John Pritchard, from the Geography Department at the University of Sheffield, was kind enough to give an overview of the process involved in the creation of these maps for this blog post:

A cartogram can be thought of as part map, part pie-chart. It attempts to keep areas (such as countries) in roughly the same place, whilst changing their size to reflect the value of a variable, for example, population. A world cartogram of population would show, for example, China and India as larger than their land area size, and Australia as smaller.

An algorithm that creates a cartogram from a map, preserving recognisable shapes whilst resizing countries, has been something of a‘holy grail’ of the cartogram world. The solution we use forWorldmapper, from Mark Newman and Michael Gastner at the University ofMichigan, is inspired by the diffusion of gas molecules. If you imagine the example of human population, the algorithm would have the effect of allowing the population of a densely populated country to ‘diffuse’, pushing back the boundaries of neighbouring, less densely-populated countries, until population density was evenly spread.

Interesting that this application to geography was inspired by chemistry!

Here are a few more maps that I found interesting. A map of War Deaths:

Finally, a great comparison of wealth in the years 1500 and 1990:

To learn more about how the maps were created, see the Worldmapper “About” page.

These maps would make a great exclamation point on a problem about percentages. For example, first you calculate the the percentage of deaths caused by war from several continents (North America, Africa, etc.). Then after the calculations, you can emphasize the findings with the appropriate map.

Most of the maps (at least, all the ones that I looked at) are accompanied with data or descriptive numerical information that you could easily build a word problem from.

Possibly Related Posts:

• David McCandless: Data Detective
• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Algebra is Weightlifting for the Brain
• Playing to learn math?

Okay, okay, I know… this is a blog for math and technology. But occasionally I have to stray just a little. I do have a degree in Chemistry too… so I am allowed!

This is totally the coolest interactive periodic table website I have ever seen! And it was created with Mathematica (believe it or not).

Surely you could use the data provided with each element for some kind of math problem? Or you could show your students the appropriate chemical element if it shows up in a word problem.

P.S. I found this site on the Wolfram Blog… which you might want to check out yourself!

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• Where’s the Math in Computer Science?
• Today I want to be a Chemist (3)
• Today I want to be a physisict
• Top 10 Open Source Tools for Math

Here is a link to the presentation this morning from Bruce Yoshiwara and Mike Martin about NSDL and MathDL.

Interesting tidbits from this presentation:

• You can search MathDL by a specific brand of software. So, for example, if you have Maple on your campus, but don’t know how to use it, you could search for Maple applications and find all the ones that are in MathDL.
• They also mentioned the Convergence website, which is a site about the history of math.
• They also talked about the Math Gateway, a portal to access the MathDL where you can organize your favorites into folders.
• JOMA, DCR, and Convergence will be merging into one site/resource called the Journal of Online Mathematics (JOM) and will have an RSS feed (this means that the site will come to you via email or RSS if you don’t want to have to go to the site).
• Mike showed us WebWork (out of the University of Rochester) which is an online homework platform for math and science. The system runs on moodle, which makes me think that it must be free to use, but I’m not positive on that. If anyone else knows, then please comment that in.
• One final note: I was able to pull up their power point presentation on my phone and click through the slides while I watched the presentation (Bruce says he produced it as a pdf for the website, so that seems to work pretty well on my phone, which is a treo).

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• World Future Society Conference 2010
• Teaching Math with Technology
• The Calculus Tweetwars
• MichMATYC 2010

I stopped by the Wolfram booth to say hi and see what they are up to… of course, you know that I love using the FREE Wolfram Demonstrations in my classes and my online lesson videos. If you are unfamiliar with the Wolfram Demonstrations, they are interactive activities that are math based. So there are pure math, science, statistics, and computer science demonstrations. They usually have slider bars so that the parameters of the equations can be altered and the physical shapes, graphs, etc. change. I am really not doing it justice in this description… I’m getting pretty mentally exhausted!

Anyways, if you haven’t seen it, check it out. As of today there were 2,034 Demonstrations available on their site.

Here I am at the Wolfram booth holding one of these cool 3-D mathematical solids.

These were printed using a 3-D printer… no kidding… welcome to the year 2007! If you can create a 3-D object using Mathmatica, I guess there is some place on their website where you can submit your 3-D file and you can pay Mathematica to print it 3-D for you. Perhaps Wolfram can comment on how you can do this if this is something you want to do.

Possibly Related Posts:

• World Future Society Conference 2010
• Extensions to Make Chrome Work for You
• Teaching Math with Technology
• MichMATYC 2010
• See ya at ICTCM

I found this nice website while looking around the website of a community college in Maine. The Famous Curves Index (published by a school of mathematics in Scotland) has 63 famous curves complete with equations, graphs (like this nice one of Fermat’s Spiral below), a short history of the curve, and a link to interactive Java code for manipulating the curve.

This one is the interactive Java code for a Hypocycloid (given by a parametric equation)… very nice!

What a great resource for Precalculus and Calculus classes. I will have to pull up some of these curves next week when we talk about implicit differentiation. If you’re teaching parametric equations or polar equations, this site would be great! I didn’t have any trouble getting the Java applets to work. Kudos to the School of Mathematics and Statistics, University of St. Andrews, Scotland for a great collection of curves!

Possibly Related Posts:

• Calculus Tweetwars: The End
• Calculus Tweetwars: 1676-1698
• The Calculus Tweetwars (1661-1675)
• The Calculus Tweetwars
• NYT Opinionator Series about Math

Line Rider, in its infancy, had only one tool, the pen. With this tool, you drew your masterpiece curve (or piecewise curves), on which, the little hatted dude rides his sled. There were rules about the curves, when drawn left to right, the were riding curves, when drawn right to left, decoration… or something like that.

However, the new version of LineRider has multicolored pens, an eraser tool (woo hoo) and now with the addition of the magical Jing program… I can easily record and share my masterpiece with you. If you watch my masterpiece, keep in mind that I have just nicely demonstrated two types of discontinuities in my work… removable discontinuities (the little dude just glides over the hole) and jump discontinuities (the little dude leaps from one part of the curve to another).

LineRider can be an interesting and fun study in slopes for algebra students, asymptotes for pre-calculus students, and limits for calculus students.

However, the true works of art are the ones created and set to music like these classic LineRiders all available on YouTube: (turn on your sound)

• Jagged Peak Adventure
• Urban Run
• Electronic Adventures
• LineRider SuperMario (okay… that one is really clever!)

These are good for a 5-minute break in class… you know… for those students that refuse to get out of their seats and stretch… they might as well be entertained! I have seriously assigned LineRider as an extra credit project, but it’s always been difficult to find a way to share the videos (until Jing).

This one is addicting… make sure you get your papers graded and your classes prepped for before you become consumed!

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• Calculus Tweetwars: The End
• Calculus Tweetwars: 1676-1698
• The Calculus Tweetwars (1661-1675)
• The Calculus Tweetwars

Possibly Related Posts:

• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Algebra is Weightlifting for the Brain
• Playing to learn math?
• Prime Number Manipulatives

I stumbled across a nice website last week called Interactivate with 140 (or so) interactive Java-based activities for algebra, geometry, probability, statistics, etc. Many of the activities are modifications of other activities, but still there are at least 30 unique game-based activities here to help your students learn.

I particularly liked “Algebra Four” (a play on the game Connect Four). I am teaching my algebra students all about solving equations right now and this would give them some good practice. The student can choose the level of difficulty (one-step, two-step, distributive, etc.). So conceivably, a student could first play at the one-step level, then the two-step level, then add the distributive property, and work their way up. This is a two-player game, which is really the only drawback, as a student at home would have to play against themself (or convince someone else to play an algebra game with them… hmm… unlikely). I do like the timer, which would encourage the student to get faster at solving equations. And if a student doesn’t want to play against the timer, it could just be set for a high time.

Another nice game here is the “function machine” like we’ve seen in textbooks, only this one is really a machine where you (or the student) inputs values, and it (the machine) processes the values and outputs them. The “game” here is to guess the function. I could see using this one in a classroom when we talk about function notation, and writing out the function notation process of each “guess” and “answer” to the side of the projected machine. A small improvement on this game would be to show the function notation to the side and then run a version that would let the all-knowing instructor input “x” at the end of the game, to show that if you input “x” or “a” into the function notation, the function notation shows you exactly what happens during the processing.

One last gem from this site is Area Explorer, which shows the student a graph of connected, shaded squares, and asks the student to find the area and perimeter. What I like is that it emphasizes the underlying principle behind area and perimeter (area is counting unit squares in the interior of the figure and perimeter is counting unit lines on the perimeter of the figure). Our students today seem to often miss this concept alltogether and just want to boil everything down to a formula, so I think this would be a great activity to have students try on their own.

All in all… kudos to this site for creating some really nice interactive materials!

Possibly Related Posts:

• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Algebra is Weightlifting for the Brain
• Playing to learn math?
• Prime Number Manipulatives

Sorry… I was remiss in my postings last week! The beginning of the semester just sucked the energy right out of me.

I particularly like these “Recognize Graphs” games (see below). These are excellent for helping students recognize characteristics of graphs without pulling out their calculator and graphing every function. Just work out enough information about the given function to rule out some of the graphs and narrow down your choice to one graph. Students can play over and over as there are around a hundred graphs in the database. I think this game could be improved by adding a timer… thus encouraging students to “beat” their own best time.

The games run with Java (so you may have to download that plug-in if you do not have it). I found that I had to “right-click” on the red buttons to get the game to show up on my screen. For my online class, I’m having them submit a screenshot of a completed game for 1 participation point (they need 30 points per chapter). If there was a timer on the game, I’d have them aim for a particular time and then submit the screenshot for 2 points.

Possibly Related Posts:

• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Algebra is Weightlifting for the Brain
• Playing to learn math?
• Prime Number Manipulatives