Monday, August 15, 2016

Book Club Week 3 {Math and Magic in Wonderland}

The third chapter of the math adventure novel Math and Magic in Wonderland, was about cracking "secret codes".  This inspired me to put together an entire spy-themed week for my children.  I sent the kids on missions around the house where they had to find and decrypt each secret message to reveal the next clue. We enjoyed reading mysteries and watching the Spy Kids movie, but didn't forget that great spies are also good at math!  Join us this week as we play with cryptography, learn about permutations of letters, discover a new ending to "The Walrus and the Carpenter", play "Battleship" to practice finding Cartesian coordinates, perform a mathematical proof, and more...

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


Decoding (and encoding) messages is a really important cognitive skill for kids because it sets the foundation for symbolic logic used in more advanced math (like algebra).  As a bonus, who doesn't enjoy playing "spy"?

You could spend weeks (or even an entire lifetime) exploring the topic of cryptography.  I put together a couple resources you might want to use this week, but feel free to jump into whatever subtopic you're the most interested in.  This video provides an overview of cryptography and is a good place to start:

For older children and adults, the BBC History videos on Code Breaking during World War II are very interesting.  Here's a clip:

The "Play Along" section of Chapter 3 mentions the Rosetta Stone.  Find out more about this important discovery:

Your Turn to Play:

  • After reading about the Rosetta Stone, make this Cypher Wheel (pdf) to crack the code and learn a bit about Ancient Egypt.
  • If you're looking for more experiments and games related to secret codes, try these:


In chapter 3, Elizabeth was surprised that out of the over four million different permutations of 7-letter words formed using the nine letters represented by the cells of the magic square, the answer was "cabbage". The best way to understand how to perform the calculation along with Elizabeth is to explore permutations yourself.

Draw three different shapes, all in a row, on a piece of paper:

With two different colored markers (let's say red-R and blue-B), how many different ways can you color these shapes, where each shape gets a single color, but multiple shapes can have the same color?  (Solution:  RRR, RRB, RBR, RBB, BRR, BRB, BBR, BBB = 8 ways, or 2x2x2).  Now increase the number of colors to three.  Keep playing with different numbers of colors and shapes until you've found a pattern for determining the number of permutations.

Your Turn to Play:

  • How many (real) words can you make using the letters from A through I (you can use the same letter multiple times)?

Cabbages and Kings

The word "cabbage" in the secret message immediately reminded Lulu of Lewis Carroll's poem, "The Walrus and the Carpenter".

This is such a fun poem to read together (and memorize if you're feeling ambitious).  I invited my children to act out the story as I read the poem aloud.

Here's the song from the 1951 Disney movie:

I learned recently (from the book "Poetry for Young People - Lewis Carroll") that a number of years after "Through the Looking Glass" was published, Carroll wrote some additional lines to the poem to be included in a musical performance.  In this new ending, the ghosts of the oysters get their revenge on the sleeping Walrus and Carpenter.

The first oyster ghost sings (while jumping on the Carpenter's chest):

"The Carpenter is sleeping, the butter's on his face, 
The vinegar and pepper are all about the place!  
Let oysters rock your cradle and lull you into rest;  
And if that will not do it, we'll sit upon your chest!  
Well sit upon your chest!  
We'll sit upon your chest!  
The simplest way to do it is to sit upon your chest!"

The second oyster ghost sings (while jumping on the Walrus's chest):

"O woeful, weeping Walrus, your tears are all a sham!  
You're greedier for Oysters than children are for jam. 
You like to have an Oyster to give the meal a zest—  
Excuse me, wicked Walrus, far stamping on your chest!  
For stamping on your chest!  
For stamping on your chest!  
Excuse me, wicked Walrus, for stamping on your chest!"

I'm not sure that heartburn is a just punishment for what the Walrus and the Carpenter did to the gullible little oysters, but my children were overjoyed when I read them the two additional verses (and proceeded to act out the scene by pounding on each other's chests).

Cartesian Coordinates

Lulu and Elizabeth activated their tickets by finding the correct symbol at coordinate 2-C on the magic square.  

Your Turn to Play:

A great way to practice using the Cartesian coordinate system is to play the classic game of "Battleship", where you "sink" your opponents ships by guessing their coordinates.  The game can be played using graph paper, or with this free printable battleship game.  There's always the Hasbro version, too, if you're looking for more durability:

It's also great practice to take out a map and find locations based on the coordinates listed in the index.

When I was young, I loved doing coordinate graphing to produce artwork:


You can use graph paper to make your own designs.  Write down the coordinates of the vertices and then challenge a friend to use your coordinates to reproduce your design.

Operations on Odd and Even Numbers

I was really excited to put together this video showing my seven-year-old daughter demonstrating a mathematical proof (without any formal lessons in algebra).  I feel like so many educators believe that children are not ready for higher-level mathematical thinking until they have a certain foundation of courses in arithmetic.  There is definitely merit in the "building block" approach to mathematics, but I believe that children have an intrinsic ability to 'understand' problems without having to know the "correct steps" to solve them.  By challenging our children to use their brains to solve more difficult problems, we are encouraging them to pull from their experiences to visualize what the question in really asking.  This is what "thinking like a mathematician" is all about, and will serve children well in life (whether they pursue STEM careers or not).

Your Turn to Play:

Using the method demonstrated in the video, prove that the sum of two odd numbers is even, and that the sum of an even number and an odd number will be odd.

Literature Connection

The third chapter of Math and Magic in Wonderland had some quotes from Lewis Carroll (you'll find many Carroll references throughout the book).  If you haven't read "Alice in Wonderland" and "Through the Looking Glass", I highly recommend these beautifully illustrated editions:


If you decide to use a "mystery" theme for the week, you may want to read some detective books.  Please leave a comment sharing your favorites.  The kids and I enjoyed this picture book that has many clues to solve hidden in the illustrations:


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
  • Word ladders
  • 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!


    1. We're really having lots of fun with the chapter and activities this week. We're also enjoying your book recommendation "The Number Devil" from a previous post. We're having lots of great number conversations. Thanks. :)

    2. We read "The Real Thief" by William Steig for our mystery - we just love that story. This week has been so much fun.

    3. We are loving this math and book club!! Thank you so much!

    4. My child had a great time with this week’s theme and so did I. Thank you so much for your help!

    5. A note for whenever you update the book: I think the answer to the "Play Along" CVC word permutation is incorrect. There are 3 choices for the vowel. Wouldn't that mean there are only 6 choices for each of the consonants? I calculate 108 possible "words." The calculation in the book limits the center letter to a vowel, but it puts no constraints on the outer letters.


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