A little problem in applied geometry for the teacher:  how many 5” x 8” rectangles can you cut from a standard 22” x 28” piece of posterboard?  The answer is at the bottom.  First, why would you want to?

Because with 42 such rectangles and 36 disk magnets (you can get magnets at a science-surplus store, or at a sewing supply store), you can make a lesson that will engage your whole class’s attention on remembering some easy math, for about 40 minutes.  WARNING:  This is NOT a lesson for higher-level thinking skills.  But not all of math (or all of life) involves higher-level thinking skills.  Algebra 1 students also need to learn that a⁵b⁸/a²b³ = a³b⁵ , and learn it well enough that they can glance at the problem and write down the answer.  Trig students need to learn sin² x + cos² x = 1, and all its standard variations, by heart.  “Concentration” is a game that works well for this.

First you make 21 matching problems based on the math your students are doing, if that is possible.  Sometimes it isn’t.  Examples below.  Then you take your 5” x 8” rectangles:  leave one side blank, and on the other side write one-half of each matching problem.  Shuffle the cards.  At the start of class (or before), arrange them on the board with magnets in seven rows and six columns.  A student or two will be glad to help, but no-o-o peeking!  The bottom row can stand on the chalk rack.  Label the columns A-F and the rows 1-7.  Go through the class in alphabetical order (or somehow), and each student gets to call one pair of cards, trying to find a match.  If they do they are rewarded with a math dollar or some other incentive  (I recommend math dollars highly).  I do not recommend letting students guess again when they find a match; a few students will practically sweep the board.  Student are not allowed to write down what is behind each card!  Since I’ve always been at the board playing Vanna White when I’ve done this I’ve always relied on students to squeal on each other, which may not be good enough.  I might even recommend having a student turn the cards while the teacher does honesty patrol.  I suppose it wouldn’t be unfair to have the student turning the cards guess in her turn as well, since she has only seen what everyone has seen.

Concentration avoids the problem I’ve had with some competitions, which is that you lose the attention of the majority of the students who are not competing at any given moment.  Here, even if it isn’t your turn to guess, watching closely gives you information you may need when your turn comes.  In my experience, 42 cards take about the right length of time for a 44-minute class period.  A little time left at the end could be devoted to a quick matching-quiz on the same problems, to enhance motivation and assess the result.

Oh, yes:  the answer to that poser at the top is 14 cards.  A solution is below.

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net