."
• Funbrain.com - Games, including Math Baseball. Not just math.
• Mathcats.com - Math explorations, math crafts, MicroWorlds, and more.
• EnchantedMind.com - Not just math. I especially like the creative java puzzles (including Tangrams and Knights's Tour). Also, Mensa puzzles, creativity, science. Upper grades and adults.

Nick's Mathematical Puzzles - just that, mathematical puzzles of varying difficulty.

Math Card Games (and more) - Play Crazy Math (like Crazy 8's), Pig, and Old Maid-type games using cards you print out from this site. Arithmetology.com.

Java Games - Some pretty good drill and practice (which generally I like to do using paper-and-pencil) games. On the basic operations and geometry terms. Part of APlusMath.com.

§» Topic Sites

Definition of a Function - from the Function Institute. Two disclaimers. (1) The Function Institute is fair, but I am not overly impressed with it as a whole. (2) I do think the "Definition of a function" page is well done. However, it is misleading to say "Domain = Input numbers = x." It should be "Domain = Input numbers = all x-values." To state "Domain = x" is misleading because the domain is a set containing many elements, and "x" appears to be one thing. The rest of the page is fine.

Math Doesn't Suck: how to survive middle school math without losing your mind or breaking a nail - Book by the TV-star and UCLA mathematics major, Danica McKellar. Great book to buy!!

MATHmodels.org - Mathmodels is COMAP’s new modeling forum. On this site, students and faculty will find a wide range of interesting contemporary modeling problems. Teachers can assign problems. Students can choose to work on problems based on math topic and application area. There are contests.

High School Operations Research - "Since 1996, we have been developing instructional materials for use in high school mathematics classrooms." Operations Research is all about applied mathematics to real-world problems (click here to find out what "Operations Research" is). Uses Case Studies from companies such as McDonalds and L.L.Bean. Sponsored by INFORMS - Institute for Operations Research and the Management Sciences.

PUMAS - PUMAS = "Practical Uses of Math And Science" (poo' · mas) -- a collection of one-page examples of how math and science topics taught in K-12 classes can be used in interesting settings, including everyday life.

Thinking Blocks - an interactive math tool developed by classroom teachers to help students learn how to solve multistep word problems.

Pascal's Triangle websites - A list a websites I put together which provide information and applets on Pascal's Triangle, Triangular Numbers, and Tetrahedral Numbers. powerpoint

Fibonacci Numbers Websites

• Pascal Triangle, Fibonacci Numbers, and the Golden Section by Radoslav Jovanovic - Lot's of great connections.
• Fibonacci Numbers and the Golden Section - Wow, real cool! Puzzles and more. By Ron Knott.
• Fibonacci Numbers and Nature - 25 pages! Also by Ron Knott.
• DiscoverySchool.com - Numbers in Nature
• Leonardo Pisano Fibonacci - biography.
• Fibonacci as Part of the Renaissance - An Annenberg/CPB Exhibit.

GoldenNumber.net - Very comprehensive web site on the golden ratio. Self-proclaimed "Phi Source."

The Golden Ratio - by David L. Narain. Drawback is that it is primarily text based.

Connect Palindromes - This is a two-player game (or play the computer) like Connect 4, but you are trying to get palindromes!

Purple Parabola Place - "Everything you ever wanted to know about parabolas, but were afraid to ask."  Includes tutorials and applications of parabolas. 

Ag in the Classroom - Agriculture across the curriculum. Tons of resources for teachers (including math connections). Lots of free resources and even grant money.

Graphics For The Calculus Classroom - lots of graphics and a few animations. A bit old now, but still some good stuff.

Visual Calculus - Has tutorials and animations for numerous Pre-calculus and Calculus concepts.  My reaction was that it might be hard to learn from these tutorials if you are learning it by yourself for the first time--however, they are useful for a teacher to use.  That is, if a teacher is there to explain things as the computer moves through the tutorial, the tutorials may be a useful teaching aid.  (In their words, "A collection of modules that can be used in the studying or teaching of calculus.")  As is often the case, some plug-ins are required, but fairly easy to obtain.

Calculus-Help.com - Has tutorials and Problems of the Week with a nice Alphabetical Index by Topic.

Calculus.org - Resources for students and teachers.

DIG Stats - Delve into Descriptive and Inferential statistics, and then proceed to Graphical analysis. Each section provides overviews with related activities. The activities contain data sets for students to use, either with spreadsheets or calculators. It seems that this site has discontinued operations.

Boxplots - nice site on boxplots. Quizzes included.

More Data Sets for Statistical Analysis - found on my My Students page.

National Center for Education Statistics - Very good site. Has both resources for teachers to use in the classroom and statistical information on the state of education. Has:

• Games and Activities
  • Explore Your Knowledge online quiz for 4th or 8th graders.
  • Create a Graph Tool - for students (others) to make statistical graphs.
• Elementary and Secondary School Factoids

Plane Math - a place to learn cool things about math and aeronautics! Grades: 4 - 7.

Prime Mathematics Enrichment - Good problem library with problems organized by topic. (This site is not just about prime numbers.) Could use for problems of the week. Also has online Tangram puzzles. Monthly magazine.

The Prime Pages - This is about prime numbers. Prime number research, records, and resources. Has a nice list of Prime Conjectures and Open Questions. Interesting facts, curiosities, and problems. Can check a number's primality (but it can't be too big :-).

Geometry Center - At Science U. Good stuff on tilings, symmetry, and more. Check out Kali, where you can interact with the frieze and wallpaper patterns.

Exploratorium - The Museum of Science, Art, and Human Perception. There is some math in here - check out the The Math Explorer.

Archimedes' Laboratory - Puzzling and Mental Activities Since 1997.

Powers of Ten - View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree just outside the buildings of the National High Magnetic Field Laboratory in Tallahassee, Florida. After that, begin to move closer all the way to the subatomic universe of electrons and protons. A Question of Scale is a similar site but zooms in on a honey bee in San Francisco.

Pi Day Ideas (I know very little about these sites for Pi Day. You'll have to verify the validity yourself.)

• The Exploratorium - Pi
• Joy of Pi (.com) - Pi links
• Pi Trivia Game - game
• World of Pi - Pi
• 300th Anniversary of Pi - from MEG-SL
• Montrose Mathematics - Pi Day
• Goudreau Museum of Mathematics - Pi Day Contest
• Math with Mr. Herte - Pi Day
• Math Forum - FAQ on pi

Exactly How Is Math Used In Technology? - Examples of how various areas of mathematics are applied to various areas of technology. High School Algebra to Differential Equations and Numerical Analysis, and Food Technology to Prosthetics.

Girl's Plus Math Camp - This is a summer mathematics program for girls ages 12 and 13 to develop an appreciation for mathematics. It is held on the Western Illinois University campus. Follow the link to see past information or apply for future summers.

Color Math Pink - designed specifically to help middle school and high school girls excel at math.

Association for Women in Mathematics (AWM) - to encourage women and girls to study and to have active careers in the mathematical sciences, and
to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences. Has a new Teacher Partnership Program.

The KnotPlot Site - A collection of knots and links, viewed from a mathematical perspective, created with KnotPlot, a computer program to visualize and manipulate mathematical knots.

IMAGES - Improving Measurement and Geometry in Elementary Schools. Has nice sections on Visualization and Spatial Reasoning, Cognitive & Developmental Issues, Instructional Activities and Lesson Plans, and more. Also, they get the best acronym award!

Investigating Patterns: Symmetry and Tessellations - This is a page of links to various activities on symmetry and tessellation. I recommend Teach-Learn inversion from Scott Kim's Inversions Gallary.

GuideMe NACME - From the National Action Council for Minorities in Engineering.

Graphics Calculator Help - Select from ten different calculators. Then click a topic for specific instructions.

Mathematics Activities for Calculator Based Labs (CBLs) and TI-83 Graphing Calculators - Topics: Algebra, Algebra 2, Complex Numbers, Curve Fitting, Calculus, Functions and Statistics, Geometry. Maintained in Kansas.

§» Learning Activities and Lesson Plans

»» Assessment

Rubrics, Rubrics, and More Rubrics - Yikes, everybody's making them. Be careful, everything on the web is not of high quality.

• Rubistar - Create Rubrics for your problem solving, project, writing, and assessment activities. Part of 4teachers.org.
• Rubrics4teachers.com - many rubrics (does not seem to have an online tool for making your own).
• Math Rubrics from across the nation - from various states.
• Rubrics for web lessons - from WebQuest. Includes templates and more.
• Rubrics from teach-nology.com - fill in a form. Has a math rubric and a general rubric generator (very flexible, but requires a lot of writing). Note that in the browser you can save the page (rubric) and then edit it with another piece of software (e.g., Word web page editor).

Balanced Assessment in Mathematics - at the Harvard Graduate School of Education (website now housed at The Concord Consortium). Contains a library of 300 assessment tasks for grades K to 12, AMUSE (Assessing Mathematical Understanding and Skills Effectively), a very comprehensive paper on assessment, and the MCAPS Scoring Tool (Mathematics Content and Process Scoring System).

Internet Learning Network - (getsmarter.org) Students can take a quiz and compare themselves to others around the world.  Games included.

ThatQuiz.com - Nice site for online quizzes. You can create your own.

MyMathTest.com - You can do an online quiz on Basic Math through Introductory Algebra. Automatically scored with quick feedback. (The required plug-in download is quick and painless.)

Understanding By Design - Grant Wiggins and Jay McTighe have some interesting work on assessment. Here is some information and a few links to get started.

Number Time - Pre-K - 2. Fun animations, games, songs, and movies.

Rounding Game - practice rounding properly.

Study Guides and Strategies - Very comprehensive. Does have a math section.

Test Prep Review - Free Practice Tests for over 60 tests from the ACT to, CLEP, Praxis, to GRE, and many more.

Online Math Tests - includes algebra, geometry, trigonometry, and more.

AAA Math - K-8 arithmetic lessons with online practice (with immediate feedback). Pick a topic, then go down to the PLAY area and click your game. (AAAMath is equivalent to www.321know.com,)

Isometric Dot Paper and Geoboard Dot Paper

Print Free Graph Paper - Cartesian, polar, isometric, and logarithmic (pdf files).

PDF Generator - Create and print pages of number lines, graph paper, dot paper, and much more -- even fretboard diagrams for guitar. This site also has calendar generators, free music, and more for most curriculum areas. Incompetech.com labels themselves "Ugly website, brilliant content."

High school Hub Mathematics - A good portal for HS students and teachers. A lot of the same links you see on this page. Part of the High School Hub.

COMETS - Clearinghouse On Mathematics, Engineering, Technology and Science. Created specifically to address the unique educational needs of hearing-impaired students, this site hosts a wide variety of lessons, resources, and workshops for education professionals in math, science, engineering and technology.

Teach Engineering - The TeachEngineering digital library provides teacher-tested, standards-based engineering content for K-12 teachers to use in science and math classrooms.

Songs for Math - Words and mp3's provided. By Vicki Young. Here is another one - mathsongs.com (this one very highly protected) - many nice books to buy.
SongsForTeaching.com - Lyrics and audio.

Logical Fallacies - Nicely organized examples and instruction on logical fallacies by Stephen Downes. How to use this Guide. Another place to find information on logical fallacies is logical fallacy from Wikipedia.

Mathematics at Science.gov - Math portion of Uncle Sam's hub for all things science. Lots of data bases of government information and more. Part of Science.gov.

NSA High School Learning Units - Lesson and unit plans From the National Security Agency (NSA).

Math Dance - Classroom activities for teaching mathematics and performing arts through whole-body movement.  For grades 4-12.  For example, check out The Four Basic Symmetries.

PBS TeacherSource - Math - Mathline. Activities, videos, and lesson plans.  Part of  PBS TeacherSource.  Part of  PBS Online.

The Futures Channel - Activities and links for interesting math and science lessons.  Includes a nice section on careers.  Updated frequently.

What Good is Math? - Everyday life applications from figuring your grades to planning a party.

Investigation/Exploration in Geometry to Discover Properties Using a Dynamic Geometry Program

Here's the process:

• (Prerequisite is that students know how to make a dynamic (e.g. GSP or Wingeom) computer sketch.)
• Describe the setup. E.g. Prop. 13: "If a diameter AB of a circle meet any chord CD, not a diameter, in E, and if AF, BG be drawn perpendicular to CD." (The setup is the if-part of the proposition.) One might also give a hand diagram.
• Tell the students what to investigate, and to make a conjecture. E.g. Prop 13: "Find the relationship between lengths CG and DF."
• Ask the students to prove (or disprove) their conjecture.

Here are some sources for investigation ideas (These are from Antonio Gutierrez's Geometry Step-by-Step From the Land of the Incas site, which includes inspirational poems and more.):

• Triangle and Squares - Level: High School, SAT Prep, College geometry.
• Proposed Problems - Level: High School, SAT Prep, College geometry.
• Archimedes' Book of Lemmas - Many at a higher level, challenging for HS and college.
• More theorems and lemmas - nice list of interesting theorems.
• Professional Development Workshop Guide - 55 page detailed (step-by-step) guide for GSP.

LEGO Links:

• LEGO Education - from the LEGO Company. http://www.legoeducation.com/
• NASA Robotics Alliance Project - many (but not all) robots are built out of LEGO. Includes an Educational Matrix, Robotics Curriculum Clearinghouse, educator links, and more. NASA is a big supporter of LEGO Robotics.
• FIRST Robotics Competition (bigger competition) and FIRST LEGO League (the "little league" of the FIRST Robotics Competition) are the result of a partnership between FIRST and the LEGO Group.
• Kansas Robotics League - students build and program real, autonomous robots to accomplish specific tasks. Focuses on local competitions.

ThinkQuest - "ThinkQuest Inc. is a non profit organization which offers programs designed to advance education through the use of technology." Have won many awards. A large website covering all curriculum areas. They do have a site tour and information page.

Math in Daily Life - Examples of math in daily life.  Includes a nice annotated list of Math Web sites.  This is part of Annenberg/CPB Exhibits.

Math Trails - You've heard of nature trails, well there is mathematics around us as well. Math trails from across the country. Click here so you can click your state.

See also Math Trails from Canada.

Math Goodies - Math Goodies is a free educational web site featuring interactive math lessons, homework help, worksheets, puzzles, message boards, and more!

N.C.T.M. - National Council of Teachers of Mathematics

• How to Access the NCTM Standards (in book form and electronically).
• Curriculum Focal Points - The Curriculum Focal Points are the most important mathematical topics for each grade level.
  • Curriculum Focal Points for Mathematics in Prekindergarten through Grade 8
• Figure This - Mathematics Challenges for Families provides interesting math challenges that middle-school students can do at home with their families.  Good problems for school use too!
• Principles and Standards for School Mathematics Electronic version - This on-line version is interactive and easier to navigate.  (The content is the same as the plain print version.)  See also the Illuminations Page for Java applets and videos. See the e-examples, especially Learning about Rate of Change, in the grade 6-8 section. See also the standards page for other resources, including the 1989 Standards.
• Curriculum Focal Points - Curriculum focal points are the most important mathematical topics for lasting learning at each grade level.
• On Math - Online Journal of School Mathematics. NCTM's newest journal.
• Manuscript access for MT authors and referees

I.C.T.M. - Illinois Council of Teachers of Mathematics - student memberships cheap.

ICTM Parent Handbook - Click here to download the handbook in PDF format. To view it you will need the Adobe Acrobat Reader, available from this site.

The 50 State Quarters® Program Lesson Plans - from the U.S.Mint. Games and more.

Best Practices for Mathematics Instruction - From It's About Time, Herff Jones Education Division.

Make the Link - Find learning activities keyed to the Illinois Learning Standards, using the Illinois Learning Standards Benchmark Grid from St. Clair County Regional Office of Education.

Helping Your Child Learn Math - Ideas for parents of PreK-7 grade children. From the U.S. Department of Education.

Helping Your Child Learn Math – A Parent's Guide - For parents of PreK-3 grade children. From Ontario, Canada.

Math and Children's Literature <<click here or the links below.

• Math and Reading Do Mix
• SMaRT Books

Math Night - Math Night is an event that allows kids and their parents to explore and enjoy areas of mathematics they wouldn't encounter in everyday schoolwork. Includes a Guide, Activities, and Pencil and Paper Games. Contains many activities on topology.

Intel Education - Technology, science, and math classroom ideas from the chip maker Intel Corporation.

Blue Web'n - A library of Blue Ribbon learning sites on the web.  They make a distinction between lesson plans on the web (which could as well been in a book) and web based learning activities that require the student to use the web, in some way, to get information.

AIMS Education Foundation - Activities Integrating Math and Science . Has a Puzzle Corner.

AIMS Association of Illinois Middle-Level Schools - "Making the middle matter!"

Twenty Questions about Mathematical Reasoning - by Lynn Arthur Steen, St. Olaf College.

TI Calculators - Lots of resources. See also resources for classroom teachers, including volume purchases and loan programs. Under the TI - Texas Instruments home page. See TI-Interactive® (there is a 30-day free demo version of this software).

• Customer Support
• eNewsletters or TI-CARES Newsletter (print) - Free newsletters of interest to teachers who want to use TI calculators to help teach mathematics. Sign up on-line.

America Counts - a multifaceted Federal initiative designed to help teachers' professional development (pre- and in-service). (This is different from MathCounts.)

Math Literacy Week - Sponsored by Digi-Block.

Homework Hints
    Helping Your Students With Homework: A Guide for Teachers
    Helping Your Child With Homework (for Parents)

NUMB3RS is a drama about an FBI agent who recruits his mathematical-genius brother to help the Bureau solve a wide range of challenging crimes in Los Angeles (CBS - Friday nights at 10/9 Central - see about the show). NCTM and Texas Instruments have partnered with CBS to put together the We All Use Math Every Day Program, which provides math activities related to the math topics seen on the TV episodes of NUMB3RS. Check it out, I think you'll like NUMB3RS and We All Use Math Every Day.

Escape from Knab - THE Adventure - Escape from Knab is an educational simulation which takes participants through a series of financial decision- making experiences in the fun and entertaining setting of the fictitious planet, Knab where visitors discover the results of their actions and decisions.  Students learn mathematics, economics, life skills (and use the Internet technology).

MarcoPolo - Links. Provides no-cost, standards-based Internet content for the K-12 teacher and classroom.

The K-12 Mathematics Curriculum Center - This site will help you build an effective mathematics education program and consider the new standards-based mathematics curricula (sponsored by the NSF). Located at the Education Development Center (EDC). Or see any of the following:

• ARC Center - for elementary curricula.
• Show-Me Center - for middle grades curricula.
  • Modeling Middle School Mathematics - video lessons and Web-based Internet materials to examine each of the five NSF- funded middle school math initiatives.
• COMPASS - for high school curricula.
• Chicago IMP - on the Interactive Mathematics Program implementation in Chicago.

Fun Facts - This large (searchable by topic and level) archive is designed as a resource for enriching your courses with mathematical Fun Facts!

Math Is Fun - Games (2, and more), platonic solids, Mathionaire Multiplication Quiz. Includes some different games such as blobs.

Millennium Mathematics Project - Large project from the UK. Has NRICH problems; Plus Magazine (targeted for secondary students) which opens a window to the world of maths, with all its beauty and applications, by providing articles from the top mathematicians and science writers on topics as diverse as art, medicine, cosmology and sport; and Thesaurus which has a large library of interactive diagrams (scroll down and click the "gallaries").

Teacher Resources on Line (trol) - Lots of stuff for math teachers from a PDF file of the first 100 digits of pi (for your wall), to missing digit puzzles, to counting problems and more. (Actually, it's for maths teachers--it's from the UK.)

MIND Institute - They use a visual and conceptual approach (which I, and many researches, also believe in). They believe teachers should "first teach students to conceptualize and solve algebra problems visually, and then integrate and connect the symbols and the numbers. In this way students first become problem solvers, and then the language and the numbers and the symbols that they learn later become tools to help them solve problems." Traditional methods have been to first teach students how to symbolically manipulate algebraic equations and then to use those skills to solve problems. Their approach is nicely demonstrated here (click Begin Tour). The MIND Institute is dedicated to education program excellence and cutting edge scientific research. The Institute has successfully transferred more than 30 years of breakthrough brain and learning research into applied education programs for K-8 students. Also click the Games and ST Challenge links. (MIND = Music Intelligence Neural Development and ST = Spatial Temporal.)

Coolmath.com - On-line Way Cool Math Things, Thinking games, Graphing calculator, 3-D Mazes, Graph game, Polyhedra Gallary, and more.

Jim Loy's Mathematics Page - Huge website covering many math topics from Algebra to Fractals and Chaos to Zeno's Paradoxes.

John Handley High School Math Page - Lots of Math Humor, Puzzles, Poems, Quotes, and more.

PurpleMath - "Your Algebra Resource." Seemed quite symbolic (not a lot of interactive applets or applications) on my first visit. Very complete. Offers a lot of explanations of topics such as factoring and intercepts. Has a good list of math links. Also has and explanation and example of the classic word problems-scroll down to the bottom (such as age, coin, and mixture problems).

WWW Interactive Mathematics Server ("WIMS") - Search engine, puzzles, online plotters and calculators, more. This site has some excellent activities. For example Correspondence (for learning about 1-to-1 and onto functions for advanced math students) and Magic Rectangle (for middle school students to practice addition and problem solving simultaneously).

Eric Weisstein's World of Mathematics - Math World from Wolfram Research. Lot's of interesting topics - many advanced topics. See also The Mathematical Explorer.

Maths Online - This page contains prepared links to more than sixty online tools for every day purposes, and some hints where you find more. Function plotters, calculators, and symbolic processors. "Maths Online" comes from oversees. Also has The Gallery which consists of interactive multimedia learning units an many topics including derivatives.

Mathematical Moments - This program promotes appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture. Download this series of pdf files. It's from the American Mathematical Society (AMS).

Math Awareness Month - Each year there is a theme intended to, you guessed it, promote math awareness. Lots of interesting activities, ideas, and archives from the Mathematical Association of American (MAA).

I.S.B.E. - Illinois State Board of Education. See also the list of ROE's. or the IARSS Site (which includes the "ROE Minimum Requirement Document," updated December 28, 2006) or a map showing the ROE's or Professional Development Activity Areas.

• Illinois Certification Testing System - click for exam dates, frameworks, and study guides, including the Assessment of Professional Teaching (APT test).
  • Basic Skills Study Guide - Click here for Suggestions For Preparing for the Mathematics Portion of the Illinois Basic Skills Exam for Teachers. At WIU, the basic skills test is taken prior to a student's acceptance into the Teacher Education Program.
  • Elementary Education Test Framework - Objectives for the content test for Elementary Education majors. (Operational July 2004.) At WIU, the content test is taken prior to student teaching.
  • Mathematics Test Framework - Objectives for the content test for Mathematics majors. Study Guide. At WIU, the content test is taken prior to student teaching. Click here for suggestions on preparing for the content test.
  • Assessment of Professional Teaching Framework (APT) Study Guide - Objectives for the general teaching test for all teacher education majors. (Operational since July 2003.) There are four versions: Secondary, Elementary, Special Education, and Early Childhood. At WIU, the APT test is during student teaching.
  • Math Content Standards for Teachers
  • Illinois Professional Teaching Standards - For all teachers. The WIU Teacher Education Portfolio is based on these Standards.
  • Endorsement Requirements for Subjects - include middle and high school
  • (Old: Requirements for Teachers of Middle Grades - Section see section 1.720.)
• Illinois Learning Standards - click to see (or download) the Illinois Learning Standards (ILS)--complete with goals, standards, and benchmarks. Be sure to see the Classroom Assessments and Performance Descriptors (click on Mathematics), a supplement to the Illinois Learning Standards. For a look at other state's standards see the World Book Resources (not affiliated with the ISBE).
  • Mathematics Assessment for the ISAT - Included are the Grade 3, 5, and 8 "Student Friendly" Mathematics Scoring Rubrics, word lists, formulas, sample items (including the extended response items), Framework for the ISAT, and more.
  • Practice items for the 8th Grade ISAT and PSAE - provided by Holt, Rinehart and Winston.
  • Interactive ISAT Multiple-Choice Sample Questions - Grades 3 to 8. Provided by Metalogic.
  • PSAE - Prarie State Achievement Exam
    • PSAE-ACT: Math
    • WorkKeys Practice
    • PSAE-Workkeys: Applied Math (all are free, except the PSAE Workkeys costs $4).
• Employment Opportunities - lists of job openings for teachers. Illinois Education Job Bank included.
• Early Childhood Learning Standards - Standards for Pre-K (similar to ILS) students. Part of the Early Childhood Education page. See also the Illinois Early Learning Project.
• My page titled "Miscellaneous Notes on Certification" - just a place I write down technical information on certification requirements.

National Mathematics Advisory Panel Final Report - On March 13, 2008, the National Mathematics Advisory Panel presented its Final Report to the President of the United States and the Secretary of Education.

Other State's Math Content Tests for Teachers (Study Guides):

• Texas

Hotmath.org - Hotmath provides free solutions for actual math homework problems in many popular textbooks, Algebra I & II, Geometry, Pre-Calculus, and Calculus (High school). The problems are worked step-by-step.

Measurement/Assessment Concepts - Glossary of Measurement Terms. (Just text.) From Harcourt Educational Measurement.

Multimedia Math Glossary - For grades 1 to 8.

IHMC Concept Mapping Software - Free! download.  Concept maps are great!  Here's software for creating, saving, updating, and sharing concept maps (you can also print, publish to the web, and more)!  From the Institute for Human and Machine Cognition (IHMC).  Here's a concept map on concept maps.  Software is referred to as CMap.

Probability Explorer - excellent! Probability Explorer is a research-based software application designed with tools that enable students and teachers to design, simulate, and analyze a variety of probabilistic situations. It costs, but there is a free demo.

MathWorlds - from SimCalc. Software for computers and for calculators. Research and development in technology and curriculum
dedicated to helping all students understand the Mathematics of Change and Variation (including ideas underlying Calculus). This Mathematics Education Research Group (at UMass Dartmouth) was lead by, the late, Dr. James J Kaput.

Poly - a shareware program for exploring and constructing polyhedra. Manipulate solids and their nets. Fold and unfold nets. Pedagoguery Software Inc. in Canada

MathematicsHelpCentral - Can print out various types of graph paper and scroll to the bottom of the page for a free program (software) for printing your own graph paper. This is written by a student, so (like all of the Internet), read carefully, realizing there may be some inaccuracies.

Peanut Software - This is great software and it's free!  "Wingeom" does many of the same things as Geometer's Sketchpad (and some new things too).  There are other titles.  Downloads are fast.  Click here for a 1-page handout on Wingeom (Word doc).

Cabri 3D - Another dy