Bagels, Pico, Fermi - Mastermind with Digits

There's a great logic game that's like Mastermind with numbers. You guess a three digit number and you get clues as to whether you got any of the digits correct and whether you got them in the correct place. When you make guesses, you get a clue. The clues are:

• Bagels means a digit you guessed is not in the number,
  
• Pico means a digit is correct but in the wrong position
  
• Fermi means a digit is correct in the correct position

For instance suppose you guess is 457 and get the clue Fermi Bagels Bagels. It means one digit is in the correct place and two are not in the number at all. But you don't know which digit the clues apply to.

You can play it on paper or a blackboard with kids. Here are the instructions.

Or you can play it online. There are no instructions on this page and you enter your guesses via pull downs, but it works fine. (When it gives you the clues it just lists the Fermis first, then the Picos, then the Bagels - it doesn't give a clue as to which digit each refers to.)

And a tidbit on the name from the instruction page. I always find these connections interesting.

"We don't know the official origin of the name of this game. Bagels are shaped like zeros and indicate that there are no correct digits. Pico (peek-oh), from the Spanish meaning 'beak' or 'peak,' is used in science as a prefix meaning one-trillionth. For example, 1 picometer = 10-12 meter. who later moved to the United States. Enrico Fermi (fair-mee), 1901-1954, was an Italian-born atomic physicist. He won the Nobel Prize in 1938."

Concrete or Abstract Manipulatives

I was talking about "virtual manipulatives" with teachers from Willow Creek Academy and some of them brought up the fact that younger students really need the concrete experience with real objects. I certainly agree since there's nothing like "hands on" experiences. But the digital versions of traditional manipulatives, like these online pattern blocks, are still great for those who are moving from concrete to abstract, and for children who might like to play online at home with parents when the real thing isn't available. It's also the case that online you can change the color of the blocks, you can have as many blocks as you like - no shortage, and you don't have to worry about bumping your pattern and messing it up. Plus students can grab a screen, put the design in a word processor and write about it, which is a wonderful way to get students to articulate ideas about patterns and other mathematical relationships.

For those who want the real thing you can find nice wooden pattern blocks online, or even Giant foam pattern blocks for the floor from Learning Resources

Tangrams - Geometric Brain Sharpener

I just love Tangrams. I'm not that great at doing them but I love to watch my mind think as I work out a solution. The shape of "the sitting man" for instance seems easy because you know right off where two of the pieces go just by looking at the shape. So there are only 5 other pieces to place. But as you do it you discover that getting those large triangles in place can be tricky, and if you listen to your mind thinking about the options you'll find it's fascinating to see your strategies of looking at the areas of pieces, and lengths of sides, and ways that pieces could fit together to fill a certain space. And for kids - if we can get them to be aware of their thinking I believe there will be a great deal of transfer to all kinds of problems related to area, distance, angles, triangles and more. Play with it and see what you think. Try Interactive Tangrams