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Friday, July 25, 2014

Publishers Weekly Sneak Preview for 2015!

Exciting news from Publishers Weekly!

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

Tuesday, July 15, 2014

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

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

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.

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
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.

10 can be thought of as a bundle of ten ones — called a "ten."

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

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).

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

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).

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.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Explain why addition and subtraction strategies work, using place value and the properties of operations.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

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.

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.

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.

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.

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.

Sunday, July 6, 2014

The Parthenon

Though I've never been to Greece, I definitely would like to visit sometime. And for all the white sandy beaches, the exquisite food offerings, and the culture that oozes out of every pore in that country, one of the top sites on my list of things to see is the Parthenon, pictured here.

The Parthenon - photo credit: Wikimedia Commons
To most eyes (mine included, if truth be told) this building represents little more than an ancient ruin, an artifact from an era long gone, and generally, a really cool building to see, even more remarkable that it's still standing.

But from a mathematician's standpoint, some say the Parthenon is one of the great wonders of the world as it represents one of the earliest examples of builders and architects understanding dimension, perspective, and ratio. Many believe the Parthenon was built according to the Golden Ratio, or phi.

The Parthenon is considered to have been a most significant temple for the ancient Greeks, build on the hill called the Acropolis. It was a symbol of military victory, and was built to honor the city's (Athens) patron deity, Athena. It was an architectural wonder, mixing Dorian and Ionic columns, and it was decorated by sculptures, the likes of which had not been seen before.

To us, however, something even bigger lie in this building. It was built between 447 B.C. and 432 B.C. So it took fifteen years to build - not that unusual for the time. However, you may note that this period of time is around 1600-1700 years BEFORE Leonardo Pisano wrote his book about rabbits and the Fibonacci Sequence.

You see, the original dimensions (lost to us through the centuries) appear to follow a very similar pattern, as you can see in the image below. By isolating square and rectangular regions of the facade of the Parthenon, you can begin to see a Fibonacci spiral grow.
The Parthenon displays the Fibonacci spiral.
Photo credit:
Scholars have debated this, and whether it was built using the Golden Ratio or not may never truly be known. But one look at the spiral and you can see that there was something special about this building.

Taking it one step further, let's look at some relative measurements of the building. Here you can see that familiar 1.618 to 1 ratio value yet again. Remember, part of the building is no longer standing, so some of this may simply be speculation. But still, the Parthenon stands as a) one of the great architectural designs of the ancient times, and b) quite possibly the oldest-standing example of the Fibonacci sequence and Golden Ratio in the world.
Photo Credit:

Now, my question to you is this: can you find other structures, either from the ancient world, or still standing today, that reflect similar dimensions? We explored this with rectangles, but are there buildings today that just seem to 'look right'? If you find one, drop me a note and let me know about it.

Note: This will likely be the final installment looking at applications and consequences of the Fibonacci sequence. From now on, be looking for quick, simple lesson plans you can use either in your classroom or even at home with your own children to explore Fibonacci. In keeping with the spirit of my upcoming book, these lesson ideas will probably differ from much of what you find online, as those lessons tend to be geared toward middle or high school students. I would like these lessons to be applicable to elementary-aged students, and if possible even the primary grades. Obviously, such lessons will rely heavily on parent or teacher support and guidance, but could easily be used in conjunction with the book itself, allowing students to read it multiple times, each time discovering a new activity that connects their reading to their learning.