.
Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Level 6
Objectives and Content - Level 3
From Here to There
(3D coordinate system)
In this module, students will:
- create three-dimensional coordinate
systems
- plot points in three-dimensional
space
- determine the distance formula
for three dimensions
- create profiles of the terrain
between two points on a topographic map
What Are You Eating?
(linear programming and solving systems
of equations)
In this module, students will:
- express constraints as a system
of inequalities
- graph feasible regions and find
the feasible points
- minimize or maximize objective
functions using the corner principle
- solve systems of linear equations
graphically and algebraically
- represent systems of linear equations
as matrix equations
- solve a matrix equation
- use matrices to solve systems
of equations
- identify consistent and inconsistent
systems of equations
What's Your Bearing?
(trigonometric ratios in general triangles)
In this module, students will:
- apply the right-triangle trigonometric
ratios: sine, cosine, and tangent
- use bearings to complete survey
maps
- divide plots of land into triangles
to minimize the number of measurements required to determine the length
of sides and areas of polygons
- develop and use the Law of Sines
- develop and use the Law of Cosines
- use trigonometric ratios to find
the areas of triangles
Taste Test (combinatorics)
In this module, students will:
- review the fundamental counting
principle
- review factorial notation
- determine the number of permutations
possible for a given situation
- determine the number of combinations
possible for a given situation
- determine whether to use a permutation
or a combination in a situation
- use permutations and combinations
to determine probability
Classical Crystals (polyhedra)
In this module, students will:
- develop spatial visualization
skills
- discover the symmetrical properties
of regular polygons
- design nets for and build models
of some classical solids
- find duals (or reciprocals) of
the Platonic solids
- explore a relationship among the
edges, faces, and vertices of polyhedra
Strive for Quality (binomial
probability)
In this module, students will:
- model sampling with binomial experiments
- develop the binomial probability
formula
- derive theoretical binomial probabilities
- determine the expected value of
a binomial experiment
Graphing the Distance (linear
and quadratic functions)
In this module, students will:
- create distance-time graphs
- distinguish between speed
and velocity
- calculate average speed and
average velocity
- calculate average acceleration
- model distance-time graphs using
linear and quadratic equations
Fair is Fair (fair
division)
In this module, students will:
- study the properties of fair division
- investigate algorithms that result
in fair divisions
- make fair divisions by dividing
an item considered continuous between two or more people
- make fair divisions by dividing
a set of items considered discrete among two or more people
Let the Games Begin
(logical connectives)
In this module, students will:
- use the logical connectives and
and or to form compound statements
- use Venn diagrams to illustrate
the logical connectives and and or
- explore the relationship between
and and intersection and the relationship between or and
union
- develop the truth tables for "p
and q" and "p or q"
- use the logical operator not to
negate statements
- develop truth tables using "not"
with statements and compound statements, such as "~p and
q" and "~p or q"
- use the logical conditional p
–> q
- use tables, the process of elimination,
and contrapositive reasoning as problem-solving techniques
What's Your Orbit? (modeling
data with polynomials)
In this module, students will:
- find models for data sets by examining
graphs
- use the principle of least squares
to determine how well a model fits the data
- model data sets using linear,
exponential, power, quadratic, and cubic regressions
- examine some of the limitations
of fitted equations as models
Our Town (graph
theory)
In this module, students will:
- organize information using graphs
- identify different graphs and
their modeling uses
- use graphs to model real-world
situations
- identify and create Eulerian circuits
- discover two traversability theorem
- use digraphs to model real-world
situations
- use matrices to analyze graphs
One Dish and Two Cones (conic
sections)
In this module, students will:
- create four conic sections by
tracing a locus of points on a geometry utility
- use the geometric relationships
among reflected objects
- investigate the local linearity
of curves
- explore the reflective properties
of the parabola
Finding Gold
(golden ratio)
In this module, students will:
- examine the golden section as
ø
- investigate numerical relationships
involving the golden section
- generate sets of Pythagorean triples
- investigate Fibonacci numbers
- explore relationships among Fibonacci
numbers, Pythagorean triples, and the golden section
- examine various proofs of the
Pythagorean Theorem
Banking on Life (mathematics
of finance)
In this module, students will:
- calculate simple interest,
compound interest, and amortization payments
- evaluate the appropriateness
of regression models
- solve linear and exponential equations
