Fences and Party Planning

While we catalog the year and review the basic component skills learned thus far, we are going to be doing extended investigations of rational expressions (in Precalc) and of quadratics (in Algebra II) in the contexts of design, projectile motion, and event planning.

Precalculus will be "Planning a Summer Camp" based on a College Board Springboard investigation with the following opening scenario:

"You have been appointed to the finance committee of a nonprofit summer camp for children.  The camp will be held in one-week sessions, beginning with breakfast on Monday morning and ending with dinner on Friday evening, each week throughout the summer.

The fixed cost for the camp, which includes rent, staff salaries, staff meals, and all equipment and materials for the recreational activities, will be $2400 per day.  Although the camp has dining facilities for the staff, ti must pay an outside vendor to provide all meals for the campers.  After contacting  a food service vendor, you learn that this additional cost will be $3 per camper, per meal.

As a nonprofit camp, the camp must cover it costs, but does not need to make a profit.  The finance committee does not know how much to charger for a week at the summer camp, so the director is requesting that the committee submit a proposal for setting the fee for reach camper based on the number of campers who are expected to attend each week."

Homework (from www.jmap.org; feel free to check your answers there!)



Algebra 2 will be working with a variety of area situations involving "Fences" and "Rockets in Flight" (the name of the Springboard investigation), which open as follows:

"You are employed by Fence Me In, a business that specializes in building fenced enclosures for both businesses and residences.  Your job is to build enclosures on your client's properties.  One client has purchased a certain length of fencing and wants to enclose the largest possible rectangular area in her yard." (Fences)

"Cooper is a model rocket enthusiast.  The model rockets in cooper's collection hve single engines and when launched can rise as high as 1000 feet depending upon the size of the engine.  After the engine is ignited, it will burn for 3-5 seconds and the rocket will accelerate upward.  Once the engine burns out, the rocket will be in free fall, because the only acceleration is due to gravity.  The rocket has a parachute that will open as the rocket begins to fall back to Earth.

Cooper decides to track one of his rockets, the Eagle, so that he can investigate its time and height while in flight.  He installs an altimeter into the nose of the Eagle.  The altimeter will record the time and the height of the rocket as it falls back to Earth and will be activated when the parachute opens.  The data for one flight of the Eagle is shown in the table below."

Homework (from www.jmap.org; feel free to check your answers there!)