WAYS TO GO
GOALS
1.
Read,
interpret, and create a variety of maps, including scale maps.
2.
Draw,
create, and interpret finite graphs and matrices.
3.
Use
organized strategies to count the number of outcomes.
4.
Calculate
the probability of a simple event and predict an expected value.
5.
Explore
and compare different representations for distances and recognize the
advantages and disadvantages.
6.
Understand
the relationship between a finite graph and a corresponding matrix.
7.
Solve
simple problems using graphs and/or connectivity matrices.
8.
Solve
simple problems using organized counting strategies, tree diagrams, and chance
trees.
9.
Organize
information and use smart counting techniques to solve combinatorial problems.
10.
Model
real-life situations.
11.
Take
a critical attitude toward the use of mathematical models.
1.
Models
differ in how closely they resemble reality.
2.
We
considered distances from three perspectives: driving distance; driving time;
and as-the-crow-flies.
3.
It
is possible to draw maps to scale reflecting each of the above distances.
4.
Maps
are usually drawn with cities in accurate geographical locations representing
as-the-crow-flies distances. To make
maps to scale for driving distances, you may have to change the locations of
the cities.
1.
Graphs
and matrices are two ways of representing information. A graph can be associated with a
connectivity matrix.
2.
Graphs
are considered the same if their connections are the same, even if the points
are in different places.
3.
The
degree of connectivity is a measure of how connected a graph is and is
determined with this formula:
Degree of connectivity = Number of edges divided by
Maximum number of edges possible.
4.
In
a maximally connected graph, there is an edge connecting every point to every
other point.
5.
The
degree of connectivity of a maximally connected graph is 100%.
6.
A
minimally connected graph has just enough edges so that you can get from any
point to any other point eventually.
SECTION C: How Many Ways
1. In
many cases, the number of possibilities is so big that you need a systematic
way to find all of them.
2. Using
letters is a convenient way to keep track of a possible route.
3. A
tree diagram can also be helpful to determine the total number of choices or
possiblities.
4. Tree
diagrams are also used to describe pairing possibilities for tournaments.
SECTION D: Chance Trees
1. In
this section you extended the chance tree to include the probability of two or
more events occurring.
2. The
chance of an event occurring = # of time an event occurs divided by total # of
possible events.
3. If
the chance that a single car will head toward D is 1/5, or 0.2, this ratio is
referred to as the probability
that a single car will turn toward point D. This probability is commonly written as p = 1/5 (as a fraction).