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Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Level 6
Objectives and Content - Level 2
Marvelous Matrices (matrix
operations)
In this module, students will:
- organize and interpret data using matrices
- use matrices in business applications
- add and subtract two matrices
- multiply a matrix by a scalar
- multiply two matrices
- interpret the meaning of the elements
within a product matrix
A New Angle on an Old Pyramid
(Pythagorean theorem and right angle
trigonometry)
In this module, students will:
- use similarity to determine unknown
measures in triangles
- use the Pythagorean theorem and
its converse to solve right-triangle problems
- use technology to develop a table
of trigonometric values
- develop and apply the sine, cosine,
and tangent ratios
- develop and apply the inverses
of sine, cosine, and tangent
When to Deviate from a Mean
Task
(measures of central tendency)
In this module, students will:
- create a frequency table from raw data
- interpret data displayed in histograms
- interpret data displayed in pie
charts
- interpret data displayed in stem-and-leaf
plots
- interpret data displayed in box-and-whisker
plots
- find measures of central tendency
- determine mean absolute deviation
- determine standard deviation
Who Gets What and Why (apportionment)
In this module, students will:
- use and interpret inequalities
involving rational expressions
- examine the geometric mean
- simplify rational expressions
What Are My Child's Chances?
(probability)
In this module, students will:
- collect data and calculate experimental
probabilities
- use Punnett squares and tree diagrams
to determine sample spaces
- determine the theoretical probabilities
of events
- compare experimental probabilities
and theoretical probabilities
- investigate formulas for determining
the probability of two or more events
- identify complementary, independent,
dependent, and mutually exclusive events
- simulate a situation involving
independent events
There's No Place Like Home
(volume and surface area)
In this module, students will:
- determine the areas of regular
polygons and circles
- determine the surface areas and
volumes of prisms, pyramids, cylinders, and cones
- calculate the surface areas and
volumes of spheres
- identify a circle as the limiting
shape for its inscribed regular polygons, a cylinder as the limiting
shape for its inscribed regular prisms, and a cone as the limiting shape
for its inscribed regular pyramids
Making Concessions
(linear programming and solving systems
of equations)
In this module, students will:
- determine constraints for linear
programming problems
- write objective functions
- interpret the meaning of points
in a feasible region
- find the corner points of a feasible
region
- develop the corner principle for
optimization
- find solutions to systems of inequalities
in two variables
- solve systems of equations in
two and three variables graphically, algebraically (by substitution),
and by using matrices
- use linear programming to make
decisions involving the buying and selling of goods
Crazy Cartoons (transformational
geometry)
In this module, students will:
- use the properties of similar
figures
- calculate distances between points
in the Cartesian plane
- explore the geometric relationships
in perspective drawings, dilations centered at the origin, translations,
rotations about the origin, reflections, and composite transformations
- write matrices for dilations centered
at the origin, translations, rotations about the origin, and reflections
- use matrix equations to transform
geometric figures on the Cartesian plane
Hurry! Hurry! Hurry! Step
Right Up! (geometric probability)
In this module, students will:
- use geometric models for determining
probability
- use expected value to determine
fair games
- explore probabilities of multistage
experiments
- examine the difference between
independent and dependent events
- explore conditional probability
Atomic Clocks Are Ticking
(negative and fractional exponents)
In this module, students will:
- develop models of exponential
decay
- examine the relationship between
negative and positive exponents
- use equations containing negative
exponents as mathematical models
- examine the relationship between
rational exponents and roots
- develop properties of exponents
And the Survey Says… (sampling)
In this module, students will:
- use a variety of sampling techniques
- predict the characteristics of
a population based on samples
- explore the role that biases play
in sampling
- use histograms to estimate probabilities
and make predictions
- investigate how sample size affects
a survey's reliability
- explore confidence statements
and margins of error
Traditional Design (geometric
properties)
In this module, students will:
- use paper-folding constructions
to examine angle bisectors, perpendicular lines, parallel lines, and
midpoints
- explore properties of angles formed
by parallel lines and a transversal
- explore geometric rep tiles
- identify relationships between
tangents and secants
- examine properties of parallelograms
(specifically rhombi)
- examine similar triangles created
by dilations
If the Shoe Fits… (linear
models)
In this module, students will:
- use the sum of the absolute values
of the residuals to compare how well linear models fit a set of data
- model data using the median-median
line
- use the least-squares method to
find a linear regression equation
- graph and analyze residual plots
Take It to the Limit (sequences
and series)
In this module, students will:
- identify sequences that are arithmetic,
geometric, or neither
- develop formulas for finite arithmetic
and geometric series
- develop a formula for certain
infinite geometric series
- explore limits graphically and
geometrically
Algorithmic Thinking (algorithm
construction and use)
In this module, students will:
- construct algorithms
- use algorithmic thinking
- examine the efficiency of
algorithms
- organize algorithms into flowcharts
- develop algorithms that use recursion
