Tower of Hanoi

When we worked on The Tower of Hanoi puzzle yesterday we tried to find a pattern that would help us solve it; some of us did it by counting the number of steps; others did it by trying to visualize a pattern as we moved the circles around; now it's time to find a way to express the pattern that we found in two ways: with a sentence that explains the pattern and finally with mathematical symbols. The link named Tower will bring you to an applet that allows you to play the game. Then answer the questions below.

1. Write a description of how you solved the puzzle for three disks.

2. How did you know that you found the least number of steps?

3. Using x = the number of disks, write a mathematical expression to describe the pattern.

Post the answers in the comment window on the link below.

The Mathematics of Flying

One of the earliest attempts to fly was with the use of a kite; in the year 1894 a man named Hargrave was lifted from the ground by a group of four cellular kites; As many of you know Ben Franklin used kites to help in his study of lightening. Kites have been used during wars to lift men high enough to see across a battle field and spy on the enemy. For the third trimester we will build our own kites to help us study the math of flying. The first step in our project is to study the different types of kites and pick one that you think you would like to make.The links to the right will bring you to pages that have articles on the history of kites, the different types of kites and how kites are made; your challenge today is to read each page and post a comment to me about which type of kite you would like to make and why.

The DaVoag Code

The next decoding tool we are going to work with is called Letter Frequency Code. The idea is to take a secret text and apply a tool to find out which letters occur the most often. We can then compare the frequency of letters occurring in the English language to those letters that show up in our secret text. The letter E is the most common in our language therefore the letter that shows up the most in our secret text is E. The next most common letters are A, O and T. Use the two links to the right to help you crack the code below. The first one to break the code will win a prize.

TFNRIUJ UZV DREP KZDVJ SVWFIV KYVZI UVRKYJ; KYV MRCZREK EVMVI KRJKV FW UVRKY SLK FETV.

Interactive Mathematics

There are many games on line that challenge us to solve an equation. Usually the game brings us to a higher lever question until we find we are stuck. While playing these games it becomes clear that there is a strategy to moving up. Your challenge this week is to play the game you find at the link to the right; when you get to the highest level you can go, copy the equation into a comments window and post it.

Tiling the Kitchen

Now that we've been practicing finding the area of a room, we should be able to apply that knowledge to out own home. The project today is to change the floor on the kitchen of your home. Here are the steps I would like you to perform:

1. Choose a room in your home that you would like to change.

2. Open a Word document in a new window and draw the room; estimate the size and label the drawing.

3. Go to homedepot.com or lowes.com and pick a tile that you like.

4. Find the price of buying enough tiles for the room you are changing.


5. Copy the word document into the comment window and post it to me.

Rubik's Cube and problem solving

One of the difficulties of solving a problem is to overcome the fear that we don't understand what is in front of us. A mathematical problem if full of symbols that may be unclear as to their meaning. A typical response is: I can't do that. Today's lesson is to begin to learn how to overcome that fear.

Task: click on the link to the right and type s to begin the game; when you think you see a pattern that will lead you to solving Rubik's Cube then post a comment.

The Virtual World

As children we have to learn to understand the world around us; over time we get good at understanding what objects are in our environment. In mathematics we learn to improve out understanding of space by using pentominoes to make different configurations. Click the link to the right. It will take you to a virtual set of pentominoes to play with. Arrange them to cover the space provided.