7th Grade Honors Blog

What Do You Think?

2010-05-14T14:03:00.001-07:00

What DO YOU THINK?!?! Help Others, Help Yourself!
Rules of the game: Provided your peers with feedback.
-You must review TWO websites in every Grade Level =SIX websites Per Person!

-You must answer the following questions FOR EVERY WEBSITE & STATE YOUR EVIDENCE!

-What does state your evidence mean?!?! State your evidence means you must give a detailed explanation for why you think what you think. You may NOT only say, “They did a good job!” or “It was horrible!” You must back up your thoughts with evidence about WHY they did a good job.

Questions:

Who are you talking about?
•    State the initials and grade level of the authors.

What do you think of the content?
•    How was the quality of the math?
•    Was it easy to understand?

Did it grab your attention?
•    What did you think of the graphics?
•    Did it make you want to do math (or at least try it out)?

What suggestions do you have?
•    What suggestions would you give to the authors?
•    What was the best part of the site?
•    What part of the site needed improvement?

What about the rubric?
•    Did they follow the rubric?
•    What section did they do the best on?
•    What section did they need to improve on?

What grade would you give you site?
•    A – B – C – D – F (and why)?

Three Monkeys

2010-04-01T13:48:00.001-07:00

Three Monkeys

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?

Lousy Lockers

2010-02-25T20:47:00.000-08:00

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

2010-02-18T21:17:00.000-08:00

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

2010-02-11T17:50:00.000-08:00

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.

Seeing Circles

2010-02-04T21:57:00.000-08:00

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.

Big Arrangement

2010-01-07T22:49:00.000-08:00

Think of a function as a math machine with an input and an output. Suppose the function is A(x) = 3x + 1. That means if you put any number (x) into this function machine, the machine will multiply the number by three and add one. For example, what is the output if five is the input? Five times three plus one equals 16 for the output. That's written A(5) = 16. Suppose you join two function machines so that the output of the first one is connected to the input of the second one. Let's make the second function B(x) = x^2, (remember that x^2 means x squared). If you put two into the A machine, out comes seven. Then seven is the input to the B machine which squares it, and out comes 49. Okay? That's written B(A(2)) = 49.

Here are five functions:

A(x) = 4x - 3

B(x) = 3x^2

C(x) = 7x + 1

D(x) = x^2

E(x) = 2x + 7

I am going to connect them in alphabetical order and use two as the input number. That would be written as E(D(C(B(A(2))))). The resulting output = 553,359.

What arrangement of functions will produce the largest output with two as the input (each function used only once)? I am looking for logical reasoning and algebra rather than just guess and check. Explain why you chose your particular arrangement. (Just write the order of your functions for the short answer.)

When it came to solving this POW you should have noticed there were two types of equations present linear and exponential. Knowing that eponentials grow so rapidly you would want to use their power as the end of the string of equations and the linears up front. You would test the class of equations to see which would produce the highest yeild in its group and order accordingly.

How did you do?

Talking Turkey

2009-11-20T10:07:00.000-08:00

A series of weighings is shown below.

All items on the scales are small toys to be used as decorations for a Thanksgiving party. There are four different kinds of toys:

1. toy 'drumsticks'
2. toy 'turkey platters'
3. toy 'Pilgrim hats'
4. toy figures of a 'Native American'.

Going from top to bottom, the first three scales (scale A, scale B, and scale C) are balanced and complete. But the fourth scale (scale D) is not.
After taking a careful look at the scales below and analyzing the information they provide, try to problem-solve to figure out how many toy turkey platters must be put on the empty side of scale D in order to form a balance with the left-hand side of that scale, which, as depicted in the ilustration, is weighed down by just one toy drumstick?

Make sure to explain your solution fully. Someone who is not good at math should be able to follow your process, understand what they are doing (and why,) and arrive at the same solution. ;-) Have fun - good luck!

Ms. L.

Beds of Flowers

2009-10-02T12:45:00.000-07:00

Dona and Dennis have a large yard and are thinking of putting in some new flower beds. Dennis went to the local garden center and came home with the following plants:

When Dona saw the flowers, she made the following requests for the beds.

The same type of flowers could not be in the same bed.
The same color of flowers could not be in the same bed.

How many beds will Dennis have to dig?
What types and colors will go in each bed?

Describe, in detail, how you solved this problem.

Friday the 25th

2009-09-25T12:37:00.001-07:00

Today you will learn how to work on the wiki.

You will need to go to our link - (Listed on the side of the page and below.)

Class Wiki

Sign up and create an account, then come and see me. I will make you a writer. You may then go looking for math games. You will add any games you find to the game page on the wiki. You will create a title for the page, write a description of the game and paste it under the correct grade level and math strand. Just like in the blog it is very wise to create everything in Word and then cut and past it into the wiki. (Make sure you have clicked the "EDIT PAGE" button to do your pasting.

See me for any help,
Ms. L.

The Mensa Toy Store

2009-09-03T20:56:00.000-07:00

There is a special organization called Mensa. Its members are people who like problem solving - not just any old ordinary problem, but rather one that takes a little extra thinking and creativity to solve.

The problem this week is similar to one that appeared on a calendar published by Mensa a few years ago. To solve it, you need to look carefully at the items being listed, then think very hard. When you see the clue, the problem is very easy.

The Mensa toy store is having a special sale of used toys. Everybody is confused about the prices. At this sale, a train costs $22, a cart costs $17, and a ball costs $17. How much would a shovel (the kind a child might use at the beach) cost under the Mensa system of setting prices? What would a truck cost?

Please explain clearly how you arrive at your solution. Now write one equation (nope not y = mx + b,) that would allow you to find the price of any toy you can think of in the Mensa toy store. Explain your equation and what your variable(s) represent.

Car Rental Quandary

2009-08-21T00:24:00.000-07:00

I need to rent a car for my upcoming trip. Rent-A-Gem charges $20.25 per day plus 14 cents per mile. Super Saver Rentals charges $18.25 per day plus 22 cents per mile. At first glance it looks as if I should go with Super Saver Rentals. Still, I'm concerned about the per-mile charge because I plan to do a lot of driving during all three days of my trip.

Which company should I use?
How many miles would I have to drive to make the cost of renting a car from Rent-A-Gem the same as the cost of renting a car from Super Saver Rentals?

Be sure that you give all the details of your solution, including comparing all three tools that can be used to determine the correct answer.

This took a bit for you to get started on, but you did a beautiful job. Make sure to keep in mind that you have three tools that will come in handy for many of these problems. Many of you choose to make a table here, but struggled with what the headings were and what kind of a scale to use. Excel seemed to help with some of those concerns.

Solution:
Super Saver Rentals is cheaper if I'm only driving a few miles, but Rent-A-Gem is cheaper if I'm going to be driving a lot of miles, at 75 miles the two costs are equal for both companies. I have included the tables that you sent to illustrate your points. They are listed below.

Ms. L.