## Monday, August 29, 2016

### Book Club Week 5 {Math and Magic in Wonderland}

Chapter 5 of the math adventure novel Math and Magic in Wonderland, is full of visual puzzles and "math art".  Crafts are always a big hit around here, and those involving fractals and tessellations were no exception.  Here's what we did...

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Mobius Strip

"Before you enter Wonderland,
Take the ticket in your hand,
And as you wrap it 'round your wrist,
Give the strip a little twist.
Once this simple deed is done,
Our two worlds will join as one."

The girls loved exploring mobius strips this week, but were not too enthusiastic about making a video about it.  The guy in these videos makes some truly magical things with mobius strips which are definitely worth trying at home!  He moves quickly, so be sure to pause the video as you try out each figure, and keep a big stack of paper handy.

Fractals

A fractal is a pattern that repeats itself on every scale.  In the novel, the example was a fractal tree, where each limb throughout the tree, down to the smallest one, follows the same branching pattern.

The kids and I discussed the attributes of fractals and then printed out some 3D Fractal crafts from The Fractal Foundation.  We then went on a nature walk to look for fractals in nature (trees, bushes, pinecones, etc..).  We looked online for even more fractal examples including ice crystals and broccoli.

E's art project was to make a fractal triangle:

She started out by drawing a single equilateral triangle.  This was a great chance to further explore angles.  In last week's book club, we learned that the sum of the angles of any triangle will form half a circle.  I challenged E to look at her protractor (which happens to be a half-circle), and figure out the size of the angles in an equilateral triangle.  From there, we had to bisect each line segment (find it's center) and connect the centers to form a new triangle.  This was a wonderful lesson in dividing with fractions.

I love E's level of concentration as she works!

The final result turned out beautiful:

• Check out some of these neat books featuring fractals:

Tesselations

In Chapter 5 of the book, the girls realize that the tree's leaves can be tessellated.  A tessellation is a tiling of shapes where there are no gaps or overlaps (think of a tiled floor, for example).

After admiring some M.C. Escher designs, the kids and I made out own tessellation crafts.  First, we played with pattern blocks:

E decided to reproduce M.C. Escher's lizard pattern:

Meanwhile, L and I made our own tessellating shapes (using the method described in the "play along" section of Chapter 5...

1. Use poster board or cardboard (we used a cereal box) and trace and cut out a starting shape which tessellates (like a square).

2. Cut out a shape on one side of your square and tape it to the opposite side.

3.  Repeat with the remaining (uncut) sides:

4. Use your shape as a template, and trace it over and over again to tile your page:

I'm no M.C. Escher, this project was a lot of fun!

Here's L's tessellating shape:

... and her final project:

She did such a great job with her tesselation!

• Make your own tessellations!  This is so fun and easy, and you can get some great ideas for shapes online.  For younger children, you can get the Animal Tessellations Templates to get them started.
• For kids who are obsessed with mazes (you know who you are), try this book of tessellating mazes.

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
• 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!