Transcript NCTM Series Focal Points - Oak

NCTM Series
Navigating through
Probability in Grades 9-12
AATM State Conference
September 27, 2008
Shannon Guerrero
Asst Professor, Math Education
Northern Arizona University
AATM Newsletter Editor
[email protected]
NCTM Navigation Series
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NCTM published series that offers
activities, ideas & materials to roadmap
implementation of Principles & Standards
Chapters organized around major
concepts of particular NCTM content
strand being targeted
NCTM Navigation Chapters
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Each chapter begins with discussion of
ensuing content & activities – provides big
picture of NCTM strand & associated
activities
Each activity consists of 3 elements –
Engage, Explore, & Extend
Each component contains suggested
materials, questions to pose, & teaching
tips
Contents of the CD-ROM
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Introduction
Table of Standards and Expectations, Number
and Operations, Pre-K-12
Applets
 Binomial Distribution Simulator
 Geometric Distribution Simulator
 Random Number Generator
 Adjustable Spinner
Blackline Masters and Templates
Readings from Publications of the National
Council of Teachers of Mathematics and Other
Sources
Why Study Probability?
What are the “big idea” of
probability for 9-12 grade students?
Why study probability?
• Chance is all around us – we do not live in
a totally deterministic world.
• People must make decisions in the face of
uncertainty.
• Probability is indispensable for analyzing
data; data are indispensable for estimating
probabilities.
“Big Ideas” of Probability with High
School Students
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Probability as long-run relative frequency
Determining probability through an
analysis of outcomes
Independence and conditional probability
Moving from sample spaces to probability
distributions
Expected value as “average” behavior in
the long run
Questions to Ponder
How could we begin to answer?
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What is the chance of an auto accident
occurring at a complicated intersection?
What is the chance that a boy will develop
hair loss if his father did?
What is the chance that a baseball player
will get two hits in three consecutive batting
attempts?
What is the chance that the stock market will
go up three days in a row?
Chapter 1 – Probability as Long-Run
Relative Frequency
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Simulation can be useful tool for estimating
probabilities
The cumulative stabilization of the relative
frequency of an outcome in a large number
of trials makes it a good estimate of the
probability of the outcome.
Chapter Two – Sample Spaces
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Students should be able to describe
sample spaces such as the set of possible
outcomes when four coins are tossed.
High school students should learn to
identify mutually exclusive, joint, and
conditional events.
All students should understand how to
compute the probability of a compound
event.
Chapter 3 – Independence and
Conditional Probabilities
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All students should understand the
concepts of conditional probability and
independent events.
Two outcomes are independent if the
occurrence of one does no change the
probability of the other.
Students can use the sample space to
answer conditional probability questions.
Chapter 4 – Probability Models and
Distributions
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Students can gather simulated data to
investigate the probability of an event.
Students can examine the declining
probabilities of strings of outcomes from
repeated trials.
All of the activities in this chapter direct
students to run multiple trials with random
numbers.
Chapter 5 – Expected Value
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Expected value – the average value in the
long run
All students should compute and interpret
the expected value of random variables in
simple cases.
Life insurance companies use expectedvalue calculations to determine premiums
that they can expect to attract customers
while ensuring a profit.