| NSES Content Standard Unifying Concepts
and Processes:
Systems, order, and organization Grades K-12, page 116 Prediction is the use of knowledge to identify and explain observations,
or changes, in advance. The use of mathematics, especially probability
allows for greater or lesser certainty of predictions.
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Benchmark 9C The Mathematical World:
Shapes
Grades 6-8, page 224
The graphic display of numbers may help to show patterns such as trends,
varying rates of change, gaps, or clusters. Such patterns sometimes can
be used to make predictions about the phenomena being graphed.
Benchmark 9D The Mathematical World:
Uncertainty
Grades K-2, page 227
Some things are more likely to happen that others. Some events can
be predicted well and some cannot. Sometimes people aren't sure what will
happen because they don't know everything that might be having an effect.
Benchmark 9D The Mathematical World:
Uncertainty
Grades 3-5, page 227
Some predictions can be based on what is known about the past, assuming
that conditions are pretty much the same now.
Benchmark 9D The Mathematical World:
Uncertainty
Grades 3-5, page 227
Statistical predictions (as for rainy days, accidents) are typically
better for how many of a group will experience something than for which
members of the group will experience it—and better for how often something
will happen than for exactly when.
Benchmark 9D The Mathematical World:
Uncertainty
Grades 3-5, page 228
Summary predictions are usually more accurate for large collections
of events than for just a few. Even very unlikely events may occur fairly
often in very large populations.
Benchmark 9D The Mathematical World:
Uncertainty
Grades 6-8, page 229
Events can be described in terms of being more or less likely, impossible,
or certain.
Benchmark 11B Common Themes: Models
Grades 6-8, page 269
Mathematical models can be displayed on a computer and then modified
to see what happens.
Benchmark 11B Common Themes: Models
Grades 9-12, page 270
The basic idea of mathematical modeling is to find a mathematical relationship
that behaves in the same ways as the objects or processes under investigation.
A mathematical model may give insight about how something really works
or may fit observations very well without any intuitive meaning.
Benchmark 11B Common Themes: Models
Grades 9-12, page 270
Computers have greatly improved the power and use of mathematical models
by performing computations that are very long, very complicated, or repetitive.
Therefore computers can show the consequences of applying complex rules
or of changing the rules. The graphic capabilities of computers make them
useful in the design and testing of devices and structures and in the simulation
of complicated processes.
Benchmark 11B Common Themes: Models
Grades 9-12, page 270
The usefulness of a model can be tested by comparing its predictions
to actual observations in the real world. But a close match does not necessarily
mean that the model is the only "true" model or the only one that would
work.
See also Chapter 11 Common Themes, Section B: Models, for precursor ideas.