Reflection September 28th

Feeling like you are working too hard? Your probably not alone. Today we will not be doing a Problem of the Week, instead we will try to help each other. Here are your tasks for today. Do not copy and paste this writing into your reply!!!!

1. Look through your book and identify a couple areas you need help in for the assessment next week. (For 8th Grade: remember that the assessments are cumulative so that means there may be problems you would want help with from chapter one as well as chapter two.) You will need to post three questions or requests for help. (I can't think of one of you that should not be able to find three things you need help with... so don't go there. :-) ) You will want to find a problem in the book that illustrates the type of help you need.

2. You will go to the "I get by with a little help from my friends" blog and post your responses under the correct book and chapter/investigations. Post an example problem in your reply and explain what you need help understanding.

3. Make sure you post your reply under the correct chapter and book.

4. Next, find and respond to at least three post that need help. Be complete and give them as much help as you can.

5. Make sure to put your intials at the top of each of your posts so I can easily find them. (Thank you in advance.)

Good luck! Ms. L.

More about last weeks post

Most of you realized there was a pattern involved with the Frog Puzzle, yet many of the explanations did not really address providing any direction or ways to solve the problem. Determining what a string of numbers as an explanation to the problem (ie... 1,2,3,4,5) were trying to say really didn't help us identify or understand which frog was moving and where the frogs were moving to. I will be adding peoples visuals to see if this helps us understand what was happening in the problem and how we might better explain and describe the actions and pattern. A good way to see if your explanation is sufficient, give you parents or a friend your written explanation and take them to the web site. Ask them what helped them understand how to win and might have been incomplete or insufficient directions. (Extra Credit: Write up the discussion you have with your parents and have them sign it for extra credit this week. Yes, don't even ask, complete sentences and correct punctuation and spelling are required.)

Last weeks POW was actually a version of a very old puzzle - The Tower of Hanoi or Towers of Hanoi. The Towers of Hanoi are a mathematical game or puzzle. It consists of three pegs, and a number of disks of different sizes which can slide onto any peg. The puzzle starts with the disks neatly stacked in order of size on one peg, the smallest at the top. The objective of the game is to move the entire stack to another peg. Easy, maybe but you have to follow the following rules: You may only move one disk at a time. You may only move the top disk from one of the pegs and sliding it onto another peg, it can be placed on another disk that may already be present on that peg. And finally, no disk may be placed on top of a smaller disk.

The puzzle was invented by the French mathematician Edouard Lucas in 1883. There is a legend that accompanies the game. It states there is a temple which contains a large room with three posts that contain 64 golden disks. According to the legend, when the last move of the puzzle is completed, the world will end. The priests of Brahma, acting out the ancient prophecy and have been moving these disks, in accordance with the rules of the puzzle. There are patterns which repeat the action over and over again, we call these iterative patterns. The Towers of Hanoi are a type of iterative pattern called a recursive pattern. A recursive pattern is a pattern that repeats itself but you have to have the results of the previous action or term to determine the outcome of the output or term you are solving for. This type of patterning is very common in computer programming and The Tower of Hanoi is a problem often used to teach beginning programming.

If you would like to try the original puzzle click on the link below:
http://www.vtaide.com/png/lesol/games/tower/hanoi-2j.html

Ms. Leckman

POW for the Week of September 17th

Let's do something a bit different this week. The POW this is week is to explain how you solved the game found at the link below. To receive credit for this weeks POW you must explain how to get all 12 frogs across all the lily pads. Include any diagrams, tables, or illustrations that help explain what you did. Have fun and come to class ready to post your answer! :-)

Ms. Leckman

Games away:
http://www.hellam.net/maths2000/frogs.html

Sept 4th POW

Ready, good. :-) Here is this weeks POW. Remember:
You may think about the problem.
You may try to solve the problem.
You may not post your responses until Friday while we are in the lab.

Mathematics Club Membership

Before the start of the fall membership drive, Mrs. Roberts wants to know how many students are in the Mathematics Club.

She asks the president of the club, "What's your membership?"

The president replies, "twice our number plus half our number plus a quarter of our number plus you is one hundred."

"Great," says the Principal, "that is exactly one more than one eighth of our total student enrollment here at Madison Number One Middle School."

Please address all of the following in your response:

1. How many students are enrolled at Madison Number One Middle School?
2. How many students are in the Math Club?
3. Write an equation that will help you either find or justify your answer.

Be sure to use comprehensive explainations when you explain how you found each answer. Good Luck. Ms. L.