The Beauty of Mathematics

There are images we can create in Mathematics called Fractals. They are objects that can be split into parts that are smaller copies of themselves. It is like looking in the mirror at the fun house and seeing your image get smaller and smaller. Today we are going to make a puzzle that will result in a Fractal if put together properly. Click on the link to the right that is called: Puzzle.

Try to rearrange the pieces the complete the image. Post a comment to me of no less than five sentences that describe your Fractal.

Spatial Relations

There is a tool in Geometry called Pentominoes; they are used to develop our sense of spatial
relations. The link at the right will bring you to a set of Pentominoes you can use online. Take the
pieces and make the following shapes:

1. A rectangle with three pieces.

2. A rectangle with six pieces.

3. A square with any number of pieces.

Call me when you are done with each problem.

Pythagorean Theorem

One of the most famous theorems in Mathematics is the Pythagorean
Theorem. This theorem allows us to find the missing side of a right triangle.
Below is a list of the three sides of five triangles. In each case use the calculator
on the link to the right to find the missing side. The formula is a² + b² = c².

1. 3, 4 and c

2. 5,12 and c

3. 3, 6 and c

4. 2, b and 3.5

Learning Styles

There are many ways to learn. There are also many learning styles. Our task today is for you to find out which learning style is best for you. Click on the link to the right that say learning styles;take the test and let the program score it and tell you what kind of learner you are.
Post the results to me as a comment. I want to know what kind of learner you are and what you think that means.

The Future of Mathematics

Stephen Wolfram in one of the great geniuses of our time; His status in England is somewhat like a modern day Isaac Newton. As a young man he solved a famous math problem that stumped mathematicians for years. His newest invention is an online tool that will compute whatever you ask of it. Some think that his new search engine will move the Internet beyond Google into a new age.

Your task today is to click on the link marked Wolfram Alpha. Once there ask the site to solve the following equations:

1. X + 5 = -4

2. Make a graph of the equation x squared plus two equals eleven.


3. Enter your birthday and find what is most interesting in the report you receive.


4. Find the distance between Hartford and Miami


5. Make up a question of your own and post both the question and the answer to me as a
comment.

Post all the answers to me as a comment.

Mathematics and Beauty

A teacher of mine would often say that he found mathematics beautiful. As I watched some of you make the curve stitching patterns I began to see how beautiful mathematics can be. Today we are going to create a pattern using computer tools. The link marked pattern tool will bring you to an interactive pattern maker using the path of a turtle. I want each of you to figure out what the controls of the tool do to change the pattern. Once you create a pattern that you like open a word document and copy and paste your image. Save the document and email it to me.

My email is: gengs001@hartfordschools.org

Finally leave a comment that answers this question: do you find the making of patterns beautiful?

Slumdog Math

In the movie Slumdog Millionaire, Jamal the main character, wins 20 million rupees. Rupees are the currency that is used in India like our dollar is used in our country; what I would like to know is how much money did he win in dollars? The link to the right named "money converter"has a list of all the currencies used around the world. Your challenge today is to convert 20 million rupees to dollars. Use the link as a tool to help you solve the problem.

Your second challenge is to use google to answer the following questions;

1. What is the population of India?

2. How many people are poor in India?

3. How much bigger is India than the US in population?

4. The major religion in India is called Hinduism; In the movie the little boy in the movie with the bow and arrow is a representation of the god Rama; There are an infinite number of gods in the Hindu religion; How many gods are there? Explain you answer in three or more sentences.

Equations as Patterns

A bird rises from a tree and creates a path in flight. If we could graph his path what could we learn? This is one of the main principals of mathematics. There are many tools online to graph patterns as equations. Your challenge today is to graph the following equations and answer the the questions that follow:


1. Graph x + 2 and answer the following questions:

What do you think the 2 does to the equation?

Does the letter x determining the picture on the graph?

2. Graph x^2 -3 and answer the following questions.

How does the x^2 change the picture?

What does the -2 do to the graph?

The Science of Patterns

Mathematics can be thought of as the science of patterns; when we study math we are always looking to see if there is an underlying pattern that can be used to create an equation; finding the equation is one of the basic tasks of mathematics; today we will start with looking for patterns within maps of the United States. I say maps because we will be looking at different data sets and how they are represented with a map. Click on the link labelled maps and use the tool to answer the following questions:

1. Which state has the most land area and how much area does it have?

2. Which state has the most people per square mile?

3. If you wanted to move to a state with the most open land, which one would you choose?

4. Where is the most gas used per person? Why do you think this is?

Tell Me a Story; Give Me an Account.

Another way of asking someone to tell you a story is to say: "Would you please give me an account of what you have been doing. An account is a story; Likewise when you put money in the bank they place it in an account; if we look at the account over time it can tell us a story about what has happened to our money. There are many tools on the Internet for helping you see what happens to money over time. Today we will use one of those tools. Click on the link on the right called "The Money Tool " and answer the questions below on the comment link.

1. If you put $100 to start your account and you add $100 per month, how much will you have after five years.


2. Interest is the amount of money the bank will give you for letting them use your money; how much interest did the bank pay you over five years on the plan in number 1?


3. Let's say you bought your first car with a credit card; the car cost $3000; if it takes you five years to pay off that credit card how much did you end up paying for the car?



4. If you open a stock market account with $100 and add $100 per month; how much money will you have after five years?

A Grain of Rice

There is an old story about a grain of rice that is a famous math problem. In a kingdom long ago a poor man saved the son of the king from drowning; the king told the man he would give him 1000 gold coins as a reward; the poor man said all he wants is one grain of rice on the first day of the month and double the amount each day of the month. The king was surprised; he told the man he was a good man for asking for so little.



Here is the math problem. Here is the question: if the man has one grain of rice on the first day; two on the second day and four on the third day; how many grains of rice will he have after 30 days?



Use the calculator and google to solve the problem.



Step 2: Click on the link to the right called A Grain of Rice. For every question you get right rice is donated to the poor by The United Nations. Find the math problems on the site and see if you can make it to level 10.

Mathematical Thinking

Finding patterns is one of the foundations of mathematical thinking; Often we need tools to help us find a complex pattern; games can be used as a tool to find patterns and express them in algebraic terms; the game called NIM is one of those tools. Your challenge today is to learn how to play Nim against the computer. Nim is a take away game similar to the one we played in class; in this case your opponent can take away only as many buttons as you take; the object of the game is to pick the last remaining buttons. Click on the link to the right to begin the game. Once you are able to bear the computer with 20 buttons call a teacher over and show them your skill.

Problem Solving and Technology

Technology is a tool that can be helpful as part of a problem solving strategy. Models that were made by hand in the past are now made on computers with virtual machines called applets. Today we are going to use technology to help us solve a problem: what are the best gears to use on a bicycle when I want to get to a friends house as fast as possible. The link on the right is an applet that will help us answer the question. Read the instruction, play the game and then answer the questions below.

1. If my friends house is in the city two miles away on flat ground, which two gears would get me there as fast as possible?

2. Why would I ever want to use the two slowest gears?

3. If you could only choose one pair of gears which would you choose and why?

4. How many possible choices would you have on the bike used in the applet?

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.