Archive for the ‘Precalculus’ Category

Collection of Math Games


The page of digital and non-digital games has grown too long and unwieldy, so I’ve finally taken the time to reorganize the content by topic area. I’ve also added all the new “Block” games on various topics in Trigonometry, Rational Exponents, and Logarithms.

If you’ve bookmarked the old Games page, you’ll see that it now just tells you how to find the new sub-pages.

Direct links to the new game pages are below:

I’ve also decided to collect your suggestions for other digital and/or paper games, puzzles, and manipulatives  using a Google Form, but before you submit a game for me to review, PLEASE check it against my criteria for Lame Games.

Submit your suggestions here.

 

 

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A reason to calculate the vertex


If you ever needed a REASON to calculate the highest point of a parabola that opens downward, here’s one.

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Using Math to Understand the Future


Futurist Peter Bishop was one of the keynote presenters at MichMATYC 2010 this year.  He spoke to us about what a futurist does, and shifted our paradigms about how to look at data trends to one that is more mindful of the cone of plausibility.  Don’t know what that is? Well, watch the talk!  If you don’t have a lot of time, then watch the last 20 minutes.  You can also get the slides here.

If you’re interested in the other sessions at MichMATYC 2010, many of the slide decks are posted in the Resources Tab of the MichMATYC 2010 Website.

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NYT Opinionator Series about Math


For a few months now, the NYT Opinionator Blog has been hosting a series of pieces that do a phenomenally good job of explaining mathematics in layman’s terms.

The latest article is about Calculus (with a promise of more to come): Change We Can Believe In is written by Steven Strogatz, an Applied Mathematician at Cornell University.

There are several other articles in this series, and if you haven’t been reading them, you really should go check them out.  Assign them.  Discuss them in your classes.

Given the discussions we’ve been having about teaching Series and Series approximations lately on Facebook, Twitter, and LinkedIn, I wonder if he’d consider writing an article explaining “Why Series?” to students.

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Sixty Symbols


Do you ever come across a Greek symbol in your reading and think, “now what does that stand for again?”  Professors and other experts at the University of Nottingham have made a series of YouTube videos that will (hopefully) jog your memory.  Their site is called Sixty Symbols (I wonder what they’ll do when they find more than 60 symbols?).

They also may make nice descriptors for those symbols you cover in class.  You can also embed the videos in an online course shell in the appropriate topics.

Here’s ∞ (infinity) for your any level of math class after the first discussion of interval notation.

And j (for imaginary numbers, which is i in many U.S. math texts).

Or how about ω (angular velocity) for that Trig class you’re teaching?

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Modern War follows a Linear Regression


Just watched an amazing 7-minute TED talk on The Mathematics of War where an interdisciplinary team of researchers (physics, mathematics, economist, intelligence, computers) figured out how to mine data from public streams of information to collect and analyze modern warfare.

It turns out that when they began plotting the number killed in an attack with the frequency of those attacks, they found the data was linear. Not only was this relationship linear, but the same linear relationship then appeared in every modern war they looked at (with slopes that varied slightly).

mathofwar1

So, next they modeled the probability of an event where x people are killed.

mathofwar2

Finally, they went back to each conflict to try to understand the meaning the slope of the line.  It turns out that the alpha value (which hovers around 2.5) has to do with the organizational structure of the resistance.  If the resistance becomes more fragmented, it is pushed closer to 3.  If the resistance becomes more organized, it is pushed closer to 2.

Anyways, it’s only seven minutes.  You should definitely watch it!

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Murderous Math Tricks


I found this one while wandering about on YouTube.  The last “trick” would be a fantastic puzzle for a Trigonometry course.

Murderous Math Tricks

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Funky function notation


At the UMD faculty workshop, one of the participants had an idea for using an Animoto video.  She suggested it might be a good way to break up a long lecture time.  This got me thinking about short lessons (like the CommonCraft videos).  Just because the video is short, it doesn’t mean it’s not effective.

I thought I would try out a short video of my own using Animoto.  This one is called “What is function notation?”  If the video doesn’t load for you, go directly to the site here or see the YouTube rendition here.  Either video can be embedded if you’d like to use them in a course shell.

 

You might be interested in the process I used to build this.  For Animoto, you need a file folder with image files.  First, I created a deck of 75 PowerPoint slides (those being relatively easy to edit).  Then I printed from PowerPoint to SnagIt (because of a special SnagIt save option). Then I saved the SnagIt file as jpg files, where each slide is saved as an individual image file. This gave me a folder of all the slides, but with each slide saved as an image.

I then uploaded the 75 images into Animoto and made sure they were in the proper order (for some reason the last slide fell first and had to be moved back to the last position). You choose the slides you want to “focus” on – places where the reader may need an extra second to think or read. Choose some music (preferably without words), and finally, choose the speed. I tried it at regular speed first (no way), but settled on 1/2 speed as a good speed to show the slides.

I don’t have any student guinea pigs at the moment, so someone play it for your students and let me know what they think! I was toying with the idea of explaining a theorem next.

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Complex Numbers, Radians, and more!


Laura Shears (a fellow Michigander) has a great site of resources for the precalculus level called LSquaredMath. I haven’t covered much precalculus material on the blog because I haven’t taught precalculus for a while, but her latest update reminded me that I should pass along her website to you!

Laura has been working with Flash for a few years now, creating animations for mathematics. She suggested to me that I should attend the MAA PREP Flash course (which I did last summer) and it was my attendance that ultimately inspired the blog. Anyways, back to the story … Laura has been working on making all her material SCORM-compliant (that means it plays nice with the gradebooks in LMS platforms like Blackboard, WebCT, etc.).

Complex Number Graphing (both Cartesian and Polar)

Addition of Ordinates (if you’ve got a Smartboard, you’ve got to try this one in class, here’s a little video demo of how I’d use it in class)

Radian Target Practice

Radian Measure and the Unit Circle (a great review exercise for Calculus Students that don’t know their Trigonometry)

You will notice that Laura lets you use all of her material from the website for free, but does charge for a SCORM compliant version. Before you start complaining about that – note that Laura is an adjunct instructor and building this stuff takes a LOT of time.

If you’re interested in creating SCORM compliant FLASH material yourself, you should take a look at Laura’s help page for SCORM here.

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Logistic Consumption Curves


This great graphic is from the New York Times (2/10/08) article entitled “You are what you spend” on the spread of consumption of a variety of consumer goods. A link to the two graphics in the article can be found here. There is a second graphic about what we spend vs. what we earn broken up by the lower fifth of earners, middle fifth, and highest fifth of salaries per household.

You will, of course, recognize the great logistic curves here. Not sure how long the links will last – often newspapers will pull down their content after a few weeks, so save the resources if you want them.

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