Tips for the "new" 7th grade AEP!

O.k. here is your chance to help out next years group. Please provide three helpful tips for successful completion of 7th grade honors.

Then provide a name, either you or one of your peers to organize the data (tips) and reorganize it in a manner that will be meaningful for our new group.

thx,
Ms. Leckman

Re-visit Function This Function That

Lovely, Lovely 8th grade students,

Just a note that this POW is a bit disasterous! Computation errors, in-accurate applications of order of operation... There are maybe two equations or answers that are correct from this blog. Please go back and re-visit the problem, then post where you think you went wrong, how you 'fixed it,' and your new equation and solutions. Whew! Scary! HELP!

Ms. Leckman

8th Grade POW

Your first task is to visit last weeks blog and post responses to the 7th graders. :-) Then find yourself a partner. Today's blog will require a bit of work and you may want some assistance. Make sure to put BOTH partners initials at the top for your post so I can credit BOTH of you. :-)
IMPORTANT!!! Be careful, some of the 7th grade questions ask for names - I WILL NOT POST WITH TEACHERS NAMES OR INTIALS. However you may discuss tough content areas and how to make themselves and their teachers happy to ensure a success and or pleasant 8th grade year. :-)

Here is your second task:

Function This Function That

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:














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? Let x = 2 (or your 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. (Make sure to include your function in well formed, symbolic notation.)

7th Grade POW

New Home for Fibonacci and Descartes

Ms. Leckman decided that the Math Club mascots, Fibonacci and Descartes, had outgrown their 10-gallon home, so this weekend she picked up a 15-gallon aquarium at a flea market. Oliver and Suzanne have been assigned the task of setting up the new aquarium. They have been instructed to fill it exactly three-quarters of the way to the top. Fibonacci and Descartes will be transferred with some of the water from their current environment to help them adjust to their new home. Unfortunately, Suzanne and Oliver can not find a clean bucket for carrying water to the aquarium. All they can find are two eight-ounce glasses. Working from the sink to the left of the aquarium stand, Suzanne takes 45 seconds to fill one glass and dump it into the aquarium. Working from the sink to the right of the aquarium, Oliver can fill one glass and dump it into the tank in 39 seconds.

If Suzanne and Oliver start at noon and keep working at these constant rates, what time will they complete their task? Which student will add the last glass of water?

Remember there are a number of ways to solve this – so be sure to explain and show how you arrived at your solution to obtain credit for this assignment.

Extra Credit: What percentage of the tank is filled by each student?