Portfolio
Projects Guidelines
To make a
portfolio, an artist selects a variety of original work to represent the range
of his or her skills. Each
of the portfolio projects that you will be assigned will give you a chance to
create a finished product that you will be proud to add to your mathematics
portfolio.
These projects
will help you develop your ability to present and communicate your ideas.
They will
also help you develop your problem-solving and reasoning abilities as you make
connections between what you know and what is new. Your
individual insight and creativity will help shape the mathematics you discover.
Let these
projects be springboards for further exploration. Feel
free to expand them to include new questions or areas of interest that arise.
Most of
all, have fun!!
Requirements:
Each portfolio
project must have:
1) A cover page
which includes the title, chapter, author’s name (that’s you) and date
finished.
2) Original
portfolio assignment sheet
3) Completed
portfolio assignment with several investigations (not just one or two)
We will begin
the first one together, so you will fully understand what is expected of you
for these projects.
AMDG
Portfolio Project
Chapter 4
Bumper-to-Bumper
Traffic volume and traffic density are two measures of the
number of cars on a highway at any given time. The average
speed maintained by cars on a highway depends in part on both the traffic
volume and the traffic density.
Traffic
volume is the number of cars per hour (cars/h) that pass a given point.
Traffic
density is the average number of cars per mile (cars/mi).
1. Suppose that
there are 2 cars in every mile of highway, and that the cars are traveling at
an average speed of 50 mi/h. What is the traffic volume?
Draw a picture and explain your method.
2. Find the
traffic volume for a highway on which cars are traveling at an average speed
of 40 mi/h with a density of 15 cars/mi.
3. For a given
stretch of highway, let s = the average speed in mi/h of cars on the
highway, let v = the traffic volume in cars/h, and let d = the
traffic density in cars/mi. Write a formula relating these
three variables.
4. For any fixed
average speed, what happens to the traffic volume as traffic density increases?
Will this always happen? Please explain.
5. Two lanes of
bumper-to-bumper traffic merge into one lane. The cars are
moving at an average speed of 10 mi/h before the merge. If
the traffic volume is the same before and after the merge, then what is the
average speed of the cars immediately after the merge? Please
explain your reasoning.