7th Grade Nov. 26th

Banana Farmer's Dilemma

A banana farmer has six monkeys who hate each other. They must be kept in pens to separate them from the bananas as well as from each other.
The farmer has created six pens of equal size using 13 equal lengths of fencing. The pens are organized in a row.

Early one morning the farmer discovers someone has stolen one of the lengths of fencing.

How can the farmer reorganize the fencing to make six new pens of equal size with the 12 remaining lengths of fencing?

Have fun. Remember to back up your document in the TO BE GRADED file and submit your responses to:

mathclasshonors@yahoo.com

Ms. Leckman

7th and 8th Grade POW Nov. 12th

IMPORTANT Please Read!!!!
I have a number of post from the 7th Grade class that have no names. :-( If one of the POWs is yours and there is no name on it you MUST see me. Mid terms are coming out if you want credit for this POW, see me before the break!!!


P.S. See below for further submission check out the final submission!

Here is one of my favorite POWS, I hope you enjoy it as much as I do. Also check out the, Your Place Link. I have added it for work that you submit that has tables, graphs, visuals, powerpoints... I will be adding more and more of your work.

Good Luck with the problem.
Ms. L.

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?

Here are a few more student posts:

B.B

When the monkeys entered they paid the fee of 30 bananas, but the clerk made a mistake and it was 25 bananas so he gave the 5 bananas to the bellboy to give back evenly. But he didn’t, to make it easier on himself he decided to give 1 to each monkey and keep the two to himself.

So when I plotted on the table missing bananas, you find out if you add it up you find there was no missing banana! ~!!YAY!!~

The equation is 29=9x3+2

Each monkey paid 10 bananas but got one back. They ended up with one banana each. The bellboy ended up with two bananas. The clerk ended up with one banana. If you add all the bananas up together, they equal 30. This shows that there is no missing banana. Each monkey paid 9 bananas so 9x3=27. The monkeys didn’t get the two bananas they should have gotten, the bellboy has them, and so if you subtract 27-2 it equals 25, which is what the clerk got. So if you add the two bananas the bellboy has plus the 3 bananas the monkeys got back plus 25, there is no missing banana. The other strategy of 9x3+2= 29 is wrong because instead of adding the two bananas, you have to subtract them so the equation would be 9x3-2=25 then 25+5=30
By AH

This table shows what had happened in the problem. The first column shows that none of the three monkeys paid. Then the next row shows that the monkeys paid for the room so the desk clerk has 30 bananas. The third row shows that when the Desk Clerk gave the Bell Boy 5 bananas because the room was actually 25 bananas, so to make things easier he gave each monkey back 1 banana and kept 2 for himself…….In conclusion there is not a banana missing.

Add On: The problem misleads you by saying they paid 9 bananas, but if they each paid 9 then the room would cost 27 not 25. It also misleads you because in reality they didn’t pay 9 each the desk clerk just had 25 Bananas.

JL

S.V

The problem asked us to figure out where a missing banana went after three monkeys paid for 1 hotel room. The “missing” banana didn’t go anywhere. I organized the problem in a table and the highlighted column shows how many bananas the monkeys all ended up with and it adds up to 30 because the desk clerk has 25 bananas, not 27 which is the way the problem words it, the bell boy had 2 bananas and each monkey has one banana. 25+2+1+1+1=30!! The way in the problem doesn’t work because of the way it’s worded. People take an approach to the problem based on the way that it’s worded but you just have to think about it more deeply and approach it from a different direction.

JW

And last but not least : The profound mathematical submission of KG EM KT - thank you gentleman, it's all so clear now!!!

Ms. L.

this is proof that the monkey ate the bananasent by:KG EM KT

8th Grade POW Nov. 5th

A Day at the Fairs
The problem this week is an old one, in fact over 500 years old. It goes back to the days in Europe when fairs were common in many cities, and merchants would travel from city to city, selling their various goods and buying other items they desired.

It seems that a humble merchant visited three fairs. At the first fair, early in the morning, he doubled his money selling his products, but spent $30 in food and buying other items.

At midday at the second fair, he tripled his money and spent $54. At the third fair in the afternoon he quadrupled his money but spent $72.

Upon his return home to his wife and ten children, late that day, he counted the money he had in his bag; there was $48.

Now, if the merchant returned home with a profit his wife was happy and she was sad if he returned home with less money than when he started with. So tell me: was his wife happy or sad when he returned? And how much did the man gain or lose, respectively?
Remember: although this type of problem could be solved by guess-&-check or reverse analysis, such an approach will not be accepted here. (You may use them separately to verify your answer; however substitution would be the best way to check your answer.) You must construct an equation for credit. Make sure to label the steps for your solution.

Extra Credit (this is very easy this week don’t over look the opportunity!): If you did your work straightforwardly, your next-to-last step of equation work was of the form (m) x = n. The number “n” is in some way rather interesting; what is it?

Good Luck Ms. L.

Many of you were on the right track. Many of you simply forgot the last step. Here is what it should look like. Our good buddy the merchant's wife was happy because the merchant made $19.

We start with the variable “m”, which is the money the merchant began with. During the first fair of trading, he doubled his money, but spent $30of that amount. This expression is: (2m-30)

During the second fair, the merchant tripled his money, but again spent $54. We keep our first expression and add on because he performed these action on the given money from the first fair, which looks like this: [3(2m-30)-54]

During the third and final fair, the merchant quadrupled his money,and again spent $72. We are just adding on again so the full expression for all three fairs looks like this: {4[3(2m-30)-54]-72}

When he went back home to his wife and ten children, he counted his money and found that he had $48. This amount after all the buying selling occurs is what we have left so it is what our expression “equals”, which looks like this: {4[3(2m-30)-54]-72}=48

Now we can just distribute (one of my favorite things to do,) to find our answer.

{4[3(2m-30)-54]-72}=48 (distribute the 3)

{4[6m-90-54]-72}=48 (distribute the 4)

{24m-360-216-72}=48 (Add like terms)

24m-648=48 (Add 648 to both sides)

24m=696 (divide both sides by 24)

m=29

Now we know that the merchant started out the day with $29 and ended up with $48, this gives him a profit of $19. That makes his wife happy(although, I don't know how long $19 will last on 10 children).

Extra Credit: The next-to-last step is where Ax=B (24m=696) is interesting because B (696) is a palindrome. If you do not know what a palindrome is please look it up, it is not just a Language Arts phenomenon. :-)

7th Grade POW for November 5th

Ann and Sue bought identical boxes of stationery. Ann used hers to write one sheet letters, and Sue used hers to write three sheet letters. Ann used all the envelopes and had 50 sheets of paper left, while Sue used all of the sheets of paper and had 50 envelopes left. How many sheets of paper and how many envelopes were in the box to begin with?

Make sure to thoroughly explain how you solved the problem. Show your mathematics and explain as you go so we understand what the numbers are and where you got them or why they are important.

Good luck,
Ms. L.

To begin the problem you had to account for the proportions or ratios of items to solve the problem. Anne used one piece of paper per letter and Sue used three pieces of paper per letter. If you thought about the number of materials per letter you could set up a table of paper and envelopes per letter. Doing so you would want to add 50 to the number of papers Anne used because she had fifty left over, and you would want to add 50 to Sue’s envelopes as she had 50 envelopes left over. Then all you needed to do was test various numbers of letters, and continue until the total paper and total envelopes were the same for both girls.

Here is the table I made. You can see from the table the girls started with 150 pieces of paper and 100 envelopes.

Here is another table done by AH:

Trying to find the best way

To all,
I have begun reading your posts for last week. I am trying to determine the best way to post these. I may begin a website just for the postings that tend to be multi-media. Give me a couple days to figure this out, I will keep you posted in class.

ms.l.