POW Dec 3

There is a bus with 7 children inside of it. Each child has 7 backpack. In each backpack there are 7 big cats. Every big cat has 7 small cats. Everything listed above is entirely in the bus. All objects are unique. There is no driver. Every child has 2 legs. Every cat has 4 legs.

QUESTION:How many legs are in the bus? Show or explain how you found your answer.

REMEMBER:

DO NOT Copy the problem and put it in your answer!!!

Your intials are the first thing you type into Blogger!!

Good Luck!

Nice job guys! Many of you not only found the correct answer but were moving towards the correct algrithm. Here is the answer for this weeks blog. have a great weekend!
Ms. L.

Correct answer:7 kids * 2 legs = 14 legs
7 kids * 7 rucksacks = 49 rucksacks
49 rucksacks * 7 big cats * 4 legs = 1,372
legs49 rucksacks * 7 big cats * 7 small cats * 4 legs = 9,604
legs14 + 1,372 + 9,604 = 10,990 legs total.

This may also be shown as a simple powers of 7 problem:
Total legs = 7^1 * 2 + 7^2 * 0 + 7^3 * 4 + 7^4 * 4. This is because there are:7^1 * 2 kids legs7^2 rucksacks (But they don't have legs)7^3 * 4 big cat legs7^4 * 4 small cat legsOf course, 7^2 * 0 could be omitted completely, but I include it just to show the progression of powers of 7.

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.

Rubric for the To Kill a Mockingbird Blog response

8th Grade,

Here is your rubric for the blog writing due on Friday. I will be handing this out on Wednesday as well. If you click on the picture you can enlarge it so you can read it. :-)

ms l

POW Oct 22 - California Wildfires

I had a seasonal POW set and ready to go, however I think the fires in California might be of more importance right now. Here is what I would like from you. I would like you to read up a bit about the fires. Look for some of the math in the web articles, on the news, and in the newspaper. See what kind of mathematical information you can share with us to make this a bit easier to understand. Think back to our 9/11 comparisons. For example I could write and post something like.

300,000 people have been evacuated from their homes as of today. To understand how many people that is we can compare them to the population of Phoenix. Currently there are 1.512,986 people who reside in Phoenix. This would be the same as evacuating 20 percent or 1/5th of Phoenix.


There are many comparisons you can make
Acres burned
Number of houses destroyed
Area of land affected by wildfires
Number of fireman engaged in fighting the fires
Comparisons to the Rodeo Chediski fires

You need to make at least three comparisons and then write a narrative using your comparisons. Adhere to the 6 plus 1 writing traits. I will be grading on math content, impact of the data through your writing, and mathematical support for your comparisons, graphs, tables etc.

Here are some websites to get you started. I will add to the list as I find good ones, however you will need to find some sites as well. Remember to credit any sites you use for your data or information such as maps or statistics. I will be posting a PowerPoint presentation on the 7th grade website tomorrow evening.

Ms. L.

Links to the California Wildfires

InciWeb
http://www.inciweb.org/state/5/6/d/0/

InciWeb Maps
http://www.inciweb.org/maps/0/

Joe Maller – very good site
http://www.joemaller.com/california_wildfires2003.shtml

Battling California Wildfires
http://www.calfires.com/

7th honors POW

Now that you have posted see if this helps clarify. When you looked at the logo you should have seen a series of three different circles.










You then solve for the area of each of the three circles. If you do a bit of subtraction you can find out how much shaded, then white or ‘non-shaded’, and total fabric you needed for this logo.






Happy Friday! Just to let you know I am seeing a vast improvement in the caliber of your writing and your explainations. Please continue to write as if you are explaining the process to someone who does not understand how to proceed with the problem at all.

Here is your problem:

Jocie was decorating her notebook with her High School’s cheer logo. The School logo is shown below. The logo includes two different fabric types. The shaded and un-shaded pieces are made of different materials.

Questions to address:
1 - How much material does she need for the shaded area?

2 - How much material does she need for just the un-shaded area?

3 - Show the steps to your solution; make sure to explain every step as you write it.

(My bad I wrote meters it should be centimeters.)


Ms. L.

7th Grade Friday Blogger Work

Happy Friday ladies and gentlemen,

Today I have provided a list of links for you to explore. I would like you to visit all of the sites listed. Complete the activities and then post a review of each of the sites.

Explain:
Did you liked the site and why?
Who would benefit from the site and why?
What was good about the site and what might the author of the page do to improve the
mathematics on the site.
Make sure to support your argument with examples from the sites.

Be sure to use complete sentences...

Sites:

Play each of the games at:

http://www.bbc.co.uk/education/mathsfile/gameswheel.html
(Just a tip in the past students have been intrigued with Builder Bob.)

http://www.bbc.co.uk/schools/ks3bitesize/maths/

http://www.visualfractions.com/

http://www.shodor.org/interactivate/activities/numbercruncher/

http://www.dositey.com/addsub/Mystery11.htm

http://www.funbrain.com/cgi-bin/gn2.cgi?A1=s&A2=10&A3=0&A14=1&A15=1

http://www.learningwave.com/abmath/hotel/index3a.html




Ms. Leckman

To Kill a Mockingbird

To Kill a Mockingbird

Please begin to investigate and address these issues. Be sure you are responsible, reflective, and respectful in your responses. These are to be answered using the 6+1 writing traits. I will be posting a rubric soon. Be thorough and comprehensive in your explanations. Use graphs or tables to support your findings. Be sure you are citing your data sources and supporting your explanation or rational with the statistics and mathematics behind your response. You should assume your reader has no knowledge in these topics. The reader should have enough information to understand and agree or disagree with your viewpoint and your mathematics.

Make sure you explicitly address how the features you choose become apparent in the book, To Kill a Mockingbird. How do you see your factors illustrated in the story or how does Harper Lee allow you to feel these factors in, To Kill a Mockingbird? How do these factors impact the characters and their actions in the story?

What were the population ratios of “Whites to Blacks?” in the early 1930’s?

What was the lifestyle of the Southern populations in the early 1930’s?

How much money did each socio-economic group make? For example: Upper, Middle, Lower socio-economic classes?

What was the average cost of living during this time? What did these kind of lifestyles look like? How are they the same or different than today?

What is the ratio of court cases of the defendant’s racial background? (Today compared to the 1930’s)

What were the ratios of Black, Latino or other “minority” attorneys in the 1930’s?

How would that impact the justice system (now and then if different?)

What was the ratio of “professionals” or “educated” “minorities” in the 1930’s?

What impact would these factors have on each classes place in society?

I look forward to your findings! :-) <(^^<) (>'-')>

Ms. L.

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.

POW August 31st

You all did a nice job on last weeks problem. Here is a problem that you can use some of the "tools" we have been talking about in class. They may come in handy in solving this problem.
:-) Good luck.
Ms. L.

P.S. Ma ke sure to put both you and your partnership intials in the box you submit your answers. I can't give you credit if I don't know who posted the response. :-)

Here is the POW for this week:

Doug and Anna plan to kayak on the river near their home. The river flows at a rate of 4 miles per hour. In still water they paddle their kayaks at a constant rate of 6 miles per hour. They start and end their trip at the same place on the river. They kayak for exactly two hours, first going upstream and then downstream. What is the total length, in miles, of their trip on the river? Express your answer as a decimal to the nearest hundredth.


You guys did a very nice job this week. Many of you were able to see that the distance there and back needed to be equivalent. The idea of writting them as two equations was a new idea to some of you. Here are two ways to look at the solution to this weeks problem.

Here are some of your peers graphs and tables. :-)

POW Aug. 20th

O.k. so here is your first POW. I know all of you have received an e-mail like this one, but why do they work? Your task is to mathematically explain this quandary. Be as specific and concise as you can. (Remember - save a copy of your work in Word just in case. :-) and use your first and last initial ONLY!!!!)

Ms. JL


Many of you sent in excellent solutions to this problem!!! You tackled it using logic, order of operation, and algebra these are all great ways to go about solving the problem!

Here is the way the author of the problem saw the answer.

Please go back and look at the ways your peers solved the problem. Feel free to post comments, questions, or commend your peers for the way they approached the problem.

If x is the number you think of, you start with x,
Then when you add 1, you get x + 1
When you double it, it turns into 2x + 2
When you take away 3, it turns into 2x -1
Adding the number you first thought of makes 3x -1
When you add 7 it turns into 3x + 6
When you divide by 3 it turns into 1x + 2
Then take away the number you first thought of (x) it leaves 2.

See you Monday,
Ms. Leckman

Welcome to 2007 - 2008 School Year

Well, its a new school year. Part of the class is to participate in the math blog. I will be providing time, probably on Friday's for us to do our posts and a class newsletter. Check this page the first week of school for the problem you will need to work. For now enjoy your summer and I will see you soon!

Ms Leckman