## Monday, August 8, 2016

### Book Club Week 2 {Math and Magic in Wonderland}

In Chapter 2 of the math adventure novel Math and Magic in Wonderland, Lulu and Elizabeth solve two puzzles based on "ancient games of skill":  Tangrams and Magic Squares.  A squirrel (who loves to speak in puns) guides them in the right direction.  Were you able to solve the riddles along with the story, or did you go off on a tangent?  Join us for Week 2 of the book club...

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Remember to use hashtag #MathAndMagicInWonderland on social media to share the fun your family is having with the book club.

Tangrams

In the "Play Along" section of Chapter 2, you are invited to make your own set of Tangrams.  There is a Tangram puzzle to complete for each of the remaining chapters in the book, so I highly recommend that you don't skip this activity.

A recent study found that spatial training using toys like Tangrams resulted in higher scores on math tests in 6-8-year-olds.

The big challenge is to create your own Tangrams by starting out with a single "small right isosceles triangle" to use as a template for the remaining six pieces in the set.  The reason that I didn't just provide a tangram printable, is that I want readers to gain an intimate familiarity with the pieces and how they relate to each other.  The best way to accomplish this is to create them by hand.  I explain the process in this video:

Your Turn to Play:

For an alternative Tangram-making technique (using a single sheet of paper which is folded and cut), try these Tangram Construction Instructions.  It's actually pretty neat to try!

For younger children, this set of Magnetic Tangrams has large pieces and a storage case.  It's a favorite at our house.

We also enjoy using our Tangrams to build the shapes from this picture book about Tangrams.

Using Proper Math Terminology

As the girls in the book were exploring Tangrams, they argued about the proper name for one of the pieces ("diamond" vs. "parallelogram").  While Shakespeare may have argued that "a rose by any other name would smell as sweet", Elizabeth was correct that math does not work that way.  In this video, I discuss how to use specific math words to describe objects (with the help of Baby L).

Ironically, in the video, I am using a block (rectangular prism or cuboid) to talk about the correct terminology for a square.  You all know that I'm talking about one of its square faces, not the 3-dimensional object, right?

It's important for parents and teachers to model how to "speak math" correctly.  I like these tips for teachers to help students develop a fluency in math as a second language.

Your Turn to Play:

Many teachers keep a "word wall" in their classrooms to showcase new vocabulary (and proper spelling).  Create a "math word wall" in your home (on the refrigerator works great too), where you define and illustrate new math terms.  Some of the math words in this chapter include:
• parallelogram
• rhombus
• isosceles triangle
• right angle
• obtuse angle
• acute angle
• tangent line
You can put new math terms on your wall, or collect them in a binder.  This math dictionary for kids is a useful reference.

Play a game where you have to describe household items or toys (like building blocks in different geometrical shapes) using "math words".  See if you can find multiple words to describe the same object and discuss which are the most specific.

Angles

In this video, E demonstrates how to solve the angle-counting puzzle found in Chapter 2:

Your Turn to Play:

Identify right, acute, and obtuse angles around your house.

Homophones and Puns

If you don't know the definition of a "homophone", I'll give you a hint:

"homo" is a Greek prefix meaning "same"
"phon" is a Greek root that means "sound"

Did you guess the meaning of the word "homophone"?  It's a word that is pronounced the same as another word but has a different meaning.  Here's an example from Math and Magic in Wonderland:

"right" means correct
"right" is a direction, the opposite of "left"
"right" can refer to a "right angle", meaning an angle formed by two perpendicular lines
"write" is pronounced the same as "right", but means to mark on a surface

Puns are jokes centered around the meaning of words.  They sometimes make use of homophones.  The second chapter of  Math and Magic in Wonderland is full of puns!  If you take some time to play with homophones and puns, you'll have a greater appreciation for the humor in the book.

After explaining homophones to my children, they began finding as many examples as they could think of and attempted creating their own jokes based on word-play.  This is actually a really sophisticated skill, so please don't skip the wonderful opportunities to play with language just because this is labeled as a "math book"!

Your Turn to Play:
• Make your own list of homophones.  Keep this list in a special journal so you can add to it as you run into new examples.
I'd love to hear the homophones and puns you've discovered.  Leave a comment on this blog!

Lines Tangent to a Circle and Hexagrams

Before realizing that "Tans" referred to Tangrams, Elizabeth assumed that "Tans" meant "tangent lines" and tried (unsuccessfully) to draw a turtle out of seven lines that were tangent to a circle.  A line that is tangent to a circle will only touch the circle at a single point.

The closest Elizabeth came to drawing a turtle using tangent lines was to form six lines into a shape called a "hexagram".  It looked like this:

It doesn't look much like a turtle, does it?  But Elizabeth had nothing to be embarrassed about - how will we ever learn if we don't make mistakes?

Your Turn to Play!
• Trace a circle and pick a point along its perimeter.  How many lines go through this point and are tangent to the circle (they can't touch the circle at any other point)?  Make up some rules about what you found and read more about the two defining properties of a tangent of a circle.

Adding Consecutive Numbers Using Gauss's Method

In the book, Lulu uses Gauss's method for calculating the sum of the numbers from 1 to 9 so she could figure out the "Magic Constant" for the magic square in the puzzle.  In this video, L demonstrates how this is accomplished:

If you want more information about Gauss's summation, watch this great video:

Your Turn to Play!
• Gather a collection of small objects of the same type (cereal, crackers, coins, blocks, etc..).  Place one object in front of you in the first row, then two objects in the second row, three objects in the third row, and so on.  Do you notice that the objects always form a triangle?  The num of consecutive numbers (which you can find using Gauss's formula) are called Triangular Numbers because they can be formed into triangles.
• How does Gauss's summation formula change if you don't start at 1 (example - add all the natural numbers from 15 to 115)?
• How does Gauss's summation formula change if you are adding only the odd numbers from 1 to 100?

Magic Squares

Once the "Magic Constant" is known, solving the magic square is just a matter of figuring out which number is missing for incomplete rows, columns, and diagonals, so they all add up to this constant.

Be sure to complete the activities in the "Play Along" section of Chapter 2 to discover some extra special properties of 4-by-4 magic squares.

Your Turn to Play!

• If you've mastered the 3-by-3 magic squares, you can progress to some 4-by-4 squares with larger numbers from this collection of 100 magic square puzzles.

Literature Connection

The books mentioned in the Chapter 2 include:

Treasure Island:

"Yo ho ho and a big bowl of yum?"... not exactly!

Here's my favorite edition of "Treasure Island" (unabridged) with gorgeous full-color illustrations by one of my favorite illustrators, Rober Ingpen:

Romeo and Juliet:

Lulu recites the famous "rose by any other name" quote from the play in this chapter.  If you'd like to introduce Shakespeare to your children, this book is fantastic:

Turtles:

If you have a turtle-lover in the family (like Elizabeth in the book, and my own E), I highly recommend this book:

Questions to Investigate

Lulu and Elizabeth read many books and research topics they are curious about, so you'll find them sharing many interesting facts in the novel.  Use an internet search or books from your local library to find out more about some of the topics mentioned in the second chapter of Math and Magic in Wonderland:
• If a carapace is back part of a turtle's shell, what is the bottom part called?
• If there are 15 days in each of the 24 cycles of the Chinese solar year, how many days are "missing"?  How are the missing days "fixed"?
• How is the hexagram related to religion and spirituality?

Be sure to leave a comment letting us know what you discovered!

Giveaway

To kick off the "Math and Magic in Wonderland" Book Club, I'll be giving away a math game to one lucky winner.  The winner will get to choose ONE of the games in this list (so the winner can pick a game that he/she don't already have and is age appropriate).  To enter, follow the instructions in the Rafflecopter.  The giveaway ends on August 19th.

a Rafflecopter giveaway

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!