A beautiful honeybee named Lisa smiled at her adopted baby brother as he slept in his crib. After her father flew into the room, she asked him, “Why don’t boy bees have fathers?” He responded, “That’s just how nature made us.

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Male bees only have a mother while females have a mother and a father.” “Don’t you wish you had a father?” “No, he replied, your grandmother was wonderful; she made me very happy.” In fact, “This discussion gives me an idea for a cool, new puzzle. To solve the puzzle, you must draw a picture that shows how many grandparents your mother and I have over three generations.

You need to draw a family tree for me and one for your mother. You’ll draw an “M” for me and an “F” for your mother. Then draw a line to connect us to our parents (or parent for me) and then draw a line from each parent to their parents (our grandparents). In each generation, you will use an “M” for grandfathers and an “F” for grandmothers. Okay, try it now. When you finish, I’m going to bring home a big bowl of honey for you and your new baby brother.” “Hmmm, yummy, I can’t wait!” she said.

Now I’m going to show you a secret order of numbers that – like magic – automatically let you know how many grand-parents are in each generation.

The numbers (called Fibonacci numbers) are: 1, 1, 2, 3, 5, 8, 13.... The pattern for male bees starts with the first “1” because they only have one parent, a female, and she’s the second “1.” For females, the pattern starts with the second “1” because they have two parents who represent the “2.” Here’s how Fibonacci numbers enable you to play a trick on your friends. Show them the drawing you just did. Then ask them to help you draw two more generations. Then you ask them to play the Bee Guessing Game. Each person has to guess how many bee grandparents are in the fourth and fifth generations in two seconds per guess. You tell everyone that it’s against the rules to count each “M” and “F.” The winner gets to keep the family tree drawing. Everyone, except you, will probably guess the wrong numbers.

You “guess” there are 21 grandparents in the fourth generation and 34 grandparents in the fifth generation. You are correct because you wrote the Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34. . . .) on a small piece of paper that you taped to the side of your table.

There are 13 members in the third generation so you know the fourth generation has 13 bees and the fifth generation has 34 bees. The Fibonacci Sequence works for every male bee and every female bee. Males start with the first “1” because they only have one parent (the second (“1”)). Females have two parents (“2”) so they start with the second “1.”    

There are 13 members in Lisa’s mother’s fourth generation and 8 members in the same generation for Lisa’s father. This is true because the Fibonacci Rule says each number is the sum of the two previous numbers. Therefore, you know 8 follows 5 because 3 plus 5 equals 8 and 13 follows 8 because 5 plus 8 equals 13. How cool is that!!

1, 1, 2, 3, 5, 8, 13, 21, 34 . . . 

Excellent job!! You drew two perfect bee family trees!! Now, how many grandparents are in the first generation? Yes! 5! The second? Perfect! 8! The third? Correct! 13! Great job!! 

Amazing Math Secrets
One Cool Bee Family Puzzle

Taken from 2016 book "Princess Sasha Rescues a Frog: Fun Algebra"     Para la versión Española, haga clic aquí.