Lousy Lockers

One hundred students are assigned lockers 1 through 100. The student assigned to locker number 1 opens all 100 lockers. The student assigned to locker number 2 then closes all the lockers whose numbers are multiples of 2. The student assigned to locker number 3 changes the status of all lockers whose numbers are multiples of 3 (think of it this way - locker number 3, which is open, gets closed, while locker number 6, which is closed, is now opened by student 3.) The student assigned to locker number 4 changes the status of all lockers whose numbers are multiples of 4, and so on for all 100 students. When student 100 is finished changing the state of the locker doors:

1. Which lockers will be left open?
2. How many lockers, and which ones, will be touched exactly twice?

Tips:

1. Look for patterns so you do not have to go through all 100 state changes.
2. Maybe organizing the state changes in some manner may help you make some predictions that you could test.

Extra Credit: Which locker(s) was (were) switched the most times?

Boxes and Boxes and Boxes

Below you see an open box.

The result of cutting along the four darkened edges and then flattening the box is shown below.

You will follow the link below to open a grid.  Save the grid to your documents - then open it in paint.  You will draw all the nets that will fold up into different open boxes with a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box.  (Each square on the grid has a side of length 1 unit.)  Be sure to show or explain how you know your net will create a box with a volume of 8 cubic units.  The dimensions alone are not enough to be concidered proof.  Be sure to also include proof that you have all the boxes you make for the given volume.

Click Here for Grid Paper

When you are finished paste your pictures into a word document along with your explaination and e-mail it to me at mathclasshonors@yahoo.com  You can not just click on the address, you will need to open your email and copy and paste this address in your "To" line.  Then attach your word document.  DO NOT cut and paste your work in the body of the email.

Ms. Leckman

Horton's Clover Hunt

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. 

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

Seeing Circles

Open the PDF called Circles and Triangles.  Here is the link to find the actual problem.

Link for Circles and Triangles

This POW may take two periods.  Answer all the questions.  You will need to use paint for this activity.  If you need help let me know.  You can put your answers in a word document (make sure to cut and paste your illustrations in the document,) and e-mail to outr math class honors email and entitle it "Seeing Circles."  Make sure you name is somewhere in the document.  (Not on the picture please.)  I will post your responses on our webpage.  I will include the link here when they are uploaded.

Some things I noticed.  Many of your comments or solutions are numbered and there is no hint of the what the question was you were trying to answer.  Be sure that you follow the 6-traits and embed the question in your response. Your illustrations of your thinking were wonderful, and most of you were spot on with your solutions.

To see your solutions you can go to our website or click on the link below:

YOUR SOLUTIONS

1. To achieve the maximum area, the triangle must have the maximum height. This maximum height is 8 units. The area of triangle ABC is  ½ • (16 units) • (8 units) = 64 sq. units.

2. An area that is half of the maximum area can be achieved by choosing a height that is half of the maximum height, which is a height of 4 units.

There are four possible points C. One of the four possibilities is pictured. For any of the four possible triangles, the area is ½ • (16 units) • (4 units) = 32 sq. units.

3. The area can be made smaller by decreasing the height. If we place C very close to A, the area of the triangle can be made as small as desired. If C actually coincides with A, the area becomes 0, but ABC is arguably no longer a triangle.