8th Grade AL

Olympic Oops!

2010-02-25T21:19:00.006-07:00

Megan and I have been watching the Vancouver 2010 Olympics, wishing we were in Canada! We both hope to attend an Olympics someday. Megan suggested we have a party to celebrate the accomplishments of all the athletes and participate in the international spirit of the Olympics.

Megan created an Olympic rings decoration and was about to put it up when I ran into her. Megan was left holding the blue ring, but the yellow, black, green, and red rings had come apart and rolled to various spots of the living room. I quickly apologized and helped her put the rings back together. We were careful to put the colors in the proper order. After we had fixed the rings and hung them on the wall, Megan wondered how many different ways there are to arrange the colors while keeping the same formation for the Olympic rings.

Determine how many arrangements can be made.
Explain how you solved this problem, what was the pattern you found or show up what you did to solve the problem.

Bonus: Generalize your results above for other combinations (if you noticed a pattern, how would it extend to the 6th, 7th, 10th, and 100th rings?).

Tips:

1. Start with less rings and add a ring at a time. So you see a pattern?
2. Do not make the mistake of thinking there are 5 rings and 5 places for the rings to go in so there must be 25 arrangements, this would not be correct. There are more arrangements than 25.

What is the relevance of the Olympic rings?

The original flag also carried the Olympic motto, "Citius, Altius, Fortius," Latin for "Faster, Higher, Stronger." The Olympic rings are the official symbol of the Olympic Movement. There are five interlacing rings of the colors blue, yellow, black, green, and red. The rings are set upon a white background.

Baron Pierre de Coubertin designed the Olympic emblem in 1913. The Olympic rings represent the union of the areas - the Americas, Africa, Asia, Oceania and Europe and the meeting of athletes throughout the world at the Olympic Games. Contrary to a popular misconception, the colors themselves do not represent any single continent. The colors were chosen because at least one of these colors is found in the flag of every nation.

What do you Mean?

2010-02-18T23:00:00.007-07:00

The table below shows the number of customers at Malcolm's Bike Shop for 5 days, as well as the mean (average) and the median number of customers for these 5 days.

Which statistic, the mean or the median, best represents the typical number of customers at Malcolm's Bike Shop for these 5 days?

Explain your reasoning using feaatures and facts from the data.

Solution: The median is the best measure. The mean is effected by the lack of shoppers on day four.

Horton's Clover Hunt

2010-02-11T20:21:00.002-07:00

Horton's Clover Hunt

Who doesn't love the story Horton Hears a Who! by Dr. Seuss. For those of you who aren't familiar with this particular tale, Horton the elephant takes on the task of protecting tiny creatures living on a dust speck that he has placed on a clover.

At one point in the story, a bird steals the clover from Horton and drops it over a very large clover field at 6:56 a.m. Ever the faithful protector and true to his promise to save them, "Because, after all, a person's a person, no matter how small," Horton begins the enormous task of searching for the lost clover.

But clover, by clover, by clover he found
That the one that he sought for was just not around.
And by noon poor old Horton, more dead than alive,
Had picked, searched, and piled up, nine thousand and five.

1. At this rate, estimate how many clovers Horton picked each minute.
2. Approximately how many seconds did Horton spend on each clover?

For each of the above answers, round to the nearest whole unit.
The story continues

Then, on through the afternoon, hour after hour...
Till he found them at last! On the three millionth flower!

You need only choose one of these questions to answer:

A. If Horton continued at the rate you calculated above without pausing, how long would it take him to reach the three millionth flower? Be sure to answer this question in a way that makes sense (in other words, don't give an answer like 72 hours when 3 days would give us a better sense of how long this is).

or

B. In the story it seems that Horton finds the clover later the same day. If he continued picking from noon until he found the clover at six o'clock that same evening, approximately how fast would he have to work?

This weeks POW is fun,
Comprehensive answers will be done,
Incomplete answers are not fine,
Nor is just having the "answer" in mind,
Working in partners will do
But don't post until your answer is true. :-)

Dr. Suesseckman

Solution: Most of you were right on the money for the rate per minute and also seconds per clover, however you were kind of all over the place for the last two questions. ;-) Please think these through carefully before posting you answers. Many of you posted the same answer, exactly! You are given the privilege of working together however when it comes to posting it needs to be your own work, thoughts and words. Duplicate posts will no longer accepted. I will accept the first post and credit it's author and then reject any posts using the same verbiage and will not credit the author with a score. Further, the posts writing has moved away from the posting requirements. Please review the requirements as future posts that do not meet the requirements will not be posted nor will credit be assigned for the problem.

TIP: I can not give credit if there is no name on the post. I am good but I am not that good! ;-)

Ms. L.

1. At this rate, estimate how many clovers Horton picked each minute.
a. 30 clovers per minute

2. Approximately how many seconds did Horton spend on each clover?
a. 2 seconds per clover.

You need only choose one of these questions to answer:

a. If Horton continued at the rate you calculated above without pausing, how long would it take him to reach the three millionth flower? Be sure to answer this question in a way that makes sense (in other words, don't give an answer like 72 hours when 3 days would give us a better sense of how long this is).
a. It would take Horton about 10 weeks of non-stop picking to get 3 million clovers.

b. In the story it seems that Horton finds the clover later the same day. If he continued picking from noon until he found the clover at six o'clock that same evening, approximately how fast would he have to work?

a. 8,308 clovers per minute to finish by 6:00 pm.

Missing Mess

2010-02-04T23:38:00.006-07:00

Here is a subtraction problem that was partially erased.

1. Can you fill in a possible set of missing digits?

(The missing digits need not be the same as one another.)

2. How many possible answers are there? What are they?

3. How do you know you found all the possible answers?

Nice job on your solutions! Here are some visuals that some of you did.