NSES Content Standard Unifying Concepts
and Processes:
Systems, order, and organization Grades K12, page 117 Orderthe behavior of units of matter, objects, organisms, or events
in the universecan be described statistically. Probability is the relative
certainty (or uncertainty) that individuals can assign to selected events
happening (or not happening) in a specified space or time. In science,
reduction of uncertainty occurs through such processes as the development
of knowledge about factors influencing objects, organisms, systems, or
events; better and more observations; and better explanatory models.

Benchmark 4E The Physical Setting: Energy
Transformations
Grades 912, page 86
Heat energy in a material consists of the disordered motions of its
atoms or molecules. In any interactions of atoms or molecules, the statistical
odds are that they will end up with less order than they beganthat is,
with the heat energy spread out more evenly. With huge numbers of atoms
and molecules, the greater disorder is almost certain.
Benchmark 9D The Mathematical World:
Uncertainty
Grades 68, page 229
How probability is estimated depends on what is known about the situation.
Estimates can be based on data from similar conditions in the past or on
the assumption that all the possibilities are known.
Benchmark 9D The Mathematical World:
Uncertainty
Grade 6, page 229
Probabilities are ratios and can be expressed as fractions, percentages,
or odds.
Benchmark 9D The Mathematical World:
Uncertainty
Grade 6, page 229
The larger a wellchosen sample is, the more accurately it is likely
to represent the whole. But there are many ways of choosing a sample that
can make it unrepresentative of the whole.
Benchmark 9D The Mathematical World:
Uncertainty
Grade 9, page 230
Even when there are plentiful data, it may not be obvious what mathematical
model to use to make predictions from them or there may be insufficient
computing power to use some models.
Benchmark 9D The Mathematical World:
Uncertainty
Grade 9, page 230
A physical or mathematical model can be used to estimate the probability
of realworld events.
Benchmark 11C Common Themes: Constancy
and Change
Grades 912, page 275
Most systems above the molecular level involve so many parts and forces
and are so sensitive to tiny differences in conditions that their precise
behavior is unpredictable, even if all the rules for change are known.
Predictable or not, the precise future of a system is not completely determined
by its present state and circumstances but also depends on the fundamentally
uncertain outcomes of events on the atomic scale.
Science for All Americans The Mathematical
World
Chapter 9, page 135
Our knowledge of how the world works is limited by at least five kinds
of uncertainty: (1) inadequate knowledge of all the factors that may influence
something, (2) inadequate number of observations of those factors, (3)
lack of precision in the observations, (4) lack of appropriate models to
combine all the information meaningfully, and (5) inadequate ability to
compute from the models. It is possible to predict some events with great
accuracy (eclipses), others with fair accuracy (elections), and some with
very little certainty (earthquakes). Although absolute certainty is often
impossible to attain, we can often estimate the likelihoodwhether large
or smallthat some things will happen and what the likely margin of error
of the estimate will be.