## Monday, October 3, 2016

### Book Club Week 10 {Math and Magic in Wonderland}

This week, we're reading Chapter 10 of the math adventure novel Math and Magic in Wonderland.  Join us as we explore square numbers, primes, the Fibonacci sequence in nature, acrostic poetry, time dilation, and more!

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Remember to share the fun your family is having with the book club.  Leave a comment at the end of this blog post and share on social media.
Add the odds to get a square,
Maybe primes are not so rare,
One-one-two-three heeds nature's call
Reveal the thing that conquers all.

The Bandersnatch's riddle holds so many fun math concepts!  Let's dive right in...

Square Numbers

A neat math "trick" is to add consecutive off numbers (starting with 1) to get square numbers.

Your Turn to Play:
• In Week 2 of the book club, we used Gauss's formula to add consecutive integers.  Can you modify his formula to add consecutive ODD numbers?  Try adding the odd numbers from 1 to 99 and use a calculator to verify that this number is a square.

Prime Numbers

A prime numbers is an integers greater than one whose only positive divisors are one and itself.  The book encourages visualizing this by using small objects and trying to put them in rows and columns to form a rectangle.  If a number can fit in a rectangle that has more than one row, it is not prime.

One method of finding some primes without testing every number is to use a technique called the Sieve of Eratosthenes.  The concept is that once you've found a prime number, you know that all its multiples will not be prime, so you can eliminate them as prime candidates.  The Sieve of Eratosthenes helps you narrow down your options when examining a smaller set of numbers (like the ones from 1 to 100).  In this video, E and I attempt to demonstrate this method.  I'm pretty sure that E doesn't completely understand what constitutes a prime (not an easy concept for a 7-year-old).  I'll keep pointing out prime numbers as we run into them.  That's the great thing about teaching advanced math concepts to younger children - it plants a seed in their brains and then when they run into the concept again, not only will it "click", but they will be able to find connections between the topic and the world around them.

Prime numbers are not just something mathematicians play with for fun in their spare time (although some do).  All numbers are multiples of primes.  For example 70 can be written as 2 x 5 x 7.  Finding the primes that "make up" a number is called prime factorization.  With very large numbers, this process is quite time-consuming, even for a computer!  That's why primes are the basis for Public Key Cryptography.  This video explains how it works:

Your Turn to Play:
• Use the Sieve of Eratosthenes and math-manipulatives to find the prime numbers from 1 to 100.
• Play the Prime Climb Board Game, which has a unique game-board visually illustrating the prime factors of each number up to 100 using colors.

Fibonacci Sequence

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...  can you find the pattern?  Here's a video explaining the Fibonacci sequence:

My kids had a great time looking for Fibonacci patterns in nature:

Counting flower petals.

Counting spirals in a pine-cone.

Finding Fibonacci spirals and the golden ratio in nature.

We also repeated some of the activities that I did with the twins four years ago (at age 3!):

Kids are never too young to play with math!  Read my post on Fibonacci Sequence for Preschoolers.

Your Turn to Play:
There are some really fun books for children about Fibonacci and his sequence:

Relativity and Time Dilation

In Chapter 10, we learned that time on Earth and time in Wonderland pass at different rates.  The book is fictional, of course, but if you like following rabbit trails, you might want to learn a bit about Einstein's Theory of Relativity and how time passes differently on a clock that's traveling on a satellite compared to a clock staying on Earth:

Acrostic Poems

SPOILER ALERT: If you haven't finished Chapter 10, skip to the next section of this blog post now.

It turns out that the Bandersnatch's poem was acrostic - the first letter of each line reveals the answer.  Lewis Carroll enjoyed these types of "secret message" poems.  Carroll ends "Through the Looking Glass" with an acrostic poem spelling "Alice Pleasance Liddell", the young girl who inspired the novel, as well as "Alice in Wonderland".

Your Turn to Play:

It's time to try your hand at writing acrostic poems.  Here are some books of acrostic poems that may provide some inspiration:

Note: "Mirror, Mirror: a Book of Reverso Poems" (the one pictured in the middle) doesn't have acrostic poems, but it does include poems that work in reverse - very cool!

Literature Connection

Chapter 10 includes a joke for those who have read The Hitchhiker's Guide to the Galaxy.  I won't explain the joke in case you haven't yet read this hilarious science fiction novel (and the rest of the books in the series) and wish to do so.

If you enjoyed "Math and Magic in Wonderland", you may also like:

Upcoming Giveaway

Next week, for our Book Club Finishing Party I'll be giving away a \$50 Amazon gift card to one lucky participant.  To enter, be sure to post an Amazon review for Math and Magic in Wonderland. Stay tuned for details!

Full Book Club Schedule

Here is the Book Club / Math Circle schedule (you can join any time):

Week of August 1st:
• Book Club Kick-Off Party!
• Read Chapter 1: Mrs. Magpie's Manual
• Alliteration
• Memorizing digits of Pi
• Palindromes
• Calculating your age on other planets
• Read Chapter 2: Magic Square
• Making tangrams
• Acute, obtuse, and right angles
• Magic squares
• Adding consecutive numbers using Gauss's trick
• Read Chapter 3: Secret Codes
• Word permutations
• Cartesian coordinates
• Operations on odd and even numbers
• Read Chapter 4: Rabbit Trails
• Drawing a perfect circle
• Making a compass
• Finding the center of a circle
• Exploring Pi
• Famous mathematicians who followed rabbit trails
• Read Chapter 5: Two Worlds Join
• Mobius strips
• Fractals
• Tessellations
• Read Chapter 6: River Crossing
• River Crossing Problems
• Build a boat and explore buoyancy
• Read Chapter 7: Seven Bridges
• Seven Bridges of Königsberg problem
• The power of exponents
• Thales's method for calculating the height of an object
• Read Chapter 8: Veracity
• Truth-tellers and liars
• Finding a fake coin using a balance scale
• Archimedes buoyancy principle
• Read Chapter 9: To Catch a Thief
• John Napier's Rooster
• Doubling pennies and calculating exponents
• Towers of Hannoi
• Read Chapter 10: The Vorpal Sword
• Square numbers
• Prime numbers
• Fibonacci Sequence
• Relativity and time dilation
• Acrostic poems
• Read Chapter 11: Two Great Powers
• Book Club Finishing Party with Prizes!

Thanks for joining us.  I can't wait to read your comments!