# Numbered Cards for Concrete Abstractions

This web page provides help making numbered cards for use with Concrete Abstractions: An Introduction to Computer Science Using Scheme, by Max Hailperin, Barbara Kaiser, and Karl Knight. These cards are used for comparing two different sorting algorithms. There are three options for making the cards:
• If you have the ability to print a PostScript file, we have a PostScript file, with three pages containing twelve cards each. You can print that out on cardstock (or normal paper, in a pinch) and cut it up using a paper cutter. You'll get a deck of thirty-six cards; that is more than you need, but it means you'll get some variety if you shuffle it and then count out 32 (or fewer) of the cards.
• Alternatively, we have GIF versions of pages one, two, and three. Most web browsers will let you view and print this out. Then you can cut it up and use it as above. Although this option will work for more browsers, the resulting images are typically more jagged and somewhat smaller.
• Finally, it really isn't that tough to make your own cards by hand. Either 3x5 index cards cut in half or standard sized business cards work great. (In fact, our PostScript cards are the same size as business cards.) We recommend writing the number on each card twice, facing opposite directions, so that while you are sorting you don't need to worry about which end is up. The numbers we used for our 36 cards are 69, 73, 28, 32, 15, 51, 56, 42, 98, 4, 59, 2, 61, 95, 25, 12, 10, 92, 49, 82, 45, 54, 90, 22, 63, 86, 84, 6, 20, 79, 40, 71, 88, 37, 35, and 76. These numbers have a couple good properties. First, there are no duplicates, which would introduce an unnecessary complication in the sorting. Second, there are no consecutive numbers, which makes it harder for a student to know in advance that a particular number must be the largest remaining one, when selection sorting. That means all the comparisons really need doing.

Another option, if you can't tear yourself away from the computer to deal with physical cards, is to instead use the simulation of card sorting which we provide as a Java applet (your web browser must support Java 1.1). Our preference is for the real cards, but the "virtual manipulative" is better than nothing.

For more information, see the parent web page, or contact Max Hailperin:
Email: max@gustavus.edu
Mathematics and Computer Science Department