Archive for the ‘Algebra’ Category

Copyright Math

This is a short TED Talk by Rob Reid (The $8 billion iPad) that tries to infuse a little “reasonability test” into our blind belief in the numbers provided by those with self-interest … in this case, the music/entertainment industry.


There are several examples that you could turn into signed number addition or subtraction problems.  In my favorite example (about 2:57 in the video), Reid uses what he calls “Copyright Math” to “prove” that by their own calculations, the job losses in the movie industry that came with the Internet must have resulted in a negative number of people employed.

Here’s the word problem I’d write:

In 1998, prior to the rapid adoption of the Internet, the U.S. Motion Picture and Video Industry employed 270,000 people (according to the U.S. Bureau of Labor Statistics).  Today, the movie industry claims that 373,000 jobs have been lost due to the Internet.

[Prealgebra] There are many ways to interpret this claim.  If all these jobs were all lost in 1999, how many people would have been left in the motion picture industry in 1999?  If the 373,000 jobs were spread out over the last 14 years, then on average, how many jobs were lost each year? Using this new “annual job-loss” figure and no industry growth, how many jobs would have been left in 1999? Can you think of other ways the quoted figures could be interpreted?  Use the Internet to see if you can find out how many people are employed in the motion picture industry today.  [Prealgebra]

[Intermediate Algebra] If the job market for the motion picture and video industry grew by 2% every year (without the Internet “loss” figures), how many people would be employed in 2012 in the combined movie/music industries?  How many jobs would have been created between 1998 and 2012 at the 2% growth rate?  If the job market grew by 5% every year (without the Internet “loss” figures), how many people would be employed in 2012 in the combined movie/music industries?  How many jobs would be created between 1998 and 2012 at the 5% growth rate?


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Scale of the Universe

One of my former students (who is still a Twitter user) pointed me to this fantastic animation of powers of 10 meters, called “Scale of the Universe 2.”  I think you’ll appreciate the design and relevance of the objects the authors, Cary and Michael Huang, use to help the user to understand the relevance of scale.  Just like Powers of 10, you can zoom from the smallest part of a cell to the edges of the universe.



The authors have a collection of science- and math-oriented animations at that might be worth checking out too.  They also have a clever little game called Get to the Top (with 82 variations).

P.S. If you’ve never seen the 1977 film, Powers of 10, it was a really incredible movie for its time and you can see it on YouTube.  Another animated version of this film can be found at the Powersof10 website.

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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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Signed Numbers: Colored Counters in a “Sea of Zeros”

The “colored counter” method is an old tried-and-true method for teaching the concept of adding signed numbers.  However, to show subtraction with the colored counter method has always seemed painful to me … that is, until I altered the method slightly.

Now all problems are demonstrated within a “Sea of Zeros” and when you need to take away counters, you can simply borrow from the infinite sea.  Voila!  Here’s a short video to demonstrate addition and subtraction of integers using the “Sea of Zeros” method.  You can print some Colored Counter Paper here.

Video: Colored Counters in a Sea of Zeros

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Math about the Electoral College

This was a surprisingly good video about the math of the U.S. Electoral College system.  At first I kept saying “but wait a minute…” but all my concerns were addressed in the video, and then some.  I was surprised by the revelation (towards the end of the video) that it is theoretically possible (although not likely) to win the seat of President of the United States with less than 23% of the popular vote.  Wow.

There is some great math of ratios and percents here.  You can find data and other pertinent information about the Electoral College here.

You might also enjoy playing the Redistricting Game with your students, where you can “recast” who wins an election based on how you draw the boundaries on a map.

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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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Exponent Block and Factor Pair Block

A few weeks ago I built two new games for algebra in one week.  These games just use the game mechanic from “Antiderivative Block” (a Calculus game), but with algebra-oriented game cards.  The game mechanic is a classic “get 4-in-a-row” so it’s pretty easy to learn.

Exponent Block (plus Gameboard) will help students contrast slightly different expressions involving exponent rules, especially negative and zero exponents.

Factor Pair Block (plus Gameboard) will help prepare students for a unit on factoring.  There are two sets of playing cards (print each set on a different color of paper if you want to be able to easily separate them).  The first set of cards works with factor pairs for natural numbers and finding the GCF for two numbers.  The second set of cards helps students start to see the GCF for monomials.

Supplies: I have found that it’s worth the investment in some bags of “marble markers” to play these (and other) games.  These can generally be found at a store like Hobby Lobby or JoAnn’s Fabric.  I’ve included markers that you can cut out and use, but trust me, that’s a pain.  It is also very helpful to print the game cards (two-sided) on cardstock, so if you don’t have a ready supply of cardstock in multiple colors, I’d pick some of those up too.  Last, small plastic bags are going to be a necessity to hold the sets of cards.

It’s interesting to watch the students play these games. Many students who seem to be uninterested in learning the fine differences between expressions in normal circumstances land in deep explanations of why these expressions simplify differently when playing the game.

Expect that students will play two ways.  Some will play the intended game mechanic, playing competitively to get four-in-a-row.  Other groups will play to “fill the board” … frankly, I can’t see what’s fun about this, but it never fails that at least two pairs of students do this.  One alternate play method that would allow you to “fill the board” would be to try to keep playing so that neither partner creates a four-in-a-row.  Then the players work collaboratively to try to create a filled gameboard where there are no wins.

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An Algebra Game for Trinomials

This week was the start of factoring in my algebra course and so, I’ve been building games involving factoring all week.  This one is the most interesting one – it’s called Trinomial Traverse.  David (one of my colleagues at MCC) and I started work on it on Tuesday with a stack of cards with monomials, binomials, and trinomials.  No matter how much we pushed at it, we couldn’t get out a decent game that involved strategy.  However, when I got home and raided my game design closet, I found some wooden cubes and the real game building began in earnest.  What you see now is roughly version 4.

We’ve carefully balanced the board for good gameplay using the probabilities of rolling any trinomial, so I wouldn’t recommend building an alternative game board unless you “do the math” too. Please feel free to download (PDF) and use Trinomial Traverse in your own classes and let us know if you have suggestions for improving it.

David has done three class tests and recommends that you don’t suggest the students using pencil and paper (it really slowed down the game).  With each role of the dice, there are only three combinations.  For students, it is probably easiest if they just work out what each combination gives them (in their head) and take a look at the game board after figuring each one out.  There are a few rules we have left out.  For example, you may want to put a penalty in place if students forget to announce their trinomial or do it incorrectly, but we decided to leave those decisions up to you.  It’s probably best (in our opinion) if the students just police each other on this one.

David and I recorded a little demo video of the game play.

One simple variation would be to play the game with “scarce resources” where all the gold is sitting on the board at the beginning of the game and can only be earned once on each space.

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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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Community Site for Algebra Activities


I rarely talk about the books I’ve written on this blog, but the Community Site for my new book, Algebra Activities,  just launched and I think it’s pretty cool.  Also, I now have an author page.  Yay!

The basic philosophy for the book is to provide easy-to-use classroom activities to instructors so that they can easily replace lecturing time with more active learning.  The book also provides instruction tips and lesson plans so that any algebra instructor, especially new ones, can have a “mentor” to guide them and help them reflect on how students learn.

If you go to the Samples section of the Community Site, you can print and use some of the activities from the book in your classes.  You can also see some of the fantastic new algebra cartoons that were commissioned as part of this project.

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