Are You Losing Your Marbles?

Due: Friday Feb. 14th 1:30 pm

Here is a visual puzzle.  Determine which marbles, labeled 1 - 6, should replace the question mark.  Explain why you chose the number of marble that you did or what you noticed about the marbles that support your selection. 

(Be sure to use the writing rubric.)

At the Movies

At the Movies

    People think that "Wicked" will win an Oscar Award this year, for the Outstanding Performance by a Cast in a Motion Picture category. Ticket prices, in our area, to see the film are approximately $12.50. Currently the price of Wicked, the musical, on Broadway cost $355.50

     The year I was born, Gigi won a total of nine Academy Awards, one being best picture. During that year, my parents purchased a movie ticket to see the movie for about $0.68. 

     Answer the questions below.  Use the math rubic that is posted in Google classroom and Canvas. 

     If ticket prices for musicals rose at the same rate as the movie tickets:

• What would it cost to see a musical version of Wicked in 1958?  
• State what the price of the ticket and illustrate how you got the price mathematically.  
• Are you surprised at the cost? Why? 
• Was your model a good predictor? Why or why not? 

In addition: Imagine that the size of the dollar bill has grown in proportion to the movie prices. What would the dimensions of the bill have been, when Gigi was in the movie theaters? 



Don't forget:
No names - initials and period only!!!! Set up your blogger profile and you will not have to worry about it again.  ;-)  Also, check the requirements for your submissions on the first post, you don't want to loose any credit.

Three Monkeys

Three Monkeys - Due Nov 26th by the end of the school day.

This is one of my all time favorites.  All that is required is some careful reading, a little thinking and simple math will solve this problem. 

Three monkeys walk into a motel on the Planet of the Apes and ask for a room. The desk clerk says a room costs 30 bananas, so each monkey pays 10 bananas towards the cost.

Later, the clerk realizes he made a mistake, that the room should have been 25 bananas. He calls the bellboy over and asks him to refund the other 5 bananas to the 3 monkeys. The bellboy, not wanting to make a mess dividing the 5 bananas three ways, decides to lie about the price, refunding each monkey 1 banana, keeping the other 2 bananas for himself. Ultimately each monkey paid 9 bananas towards the room and the bellboy got 2 bananas, for a total of 29 bananas. But the original charge was 30 bananas.

Where did the extra 1 banana go?

That's Impossible - or is it?

Due Nov 15th 

What happened?  Why is there an extra space? 

I would suggest that you grab some graph paper and try it yourself.  Your task is to explain why there is an extra space when the colored area blocks are moved.  You can support your statement with an illustration if you want but you must write out an explanation.  If you support your argument with an illustration bring it to me so I can post it, it might help us make sense of the problem.  

Good Luck 

Ms. L. 

SOLUTION:

As we have discussed in class.  You can not eyeball and answer a geometry problem and this is a prime example.  Here is what happened in this problem:

The key to the puzzle is the fact that neither of the 13×5 "triangles" Are a triangle. Because of the measures Is what appears to be the hypotenuse, is actually bent. In other words, the "hypotenuse" does not maintain a consistent slope, even though it may appear that way to the human eye.

A true 13×5 triangle cannot be created from the given component parts. The four figures (the yellow, red, blue and green shapes) total 32 units of area. The apparent triangles formed from the figures are 13 units wide and 5 units tall, so it appears that the area should be S = ⁠13×5/2 = 32.5 units.

So as well as the hypotenuse being bent the areas are not the same.  Here is a visual to help you think about what is happening here.

Exquisite Election

Be sure to use the writing rubric posted on the first page of the blog. Answer the questions below but be sure to explain how you got your answers.  

Also remember the format for submission.  If you do not follow the format, your solution will be posted but I have no way to give you credit.  example - JL per. 3

Due Nov 8th

Solution:

    Most people use a probability tree to start sorting out their combination totals for each item.  Here is an example. 

Also, I decided to give an accurate solution put together by a Middle School Student from California. Their method to use x! is a probability technique that is practiced in middle school across the country - state standards. 

From: 

Maya George, age 12

School: Howell Township Middle School North, Howell, NJ

There are 716,636,160 possible combinations.

The odds that both Kaylee's and Kelly's names will be first in the different combinations is 1 to 17.

To solve the first question of this problem, I took the problem step by step. Since there are 4 students running for the position of president, I started with using the letters "A,B,C,D" to represent each student. Then I listed the possible combinations:

                 ABCD BACD CABD DABC

                 ABDC BADC CADB DACB

                 ACBD BCAD CBAD DBAC

                 ACDB BCDA CBDA DBCA

                 ADBC BDCA CDBA DCAB

                 ADCB BDAC CDAB DCBA

This made a total possible of 24 arrangements for the president

position alone. 

There are a total of 3 students running for the position for vice-

president. So I used the letters "A,B,C" to represent each student. I

then listed all the possible combinations:

                    ABC  BAC  CAB

                    ACB  BCA  CBA

This made a total of 6 possible arrangements for the vice president

position alone. Now I looked at the two lists I had made. The first

one had 4 people running for president, and resulted in 24 possible

combinations. The second had 3 people running for vice-president, and

resulted in 6 possible combinations. 

After thinking for awhile, I realized that if there were "x" people running for the position, the

formula for finding the number of combinations would be x*(x-1)*(x-2)* (x-3)...1  For example, in the first set of arrangements, there were 4 people running for president and the number of combinations was 4*3*2*1=24. In the second set of arrangements, there were 3 people running for vice-president, and the number of combinations was 3*2*1=6.

     Using this formula, I came up with a table. This is how it looked:

                       POSITION | NUMBER OF COMBINATIONS

        ------------------------------------------------------

                       PRESIDENT| 4*3*2*1= 24

                  VICE-PRESIDENT| 3*2*1= 6

                       SECRETARY| 4*3*2*1= 24

                       TREASURER| 2*1=2

        8TH GRADE REPRESENTITIVE| 3*2*1=6

        7TH GRADE REPRESENTITIVE| 4*3*2*1= 24

        6TH GRADE REPRESENTITIVE| 6*5*4*3*2*1=720

               Now, to find the TOTAL number of possible combinations, I multiplied the number of combinations by each other. So I multiplied 24*6*24*2*6*24*720. I got a resulting product of 716,636,160. So this was then my final answer for the first question.

               To find the odds that both Kaylee and Kelly's name will be first on the list of representatives, I first had to find the odds that each of their names will be first on this list, and I would then multiply them together. To do this, I took Kelly first. He was one of the 6 people running for 6th grade representitive. So he had a one out of six chance of being first on the list. This means that the probability that his name will be on top of the list is 1/6.

             

            Kaylee was one of the three people running for 8th grade representative. So she had a one out of three chance of being first on the list, and so the probability of her name being first on the list would be one out of three, or 1/3.

             Now I multiplied these together to find the total probability that their names will be on top. 1/3*1/6= 1/18, so 1/18 is the total PROBABILITY that their names will be on top. Now I needed to convert this to the odds.

             1/18  stands for the number of total combinations that Kelly and Kaylee are BOTH listed first as a fraction of the total number of all possible combinations. If the number of combinations that their names are listed first is 1/18, 17/18 is the number of arrangements when their names aren't listed first. Since the definition of ODDS is the number of chances for an event to happen versus the number of chances against the event happening, the ODDS

that they both are listed first in their respective races is 1 to 17.

Aggravating Angles

Triangle ABC is isosceles with AC = BC and a vertex angle of 50 degrees. 

If AD = BE, what is the measure of angle ADE? 

State your solution and be sure to explain your reasoning clearly.  Explain what steps you took to get your answer.  Use complete sentences and grammar. Use the rubric I posted this week to help you determine what grade you will get on your writing.

REMEMBER: Your work is due by Friday Oct. 25th before school is over. 

 

To all:

I have graded the first problem... Mango-a-go-go.  Many of you didn't do the problem.  These points are going to add up and really hurt your grade.  You know I do not give homework, which is why I feel one problem, that you can work on all week, is not a lot to ask of you.  Do the POW'

Keep in mind how I am grading your work: your writing,  I am posting a rubric for you to judge your work by.

• your ability to be clear in your explanation
• clear about how you got your solution, in other works - your thinking and persistence
• and finally your solution. 

Good luck with this weeks POW!  Don't forget:  first and last initial and the per of your class.  I can't give you a grade if I don't know who's work it is.  It is due by the end of the school day on Friday the 28.