Archive for the ‘Algebra’ Category

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.

Possibly Related Posts:

• History of Numeration Systems
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• Math about the Electoral College
• Teaching Math Without Words
• A reason to calculate the vertex

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

Possibly Related Posts:

• History of Numeration Systems
• Collection of Math Games
• Math about the Electoral College
• A reason to calculate the vertex
• Exponent Block and Factor Pair Block

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.

Possibly Related Posts:

• History of Numeration Systems
• Collection of Math Games
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• A reason to calculate the vertex
• Exponent Block and Factor Pair Block

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

Possibly Related Posts:

• Collection of Math Games
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• Math about the Electoral College
• Exponent Block and Factor Pair Block
• An Algebra Game for Trinomials

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.

Possibly Related Posts:

• Collection of Math Games
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• Math about the Electoral College
• Teaching Math Without Words
• A reason to calculate the vertex

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.

Possibly Related Posts:

• Collection of Math Games
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• Math about the Electoral College
• Teaching Math Without Words
• A reason to calculate the vertex

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.

• From Fish to Infinity (Jan. 31, 2010)
• Rock Groups (Feb. 7, 2010)
• The Enemy of My Enemy (Feb. 14, 2010)
• Division and Its Discontents (Feb. 21, 2010)
• The Joy of X (Feb. 28, 2010)
• Finding Your Roots (March 7, 2010)
• Square Dancing (March 14, 2010)
• Think Globally (March 21, 2010)
• Power Tools (March 28, 2010)
• Take It to the Limit (April 4, 2010)

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.

Possibly Related Posts:

• What if you don’t have enough whiteboards?
• History of Numeration Systems
• Collection of Math Games
• What does the classroom say?
• Signed Numbers: Colored Counters in a “Sea of Zeros”

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 Amazon.com 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.

Possibly Related Posts:

• What if you don’t have enough whiteboards?
• Collection of Math Games
• What does the classroom say?
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• Math about the Electoral College

This was my presentation on Friday in Austin, Texas at the Developmental Education TeamUp Conference.

The process of learning algebra should ideally teach students good logic skills, the ability to compare and contrast circumstances, and to recognize patterns and make predictions. In a world with free CAS at our fingertips, the focus on these underlying skills is even more important than it used to be. Learn how to focus on thinking skills and incorporate more active learning in algebra classes, without losing ground on topic coverage.

Possibly Related Posts:

• Abandoning ship on using Wolfram Alpha with Students
• Collection of Math Games
• What does the classroom say?
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• See you at AMATYC 2011

This presentation, built yesterday, is my philosophical argument for why we should be actively pursuing games as a way to teach algebra. In fact, you’ll find that many of the definitions of games and game design principles sound like they are describing algebra. Of course, the presentation misses something without my accompanying talk, but it has enough to get you started thinking about where we could be going with math education.

It took me 12 hours just to build the presentation you see below … and collaboration with my assistant and an illustrator.  I’ve been obsessively reading and thinking about this topic for about two years.

Possibly Related Posts:

• Collection of Math Games
• Signed Numbers: Colored Counters in a “Sea of Zeros”
• Math about the Electoral College
• What skills should we be teaching to future-proof an education?
• A reason to calculate the vertex