A Fibonacci Number Trick

Summer is definitely getting the best of me. I’ve been distracted by the usual summer pastimes like surfing and bungee jumping - only on TV, of course. Mowing grass is more my speed… I can’t believe how fast grass actually grows. This current east coast hot spell should slow it down a bit so I can have more time for watching the surfing channel.

One of the things I said I would do is to share with you some neat activities that Mr. Jacobs has "hidden" in his treasure trove Teacher’s Guide (Editions 1 and 2) and Instructor’s Guide (Edition 3). The following activity made the cut for all three editions and was one of my favorite activities to do with my students back when I was earning an honest living.

It's a number trick based on the Fibonacci sequence that Harold uses as his opener to Chapter 2, lesson 6. Below you will find his write up of it taken from Edition 1.

Here's my summary of the activity:
Tell your students that you have a special talent for adding lists of numbers in your head. To show your talent ask them to:
1. Number a piece of paper column-wise from 1 to 10.
2. Write a 2 digit number next to number 1.
3. Write a different 2 digit number next to number 2.
4. Add the two 2 digit numbers and write your answer next to 3.
5. Add the numbers next to 2 and 3 and write the sum next to 4.
6. Continue adding the previous 2 numbers and write down the answer on the next line until you have a number next to each of the numbers 1 to 10.
Your list should look something like this:
7. Add up the 10 numbers you wrote.
8. Hide the answer so that no one else can see it.

At this point you announce that you already know what the sum is. All you need to know is the 7th number on the list which you can easily see if you look at the student's paper before they finish their list. In the example above the 7th number is 387. Simply multiply this number by 11. (There is a shortcut way to multiply by 11.)

Have the students try 2 other numbers to see if the trick still works.

Click here to play this video of me showing how a Google Docs spreadsheet can be used to demonstrate the trick.

Can you explain why this trick works? (Hint: a little algebra can be of help here. For a further hint read Jacob's description of the activity below.
Google Docs is available at this site.

Chap. 2, Lesson 6 – The Fibonacci Sequence

(Click above for larger image.)

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