.
Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Level 6
Objectives and Content - Level 4
Colorful Scheduling (coloring
theory)
In this module, students will:
- determine the chromatic number
of a map
- investigate the four-color theorem
for maps drawn on flat surfaces and spheres
- create graphs of maps
- solve scheduling problems using
graphs and coloring theory
- identify topologically equivalent
graphs
- identify planar graphs
- determine the relationship between
chromatic number and the number of vertices of a complete planar graph
Can It!
(trigonometric functions)
In this module, students will:
- identify circular functions by
shape
- identify the amplitude and period
of a circular function
- write the equations of sine or
cosine curves from graphs
- graph sine or cosine curves given
an equation
- use sine or cosine curves to model
real-world data
- determine the transformations
of the graph of the circular function f generated by a,
b, c, and d when
- find the inverse trigonometric
function y = af (b(x+c)) +d
- use inverse functions to solve
trigonometric equations
Motion Pixel Productions
(transformational geometry)
In this module, students will:
- represent reflections, rotations,
translations, and dilations of objects in the plane using matrices
- represent points in homogeneous
matrix form
- express transformations and compositions
of transformations as single 3 x 3 matrices
- find the image of a figure under
a composite transformation
- express a glide reflection as
a composition of a reflection and a translation
Drafting and Polynomials
(polynomial functions)
In this module, students will:
- use the distributive property
to expand polynomials
- recognize and identify the graphs
of polynomial functions
- recognize the relationships among
the zeros, degree, and factors of a polynomial function
- use quadratic functions as mathematical
models
- use polynomial functions and their
graphs to model data sets
Log Jam
(exponents and logarithms)
In this module, students will:
- explore the properties of exponents
- use logarithmic scales to represent
data that covers a wide range of values
- explore properties of logarithms
- use base-10 logarithms to solve
equations
- interpret real number exponents
More or Less
(inequalities and pre-limit notions)
In this module, students will:
- interpret and solve linear, absolute
value, and polynomial inequalities
- create a graphical representation
leading to the concept of limit
- determine a set of images given
a set of pre- images and vice versa
Nearly Normal
(normal distribution)
In this module, students will:
- organize data using relative frequency
tables and graphs
- apply standard deviation
- explore the following types of
probability distributions: discrete, continuous, uniform, binomial,
and normal
Big Business (rational
functions)
In this module, students will:
- graph and interpret rational
functions, including domains, discontinuities, and asymptotes
- evaluate functions around
discontinuities and when |x| becomes large
- graph nonlinear inequalities
and systems of relations
Believe It or Not (proof)
In this module, students will:
- identify the hypothesis and
conclusion of a conditional statement
- identify the truth value of
a conditional
- use Venn diagrams to represent
conditionals
- negate conditionals
- find the converse, inverse,
and contrapositive of a conditional
- identify logically equivalent
conditionals
- write proofs using a chain
of if-then statements
- explore proof by exhaustion
- find counterexamples
- use deductive reasoning
- write direct proofs
- develop indirect proofs
Fly the Big Sky with Vectors
(vectors)
In this module, students will:
- define vectors
- add vectors
- multiply vectors by scalars
- use the laws of cosines and sines
- resolve vectors into components
- add vectors using components
Everyone Counts (combinatorics)
In this module, students will:
- review factorial notation and
the fundamental counting principle
- use tree diagrams, lists, and
charts to organize information and solve problems
- develop and use a formula for
permutations
- develop and use a formula for
combinations
It's All in the Family (function
transformations)
In this module, students will:
- recognize parent functions for
selected exponential, logarithmic, rational, and periodic functions
- develop skills for transforming
functions
- categorize functions into families
- find equations to model data sets
Confidence Builder (confidence
intervals)
In this module, students will:
- write null and alternative hypotheses
- create confidence intervals using
given data and data the students have generated
- use confidence intervals to make
decisions about null and alternative hypotheses
- design a simple experiment that
uses simple statistics to investigate a question of interest
Transmitting through Conics
(conic sections)
In this module, students will:
- examine a circle as a locus
of points
- develop the standard form
of the equation of a circle
- develop the distance formula
using the Pythagorean theorem
- examine a parabola as a locus
of points
- develop the standard form
of the equation of a parabola
- examine an ellipse as a locus
of points
- develop the standard form
of the equation of an ellipse
- examine a hyperbola as a locus
of points
- develop the standard form of the equation of a hyperbola
Controlling the Sky with
Parametrics (parametric equations)
In this module, students will:
- discover uses for the parametric
grapher
- use parametric equations to graph
functions
- discover how to use parametric
equations to graph conics
Having a Ball (non-Euclidean
geometry)
In this module, students will:
- describe the different types
of intrinsic curvature as they relate to the angle-sums of triangles
- explain why the Euclidean
property of similarity does not hold on spherical surfaces
- compare and contrast the Euclidean
properties with spherical properties
- compare and contrast spherical geometry with hyperbolic geometries from the historical context of Saccheri quadrilaterals
