Back in the late 90's, in the early days of the internet, Looney Labs ran a bunch of email discussion lists for various topics, including a list of 100+ fabulous teachers, therapists, and parents who occasionally discussed the educational merits of Looney Labs games.
Am trying to mine these archives for math games ideas (esp. for pyramids)...any ideas?
Laurie, thanks for your reply! Mathematics 7-12 grade. I'm interested in any and all topic-specific use of the pyramids, basic algebra through calc. Number of players can vary (1-4 is probably best), as can performance level and time available. As for number of stashes and their colors, I'd like to keep it low since any initial use in-class will probably use pyramids I ponied up the cash for and will be during students' "preferred activity time"; eventually, though, I'd like to justify school spending or write a grant for a "class set" of two rainbow stashes per student.
I think it might be a good idea to think about games that can be played with IceDice game components...plenty of pyramids plus the dice for $20.
Hi David! I am not aware of many pyramid games that specifically teach algebra through calculus, but every single pyramid game definitely teaches or requires visual-spatial skills and/or strategy/logic. There is one game I know of that requires measurement, which is Armada. And Treehouse teaches about transformations, and has related lesson plans and standards correlations. I also highly recommend Zendo, though it best teaches the scientific method rather than math concepts. That's not to say there aren't any more games that specifically teach math concepts, it's just to say that I don't know of any. But you will find nearly every game invented for the pyramids here, broken down by number of players, number of stashes, time required, etc. Very cool site! :o) So that's where I would start if you wanted to teach pyramid games to kids as a way of building general logic and thinking skills. If you need to prove to anyone that this is a worthwhile pursuit, here is a list of how gaming relates to math concepts, and here is one company's justification for using games to teach anything.
One homeschool parent who had a monthly K-12 pyramid games get-together introduced the following games to the students: Ice Castles, Black Ice, Thin Ice, Volcano, Martian Match Up, Martian Chess, Martian Backgammon, and Rambots. I don't know whether this is actually a good educational bunch of games or not, as I've only played a couple of these, but it worked for her group.
Regarding eventually buying more pyramids, I highly recommend that. The actual Looney Labs pyramids are wonderful to work with and well worth the cost. In the mean time, there are three other options. First, you can make your own out of wood, Sculpy clay, or any number of other materials. If you wish to do this, here are the standard dimensions of the pieces. Second, you can make paper versions of the pyramids. There are quite a few options to choose from as follows:
2D version is difficult to work with, but nice for when you need to conserve space
Print, cut, and glue version on Board Game Geek with many different designs (I am also uploading a file of it in case you don't have a Board Game Geek account--it's BGG 1.)
Print, cut, and glue version on Board Game Geek that fits on one page per stash (attached file is BGG 2).
Origami version on Board Game Geek (attached file is BGG 3).
Origami version that is not stackable/nestable.
Complicated origami version that is stackable/nestable.
Most truly authentic origami instructions (not pre-printed).
Note that there's a lot of math here to be taught during the making of the pyramids, particularly geometry. Rather than giving them the "official" measurements, you could have the students measure a set of actual pyramids themselves. This could morph into lessons about accuracy of measurement and significant figures. You could also challenge your students to figure out how to make a giant pyramid set out of cardboard. They would need to determine the height (and exactly how they want to measure that), width, and thickness of each piece so that they nest and stack well. This is not an easy task, as is evidenced by a very lengthy discussion that was had on the Icehouse mailing list. There are other months that also had discussion, but March 2007 is a good place to start. Not only are geometry concepts included in the discussion, but also precalculus concepts such as trigonometry, logs, and exponential growth. I encourage you to read all of the posts to this mailing list, as they are wonderful reading!
Another discussion that could arise during the making of the pyramids is that geometry calls these particular pyramids "square pyramids." The students could discover why that is, figure out how to make other pyramids with different bases, and discuss whether these pyramids would work just as well for gaming, or not, and why. You could also bring in other 3D shapes such as all the prisms, plus cylinders and half-spheres or combinations thereof as possible shapes for gaming.
The third option for playing pyramid games without buying pyramids is to play online at Super Duper Games. This site has been mostly abandoned by the site administrator, but still works well and has a great bunch of people to play with. It is a play-by-email format, even though it's web based. In other words, rather than playing in "real time," most games are played over days or weeks as the players have time. This could be particularly useful in a classroom setting with not much available computer time. SDG offers the following pyramid games (as well as many other great strategy games): Alien City, Blam!, Branches Twigs and Thorns, Homeworlds, Martian Chess, Penguin Soccer, Pikemen, Sprawl, Subdivision, Volcano, and Zendo. An added bonus that is very appropriate for your math students is the Number Zendo variant. This variant uses the standard Zendo rules of play, but the koans are numbers, rather than pyramids, and the way to enlightenment usually involves quite a bit of math. Your students could play new games, but would also greatly benefit from examining the archives of already completed games and attempting to guess the rule with the given information. This could even be a solitary desk activity to be printed out and mulled over.
The final way that the pyramids may be used to teach math concepts is by using them as a scoring system. They can be used in a very simple, straightforward manner to score Treehouse. But each size can also be designated to be a certain value in order to scores games such as Cosmic Wimpout and Hearts... though really any game requiring scoring would work. The mathematical value is in the mental math done to count the pieces and make change as needed. For example, if the small pyramids count as 1, the mediums as 5, and the larges as 10 (like U.S. paper money denominations), then how do you record a score of 8? And what is the score if a person has 2 larges and 3 smalls? Each time you change what the pyramids stand for, the counting and change making process starts again. You could even have students figure out for themselves what the best designations are for the three sizes, based on the scores that are typical for a particular game.
This score keeping practice can eventually lead into a discussion of bases, such as decimal (our common base 10), binary (base 2), hexadecimal (base 16), and others. In this case, you might have a scoring board to help them conceptualize. For example, in binary, there would only be 1 space in each place value position, whereas in decimal, there would be 9 in each (units, tens, and hundreds). Smalls can represent units, mediums the next place value to the left, and larges the next. You might also compare this system to a standard Base 10 Block set. Students will note that units are measured in small cubes, tens in sticks ten cubes long, and hundreds in squares ten units by ten units. Thousands begin repeating, by creating a larger version of the unit cube. This is true in any base. It is only the size of the cubes, sticks, and squares that changes. This discovery may lead to spontaneous discovery on the students' part of how to more quickly and easily convert counting pyramids from any base into base 10. For example, in base 6, the units will still be units (6^0), the next place value over will be sticks six units long (6^1), and the third place value over will be squares that are six by six (6^2). So a large, 2 mediums, and 3 smalls, for example (123 in base 6), would be 36 + 6 + 6 + 3 = 51 in base 10.
I hope this gives you some good ideas for your classes. Let me know if you need anything else!
Apologies for the belated response! This reply of yours has proved to be AWESOME. Thanks for taking so much time and writing out such great options! I *love* that you hit upon using them as counters in a non-base-10 system, which was something I had been thinking about, too, and it's something that might be useful for history of math (which I'm trying to incorporate).
Re: scoring systems. I've put together a game similar to martian poker and battlestar galactica's "pyramid" game that uses interesting arithmetic scoring rules ("build the highest-scoring hand" type game). I've looked (but have yet to find) a game of numbers similar to rithmomachia, and would love to hear about one or collaborate on building one.
I'm glad you found my post useful! Best of luck in your endeavors. :o)
Your game ideas sound interesting. I had never heard of rithmomachia before... thanks for the information! As for other "games of numbers" similar to this, I'm not sure exactly what you mean. There are quite a few games that require basic math, such as Equate and Flip 4. But I think you're probably looking for something more specific?
If you'd like feedback regarding your games, feel free to email me at firstname.lastname@example.org. As for collaborators, how about your students? Kids love to design games, and they'll do a lot of math along the way! :o)
Take care and happy teaching!