Monday, April 6, 2009

Math Teachers at Play #4, Krypto, Updates (Odds and Evens),...

1) The latest "biweekly" edition of our new Carnival, Math Teachers at Play, is currently being hosted by Misty over at Homeschool Bytes. I enjoyed the "step by step" approach, progressing from primary math activities like Candy Math through middle school posts like Division of Fractions Conceptually to secondary articles like Ten 16th Century word problems. I contributed a post on Function Questions for the SATs. I'm not including any direct links to these articles. Go to Misty's site to enjoy this carnival!

2) I'm putting a lot of effort into the SAT Math Tips feature in the sidebar (readers of my feed won't get to see this of course unless they visit the site). I realize a good part of the country takes the ACT but the suggestions may be applicable to any standardized test and the math content is valid for anyone who wants to use it.

3) The Read More feature I recently instituted has some bugs as I'm sure you noticed. It doesn't work in RSS or Atom feeds of course and it sometimes doesn't work properly even on this site. I'm a coder at heart but I'm not sure it's worth all the effort. Clearly the Blogger developers are not interested in making things easy for us. You may see Read more... even if there is nothing else to see or it may not work all! Too late for me to migrate to Wordpress at this point... Please be patient with me here as I work through this.

4) The Math Problems of the Day in the sidebar are of good quality and are challenging but I'm seeing more repetition of questions. I will evaluate this and decide if I want to keep this feature.

5) No, I haven't forgotten about the next MathNotations contest I promised for April or May. Stay tuned...

6) Ever hear of Krypto or 24 (the game not the TV show!) or the more well-known "Four Fours Game"? I played many years ago and have always enjoyed the challenge of this tantalizing arithmetic game. I've used it effectively in upper elementary and middle school classrooms when I was a math staff developer to reinforce order of operations and basic fact recall (no calculator allowed!). Ok, so I'm now driving you crazy with another KenKen-like game!!
Click on Read more to learn more. (if this works!).

Here is a sample play of Krypto:

Suppose you're dealt the following five number cards:
5, 9, 4, 11, 1.
A 6th or objective card is turned up, say 2.
Using some or all of the four basic arithmetic operations and the 5 numbers exactly once, produce the objective number. This one is straightforward using only addition and subtraction:
11 + 5 - 9 - 4 - 1 = 2. Krypto! You've Won!

It is possible to be dealt an "impossible" hand for which there is no solution or there could be many solutions for the same hand! The original game did not allow the use of parentheses but you could choose any variation you wish, including reducing the number of cards to 4. An ordinary deck could be used modifying the face cards to be 11,12, etc.

If you want to play the online version from mphgames, go here for instructions and play. Your browser must be java-enabled but most are. For more background on the game and a discussion of the underlying combinatorial mathematics and a discussion of the computer program which generates it, look here.



Anonymous said...

That is another of my favorite math club warm-up games, though I hadn't heard it named Krypto before. We usually deal four cards, then allow the drawing of a fifth if one cannot make the target with that hand. If we have students at about the same math level (not always easy with homeschoolers), we will race---everyone going for the same target number. Fun!

Anonymous said...

I learned krypto in 1976. We made our own cards and took them home. I made new decks when I was running extracurricular enrichment classes for 7th and 8th graders a few years back, and made them make their own cards. And now I have 9th graders play. I use the possibility as motivation to work a bit faster (if we finish...) But, I learned that it is commercially available

Anyhow, I still play with the kids. Had a showdown with a junior two years ago. He was fast. A crowd gathered round...

(he had been playing immediately before, which I didn't know, and he was focused. I rapidly fell behind. But then I started to catch up, rattled him, and saved my reputation.)

Anyhow, yes, I use krypto, too.


Dave Marain said...

I like your variations and, yes, it is a fun game for a small group, competitive or noncompetitive. Did you allow parentheses which definitely has an effect on the game IMO. For example, with parentheses you may be able to group some numbers to make a value of 1 or zero which can be useful.

You might want to try the online game I linked to. It's a 'no-frills' version but it is fairly challenging and works well. The other link gives some very interesting background on the game. If your students use it, tell me how they react to it.

Krypto has been around for awhile and, in fact, there used to be international competitions!

Dave Marain said...

Our comments crossed each other in cyberspace! Anyway, remind me not to have a Krypto showdown with you - I have a feeling I'd get "hustled"!

Lynx said...

I learned Krypto from my principal in 7/8th grades while she taught us algebra. Loved it.

When I became a teacher, I bought a deck myself. I post a new one daily on the bulletin board. It's a useful "When Finished Early" activity and completing 5 of them (written as one long equation) can earn the kids a few bonus points on their homework grade. I've got a few who are really into it and are annoyed on the days I forget to update it.

I've got a fraction expansion pack that also frustrates some of them.

Dave Marain said...

Looks like many of us have a secret passion for this game!

Could you post a link for ordering the deck or the fraction expansion pack?

I like how you use the game. For some kids it could become addictive! Uh, these are the kind of kids who grow up like us!

Lynx said...

Sure, Dave. Here you go: You can also order a Primary version and school packs. These games come with score sheets for several rounds of play, similar to Yahtzee.

Anonymous said...

For my homemade version, we allow just about anything, except multi-digit numbers. It's like the year game or four 4s problem. Parentheses are definitely allowed.

Dave Marain said...

Thanks both for myself and our readers. I can make a deck myself but I miss working with the real deck. I'll check out those "lynx!"

Sounds like your students really enjoy your home-made version! I do think working with 1- or 2-digit numbers is more challenging however (that's how the online version plays). It definitely challenges my mind to work with 2-digit numbers (I have not yet seen a "deal" requiring two 2-digit numbers to be multiplied). By the way, the online version is decent but it was developed about a decade ago before Flash programming so kids may find it less attractive and harder to work with. The other more important issue is that online versions like this tend to be one-player games whereas having a deck of cards encourages group play which is far more desirable.

It occurs to me that we all miss those wonderful board and card games we grew up with. Kids still occasionally play these but not nearly as much thanks to electronic versions of almost everything. IMO, there's no substitute for being the 'banker' in Monopoly and feeling that awesome power of controlling thousands of dollars! (Not to mention how much it helps to reinforce the meaning of money and quick mental calculations).

Misty said...

Thanks for the game idea! And the nice comments about my carnival post. I tried the online krypto and it's definitely a brain stretcher. Thanks!

Dave Marain said...

Thank you, Misty!
I agree - the online game is definitely challenging. The solution displayed by the program is not always the most efficient but pressing Krypto always checks your attempt. I did find some bugs in it but, overall, it's pretty good.

In the end, having kids play with a deck of cards is probably better.

Mike said...

We play something like Krypto using cards (cheaper). Because there's such a wide skill level in our (grade 7) class everyone has their own "=" number. Easier numbers below 10, I play at around 12-15 and a couple of my smarty students are in the 20's. If you lose your number goes down by 1, if you win it goes up by 3... works really well. You don't have to use all 5 cards to make your number.

Dave Marain said...

Nice variations, Mike... Do you allow parentheses?
I like how you adapted this to different ability/skill levels.
How many minutes do you give the activity and how often is it played?

Mike said...

Parentheses allowed (though not called parentheses yet) but not putting cards together to make multi-digit numbers. 32 cards gives a 5 min game. Played not as often as I would like. Even though it's a game, it is still a math game :(

Adapting games to different abilities is the challenge of the classroom. It has to be a game that can give some success whatever entry point (like Haggle for algebra or Pit for loud time)or a game that has flexible winning conditions like modified Krypto.