Years ago, before my husband, kids, or grey hair, I taught first grade at an all-girls school. A fellow first grade teacher had a fun math game that she played with her students. I had never seen kids react like this to a math game. They would beg to play. It made a great time filler if there were a few minutes left at the end of the day. I was always amazed to watch the gears turning in the girls’ heads as they played the game. I loved the math game so much, I later went on the play it with a preschool and kindergarten class. When my kids got to be old enough, I introduced it to them as well and now they often beg to play. The game is called “Bagel, Pico, Fermi“. Now, you might be wondering “What is Bagel Pico Fermi and how do I play?” Read on…
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Bagel Pico Fermi is a math game where one person writes down a 3 or 4 digit number and the guessers try and figure it out based on process of elimination and strategy. If you have ever played the board game Mastermind, it is similar to that. This game can be played with pencil and paper or a white board and dry erase markers. We prefer to play it with a small whiteboard and dry erase markers since it saves paper.
There are a few variations on the game that will adjust its difficulty. I will share three of the them. The first variation is the easiest, most basic way to play and works well with new players or young children. I have played this version with kids as young as four, but my second graders love it as well. In this variation, a child thinks up a three digit number (with no repeating numerals) and writes it down on a piece of paper. They hide this paper from the other guessers though the person who is writing on the board can see it. With younger children, it is helpful to have an adult be the writer. As older kids get more experienced with the game and its rules, they can take over the duties of writer.
The guessers take turns guessing a 3 digit number. The first guess is usually a shot in the dark. The writer writes down the first guess and then writes a 3 letter code next to it. A Bagel (B) means the number is not correct — not in the answer at all. A Pico (P) means the number is correct, but it is in the wrong spot. A Fermi (F) means the number is correct and it is in the correct location. In this variation, each letter refers to its corresponding number — the first letter reflects the correctness of the first number, and so on.
The easiest way to explain the game is to show you. In the above example, my daughter selected the number 987. The first guesser guessed 123. That number was written down along with the letters BBB next to it since none of the digits were in the number.
The next guess was 456 and as you can see that got BBB also since none of those digits appeared in the number. The guessers then knew that the numbers had to be 7, 8, and 9, and shockingly, the next guess was 987! Using the information they had gleaned from the two previous guesses, my kids were able to figure out the number on the third guess. Trust me, this is pretty rare.
Once you have mastered the three digit number, you can move on to four digit non-repeating numbers.
The process is very similar, but it is more challenging since there are now more digits that need to be guessed and put into the correct order.
As you can see, this took a lot more guesses to figure out. When it was my five year old’s turn to guess, she was a little confused by what numbers hadn’t been guessed yet so we wrote all the possible choices on the bottom and crossed out the ones that had been eliminated.
She was very proud of herself when she finally figured it out.
Another, even trickier variation of the Bagel Pico Fermi math game is for the writer to write the letters in random order. Rather than having each letter refer to its corresponding number, they’re in no particular order. So if the writer writes “Fermi Pico Pico”, this doesn’t mean that the first digit is necessarily correct. (This is the same approach used in Mastermind.) Oh, and for a real challenge (for older kids and adults), allow duplicates as well.
This is a fun game to play on long car rides and really sharpens reasoning and deductive skills. Try it and tell me what you think!
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