## Monday, September 5, 2016

### Book Club Week 6 {Math and Magic in Wonderland}

Chapter 6 of the math adventure novel Math and Magic in Wonderland centers around the classic "River Crossing" logic problem.  If you take the time to follow rabbit trails, however, there are so many more learning opportunities to be found...

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Remember to comment and share the fun your family is having with the book club.
River Crossing

The River Crossing logic problem is a classic.  The kids made their own spoon puppets to retell the story:

Here's L explaining the solution:

• The "Play Along" section of Chapter 6 contains additional "River Crossing" problems to solve.  Do you see a pattern to the logic used to solve these types of problems?  Try writing an algorithm (step by step instructions) for solving river crossing problems.
•   Try this river crossing game from ThinkFun:

"Work Rate" Problems

"In three hours, three men can build three boats.
How long for one man to build one boat that floats?"
This problem is a simple example of a type of word problem involving rates of work.  I made up a couple more problems like these (also involving boats):
• Little Bill can build a boat in 12 hours.  White Rabbit can build a boat in 8 hours.  How long will it take them to build a boat if they work together?
• Your boat has a hole  The leak will fill the boat and sink it in 20 minutes.  Forgetting about this hole, you get into your boat for an afternoon nap.  You wake up 20 minutes later with the boat on the verge of sinking!  Fortunately, you have a bucket with you and know that you can empty a boat full of water in 15 minutes.  But the hole hasn't been fixed yet!  How long will it take you to get all the water out of the boat while it is still leaking?
To solve these problems, we drew pictures and broke up the time into smaller intervals.  Who says that elementary-age children can't solve problems without algebra?

• Try your hand at the two problems above.
• Learn more about the art of boat building.  This can take you down so many rabbit trails (history, engineering, and more!).

Exploring Buoyancy

The leaky boat in the story filled up with more and more water as the characters crossed the river.  What determines how much water a boat can hold before sinking?  We made our own aluminum foil boats and performed some experiments to find out more about buoyancy.

The experiments began with pots full of water in the bathroom, but the next day, the kids tried their vessels out at the lake:

E even caught a fish to study, using only a toy net and plastic bottle:

Literature Connection

Who is Pepper Pig?  See if you can find him as a little piglet in Alice in Wonderland.

If you haven't read "Alice in Wonderland" and "Through the Looking Glass", I highly recommend these beautifully illustrated editions:

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!