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Level 1 | Level 2 | Level 3 | Level 4 | Level 5 | Level 6
Objectives and Content - Level 5
Re-Invent the Wheel (curves
of constant width)
In this module, students will:
- explore curves of constant width
- construct and use lines of support
for curves
- develop a formula for the perimeter
of curves of constant width
- determine the area of curves of
constant width
- explore applications of curves
of constant width in real-world situations
Sunken Sub (geometric
probability)
In this module, students will:
- use geometric models to describe
events and sample spaces
- examine geometric probability
in one and two dimensions
- combine geometric probability
and conditional probability in multistage settings
How Long Is This Going To
Take? (scheduling theory)
In this module, students will:
- apply the nearest neighbor and
cheapest link algorithms
- use network diagrams to analyze
scheduling problems
- revise schedules given specific
constraints
- use bin packing to analyze problems
A Ride With Markov (matrices)
In this module, students will:
- calculate the probabilities of
transitions
- create and interpret transition
diagrams
- identify Markov chains and the
states of Markov chains
- create and interpret transition
matrices and state vectors
- identify and use stable state
matrices and vectors
Let There Be Light (conic
sections)
In this module, students will:
- investigate the reflective
properties of the four conic sections
- write equations for conics
in standard form
- use conics to design curves
for practical applications
Risky Business (expected
value)
In this module, students will:
- examine the law of large numbers
- analyze the significance of the
law of large numbers in making predictions
- explore random variables and their
probability distributions
- use expected value to set insurance
premiums
Wilderness Wanderings (vectors)
In this module, students will:
- use vector terminology
- model displacement, velocity,
and force with vectors
- represent vectors graphically
and as ordered pairs
- find resultant vectors both
graphically and algebraically
- determine the horizontal and
vertical components of vectors both graphically and algebraically
Making Cents of Your Income
(confidence intervals)
In this module, students will:
- estimate a population mean
using sample means
- estimate the standard deviation
of a population using the standard deviation of a sample
- use the standard deviation
of a sample to construct confidence intervals
- use the 68%-95%-99.7% rule
to determine the probability that the population mean lies within certain
confidence intervals
- formulate null and alternative
hypotheses
- use confidence intervals to
estimate a population mean
- use confidence intervals to test a hypothesis
Is It Really True? (logic)
In this module, students will:
- define the negation of statements
using the quantifiers some, all, and none
- recognize and write logically
equivalent statements
- write negation statements
- determine the difference between
the inclusive or and the exclusive or through truth tables,
Venn diagrams, and English usage
- investigate the negations of compound
state ments through truth tables, Venn diagrams, and De Morgan's laws
- determine the truth values of
a conditional statement using truth tables
- investigate the converse, the
inverse, and the contrapositive of the conditional
Pixel This (algorithms)
In this module, students will:
- study the characteristics of algorithms
- write algorithms for general and
specific applications
- use transformation matrices to
generate graphs of relations and functions
A Fitting Explanation (regression
equations)
In this module, students will:
- calculate the correlation coefficient
r of a regression line
- calculate the coefficient of determination
r2 as
a percentage of variation
- use r2
to explain the linear association of the variables in a set of data
- use regression equations to make
predictions and determine approximation intervals
- analyze appropriate and inappropriate
uses of regression equations
The Game of Life (game
theory)
In this module, students will:
- investigate the properties of
strictly determined games
- construct and interpret payoff
matrices
- find and interpret the saddle
points of payoff matrices
- find the expected values of games
- identify when pure strategies
or mixed strategies should be used
- find an optimal strategy for each
player in a game
A Walk on the Wild Side
(sampling procedures and confidence
intervals)
In this module, students will:
- take simple random samples from
populations
- use technology to simulate sampling
procedures
- develop sampling distributions
- develop the 68%-95%-99.7% rule
of sampling distributions
- determine confidence intervals
from random samples
- use the capture-recapture method
to estimate population size
Catch a Wave (trigonometric
functions)
In this module, students will:
- use radian measures for angles
- pair the real numbers with
the points on a unit circle
- graph sine, cosine, and tangent
curves
- identify the amplitude and
period of a circular function
- use the sine and cosine functions to model circular motion and sound waves
