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.

________________________________________________________

Publishers Weekly Sneak Preview for 2015!

Exciting news from Publishers Weekly!

ARBORDALE

Arbordale pricks up its ears for Sounds of the Savanna by Terry Catasús Jennings, showcasing a habitat alive with noise; Achoo!: Why Pollen Counts by Shennen Bersani, featuring an allergic baby bear; Fibonacci Zoo by Tom Robinson, illus. by Christina Wald, in which a boy discovers a pattern at an unusual zoo; Wandering Wooly by Andrea Gabriel, focusing on how Little Wooly uses her senses to find her way back to her family; and Tornado Tamer by Terri Fields, illus. by Laura Jacques, an adaptation of The Emperor’s New Clothes in which a weasel promises to build a special cover to protect the town from tornadoes.

Here's the full link to the preview:  Publisher's Weekly 2015 Sneak Preview

Common Core State Standards

I'm not suggesting that kindergartners and their parents will pick up this book with the sole intent of using it to meet the new national math standards known as the Common Core State Standards (CCSS). However, Arbordale Publishing and I both agree on an important philosophy - that learning math and science is not only possible through reading, but is actually enhanced through reading. And so, during those critical primary school years (grades K-3 or so) while children are making such great strides in both their reading fluency and comprehension, we believe this is a unique opportunity to encourage them to develop their math literacy (sometimes called 'numeracy').

This is where Fibonacci Zoo comes in. This book takes its readers on an adventure through a most unusual zoo. Children will meet, in order, an alligator, a bison, camels, dolphins, elephants, flamingos, gorillas, hippos, and iguanas. Many will notice that these animals arrive in alphabetical order so even the youngest children can begin to practice their ABCs, even while they grow their reading skills. But Fibonacci Zoo continues as children meet the Fibonacci sequence, and learn to count, explore number patterns, make predictions, and then see their predictions tested. These 'inductive reasoning' skills will become powerful tools for these children as they grow into pre-adolescents and adolescents and begin their formal mathematics careers in earnest.

And so, in the spirit of celebrating Fibonacci Zoo as "more than just a picture book," I have identified some of the CCSS math standards for grades K-4 that this book may address. Please understand that by no means am I suggesting that the book on its own is sufficient to meet all of these standards completely. In fact, my hope is that parents, teachers, math coaches, administrators, librarians, and indeed children themselves use it as a tool for enrichment, for exploration, and for extension of the basic skills they are already learning. Over the next several posts, I will be sharing lesson ideas (around ten when we get done) for teachers and parents to use at their leisure to develop the skills necessary for success in mathematics for their children. In time, I envision this book becoming a critical component of elementary school mathematics instruction from Alaska to Florida, from Maine to Hawaii.

Thanks for coming on this journey with me. It promises to be quite a ride!

Common Core State Standards - Math - Grades K-4

CCSS - Kindergarten

CCSS.MATH.CONTENT.K.CC.A.2

Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

CCSS.MATH.CONTENT.K.CC.B.4.A
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

CCSS.MATH.CONTENT.K.CC.B.5
Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

CCSS - First Grade

CCSS.MATH.CONTENT.1.NBT.C.4

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

CCSS.MATH.CONTENT.1.NBT.B.2.A
10 can be thought of as a bundle of ten ones — called a "ten."

CCSS.MATH.CONTENT.1.NBT.B.2.B
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

CCSS.MATH.CONTENT.1.NBT.B.2.C
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

CCSS.MATH.CONTENT.1.OA.A.1
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.¹

CCSS.MATH.CONTENT.1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

CCSS.MATH.CONTENT.1.OA.D.7
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

CCSS - Second Grade

CCSS.MATH.CONTENT.2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

CCSS.MATH.CONTENT.2.NBT.B.9
Explain why addition and subtraction strategies work, using place value and the properties of operations.¹

CCSS.MATH.CONTENT.2.OA.A.1
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.¹

CCSS.MATH.CONTENT.2.OA.B.2
Fluently add and subtract within 20 using mental strategies.² By end of Grade 2, know from memory all sums of two one-digit numbers.

CCSS - Third Grade

 CCSS.MATH.CONTENT.3.OA.D.9

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

CCSS - FourthGrade

CCSS.MATH.CONTENT.4.OA.C.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

CCSS.MATH.CONTENT.4.NF.C.6
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

CCSS.MATH.CONTENT.4.NF.C.7
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.