Big Arrangement

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

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

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

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

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

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.