Lesson #3 - Find a Flower

Sorry for the delay. I was working in Italy this past month, and was fortunate enough to spend time in Fibonacci's home town (Pisa). In fact, here is a photo of me at the top of the Leaning Tower with my friends, Chris, Bern, and Mike, the coaching staff of the University of Pennsylvania women's basketball team.

Standing on top of the Leaning Tower of Pisa, home of Leonardo Pisano,
better known as Fibonacci (that is, Pisa was his home, not the tower!)
That's me on the left! August 2014

Lesson #3 - Find a Flower

Objective: Students will locate and pick flowers with petals that represent one of the Fibonacci numbers.

Task: Look around your house, your school, or your local community for flowers with petals. Make sure you are allowed to pick the flowers. If you are not sure, just take a picture of it. If you are completing this task at at time of year in which there are no flowers blooming, look for plants or trees with leaves if possible.

Count the petals and try to find one example of each of the first few Fibonacci numbers:

1, 1, 2, 3, 5, 8, 13...

After you have selected your flowers, present them to your teacher. Finally, rate yourself using the scale below:

1 flower: Way to go - you found one!
2 flowers: Excellent! Keep your eyes open for more Fibonacci numbers around you.
3 flowers: Outstanding! Fibonacci would be proud of you!
4 or more flowers: Incredible! You might be the next Fibonacci!

 

Lesson #2 - The Fibonacci Breakfast

Lesson Objective: Students will use the Fibonacci Sequence to determine how many pieces of cereal are

Photo credit: Wikipedia

necessary to produce a satisfying bowl of breakfast cereal.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Task #1:
Use a cereal with individual pieces that are easily counted.
Good examples include choices such as Cheerios, Trix, Cocoa Puffs, Kix, Lucky Charms.
Bad examples include choices such as oatmeal, granola, Rice Krispies.

Your task is to determine, by adding pieces of cereal in increasing order of the Fibonacci Sequence, which number finally makes what you would consider to be a full bowl of cereal.

Procedure:
1. Place ONE  piece of cereal into your bowl.

• Is this enough cereal to make a full bowl?

2. Next, place ONE more piece of cereal into your bowl (making a total of two pieces).

• Is THIS enough cereal to make a full bowl?

3. This time, place TWO more pieces of cereal into your bowl (making a total of four pieces).

• Is THIS enough cereal to make a full bowl?

4. Continue this process, each time adding the next Fibonacci number in the sequence until your bowl is filled to an acceptable level. How many numbers did it take? Was it more or less than you predicted before you began?

Task #2:
In this task your job will be to predict which exact Fibonacci number will represent the correct number of pieces of cereal necessary to make a full bowl.

For example, are 55 pieces enough? What about 89? Something more than that? This task differs from Task #1 because your answer to Task #1 will not likely be an actual Fibonacci number. For this task, you are predicting, using only the numbers in the sequence, how many pieces are necessary to fill a bowl.

Make a prediction, then count that many pieces into your bowl. If you happen to be incorrect, just change your prediction and keep trying!

Extension activity: Try changing cereal. How does changing the cereal type and/or size affect your answer to this task?

Cover Art Sneak Preview!

I am so very pleased to announce that the cover art for Fibonacci Zoo is here! Check it out and look for my book on the shelf of your favorite bookstore (or in cyberspace) in February 2015.

Lesson #1 - Solutions

Lesson #1 - Solutions

Part I:
a) Pattern: add 2; Next two terms: 11, 13
b) Pattern: add 3; Next two terms: 17, 20
c) Pattern: add 5; Next two terms: 34, 39
d) Pattern: add 10; Next two terms: 60, 70
Bonus: Pattern: add 2.5; Next two terms 15.5, 18
Wrap-up: Each sequence involves ADDING the same value each time.

Part II:
a) Pattern: subtract 5; Next two terms: 5, 0
b) Pattern: subtract 4; Next two terms: 5, 1
c) Pattern: subtract -6; Next two terms: -10, -16
d) Pattern: subtract 2; Next two terms: -7, -9
Bonus: Pattern: subtract 1.5; Next two terms: 1.5, 0
Wrap-up: Each sequence involves SUBTRACTING the same value each time.

Part III:
a) Pattern: multiply by 2; Next two terms: 64, 128
b) Pattern: multiply by 3: Next two terms: 324, 972
c) Pattern: multiply by 1/2 (also, divide by 2, but for consistency, we'll stay with multiplication); Next two terms: 2.5, 1.25
d) Pattern: multiply by 5; Next two terms: 625, 3125
Bonus: Pattern: multiply by 1.5; Next two terms: 50.625, 75.9375
Wrap-up: Each sequence involves MULTIPLYING each term by the same value each time. (Note that on Question C, dividing by 2 is the equivalent of multiplying by 1/2.)

Part IV: At the conclusion of these exercises, it may be a good time to introduce children to the Fibonacci Sequence, which is given at the end of the solutions. See if they can identify the sequence as similar to those given in this section.
a) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 23, 37
b) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 45, 73
c) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 142, 230
d) Pattern: add up any two consecutive numbers to find the next number; Next two terms: 16, 26
Bonus: Pattern: add up any three consecutive numbers to find the next number; Next two terms: 68, 125
Wrap-up: Each sequence is defined by adding up previous numbers to find the next number.

Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, ....

Lesson #1 - Number Patterns

Learning Objective: Students will identify number patterns and use conjectures

 to predict the next terms in the pattern

Part 1

Describe (in words) the pattern in each sequence of numbers and use that pattern to fill in the next two numbers in the sequence.

a. 1, 3, 5, 7, 9, __, __

Pattern ______________________

Next two numbers ____, _____

b. 2, 5, 8, 11, 14, __, __

Pattern ______________________

Next two numbers ____, _____

c. 4, 9, 14, 19, 24, 29, __, __

Pattern ______________________

Next two numbers ____, _____

d. 10, 20, 30, 40, 50, __, __

Pattern ______________________

Next two numbers ____, ____

Bonus: 3, 5.5, 8, 10.5, 13, __, __

Pattern ______________________

Next two numbers ____, _____

Wrap up: What do all of these number sequences have in common?

________________________________________________________

Enrichment: Make up your own number sequence that follows the same kind of rule you identified in this section.

________________________________________________________

Part II

Describe (in words) the pattern in each sequence of numbers and use that pattern to fill in the next two numbers in the sequence.

a.  25, 20, 15, 10, ___, ____

Pattern ______________________

Next two numbers ____, _____

b.  25, 21, 17, 13, 9, __, __

Pattern ______________________

Next two numbers ____, _____

c.   14, 8, 2, -4, __, __

Pattern ______________________

Next two numbers ____, _____

d.  1, -1, -3, -5, __, __

Pattern ______________________

Next two numbers ____, _____

Bonus:   9, 7.5, 6, 4.5, 3, __, ___

Pattern ______________________

Next two numbers ____, _____

Wrap up: What do all of these number sequences have in common?

________________________________________________________

Enrichment: Make up your own number sequence that follows the same kind of rule you identified in this section.

________________________________________________________

Part III

Describe (in words) the pattern in each sequence of numbers and use that pattern to fill in the next two numbers in the sequence.

a.   2, 4, 8, 16, 32, __, __

Pattern ______________________

Next two numbers ____, _____

b. 4, 12, 36, 108, __, __

Pattern ______________________

Next two numbers ____, _____

c. 40, 20, 10, 5, __, __

Pattern ______________________

Next two numbers ____, _____

d.  1, 5, 25, 125, __, __

Pattern ______________________

Next two numbers ____, _____

Bonus: 10, 15, 22.5, 33.75, __, __

Pattern ______________________

Next two numbers ____, _____

Wrap up: What do all of these number sequences have in common?

_______________________________________________________

Enrichment: Make up your own number sequence that follows the same kind of rule you identified in this section.

________________________________________________________

Part IV

Describe (in words) the pattern in each sequence of numbers and use that pattern to fill in the next two numbers in the sequence.

a.  1, 4, 5, 9, 14, __, __

b.  5, 6, 11, 17, 28, __, __

c. 14, 20, 34, 54, 88, __, __

d. 0, 2, 2, 4, 6, 10, __, __

Bonus:  1, 2, 3, 6, 11, 20, 37, __, __

Wrap up: What do all of these number sequences have in common?

_______________________________________________________

Enrichment: Make up your own number sequence that follows the same kind of rule you identified in this section.

________________________________________________________