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### Benchmark Standards

The following are the *Benchmarks for Scientific Literacy Standards *
that apply to the activities and materials found within this book. *Benchmarks
for Science Literacy *are recommendations for what all students should know
or be able to do in science, mathematics, and technology by the end of grades 2,
5, 8, and 12. The following benchmarks are divided by grade level and contain
the benchmark area, subsection and description of the benchmark.

Grades 3-5 |
Grades 6-8 | Grades 9-12

**Grades 3-5 **

Common Themes: Models

Geometric figures, number sequences, graphs, diagrams, sketches, number
lines, maps, and stories can be used to represent objects, events, and
processes in the real world, although such representations can never be exact
in every detail.

Common Themes: Models

Seeing how a model works after changes are made to it may suggest how the
real thing would work if the same were done to it.

The Designed World: Information Processing

Computers can be programmed to store, retrieve, and perform operations on
information. These operations include mathematical calculations, word
processing, diagram drawing, and the modeling of complex events.

The Living Environment: Evolution of Life

Fossils can be compared to one another and to living organisms according to
their similarities and differences. Some organisms that lived long ago are
similar to existing organisms, but some are quite different.

The Mathematical World: Numbers

Measurements are always likely to give slightly different numbers, even if
what is being measured stays the same.

The Mathematical World: Numbers

When people care about what is being counted or measured, it is important
for them to say what the units are (three degrees Fahrenheit is different from
three centimeters, three miles from three miles per hour).

The Mathematical World: Shapes

Scale drawings show shapes and compare locations of things very different
in size.

The Nature Of Mathematics: Mathematical Inquiry

In using mathematics, choices have to be made about what operations will
give the best results. Results should always be judged by whether they make
sense and are useful.

The Nature Of Mathematics: Patterns and Relationships

Mathematics is the study of many kinds of patterns, including numbers and
shapes and operations on them. Sometimes patterns are studied because they
help to explain how the world works or how to solve practical problems,
sometimes because they are interesting in themselves.

The Physical Setting: Motion

Changes in speed or direction of motion are caused by forces. The greater
the force is, the greater the change in motion will be. The more massive an
object is, the less effect a given force will have.

The Physical Setting: Processes That Shape the Earth

Waves, wind, water, and ice shape and reshape the earth's land surface by
eroding rock and soil in some areas and depositing them in other areas,
sometimes in seasonal layers.

**Grades 6-8 **

Common Themes: Models

Different models can be used to represent the same thing. What kind of a
model to use and how complex it should be depends on its purpose. The
usefulness of a model may be limited if it is too simple or if it is
needlessly complicated. Choosing a useful model is one of the instances in
which intuition and creativity come into play in science, mathematics, and
engineering.

Common Themes: Models

Mathematical models can be displayed on a computer and then modified to see
what happens.

Common Themes: Models

Models are often used to think about processes that happen too slowly, too
quickly, or on too small a scale to observe directly, or that are too vast to
be changed deliberately, or that are potentially dangerous.

Habits Of Mind: Computation and Estimation

Estimate distances and travel times from maps and the actual size of
objects from scale drawings.

The Living Environment: Evolution of Life

Many thousands of layers of sedimentary rock provide evidence for the long
history of the earth and for the long history of changing life forms whose
remains are found in the rocks. More recently deposited rock layers are more
likely to contain fossils resembling existing species.

The Mathematical World: Shapes

The scale chosen for a graph or drawing makes a big difference in how
useful it is.

The Nature Of Mathematics: Mathematics, Science, and Technology

Mathematics is helpful in almost every kind of human endeavor-- from laying
bricks to prescribing medicine or drawing a face. In particular, mathematics
has contributed to progress in science and technology for thousands of years
and still continues to do so.

The Nature Of Science: The Scientific Enterprise

Computers have become invaluable in science because they speed up and
extend people's ability to collect, store, compile, and analyze data, prepare
research reports, and share data and ideas with investigators all over the
world.

The Nature Of Science: The Scientific Enterprise

Important contributions to the advancement of science, mathematics, and
technology have been made by different kinds of people, in different cultures,
at different times.

The Physical Setting: Processes That Shape the Earth

Sedimentary rock buried deep enough may be reformed by pressure and heat,
perhaps melting and recrystallizing into different kinds of rock. These
re-formed rock layers may be forced up again to become land surface and even
mountains. Subsequently, this new rock too will erode. Rock bears evidence of
the minerals, temperatures, and forces that created it.

The Physical Setting: Processes That Shape the Earth

Sediments of sand and smaller particles (sometimes containing the remains
of organisms) are gradually buried and are cemented together by dissolved
minerals to form solid rock again.

The Physical Setting: Processes That Shape the Earth

Thousands of layers of sedimentary rock confirm the long history of the
changing surface of the earth and the changing life forms whose remains are
found in successive layers. The youngest layers are not always found on top,
because of folding, breaking, and uplift of layers.

Grades 9-12

Common Themes: Models

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.

Common Themes: Models

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.

Common Themes: Models

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.

Habits Of Mind: Communication Skills

Make and interpret scale drawings.

Habits Of Mind: Computation and Estimation

Consider the possible effects of measurement errors on calculations.

Habits Of Mind: Computation and Estimation

Find answers to problems by substituting numerical values in simple
algebraic formulas and judge whether the answer is reasonable by reviewing the
process and checking against typical values.

Historical Perspectives: Extending Time

Scientific evidence indicates that some rock near the earth's surface is
several billion years old. But until the 19th century, most people believed
that the earth was created just a few thousand years ago.

Historical Perspectives: Extending Time

The idea that the earth might be vastly older than most people believed
made little headway in science until the publication of Principles of Geology
by an English scientist, Charles Lyell, early in the 19th century. The impact
of Lyell's book was a result of both the wealth of observations it contained
on the patterns of rock layers in mountains and the locations of various kinds
of fossils, and of the careful logic he used in drawing inferences from his
data.

The Mathematical World: Shapes

Distances and angles that are inconvenient to measure directly can be found
from measurable distances and angles using scale drawings or formulas.

The Mathematical World: Symbolic Relationships

Any mathematical model, graphic or algebraic, is limited in how well it can
represent how the world works. The usefulness of a mathematical model for
predicting may be limited by uncertainties in measurements, by neglect of some
important influences, or by requiring too much computation.

The Nature Of Mathematics: Mathematical Inquiry

Much of the work of mathematicians involves a modeling cycle, which
consists of three steps: (1) using abstractions to represent things or ideas,
(2) manipulating the abstractions according to some logical rules, and (3)
checking how well the results match the original things or ideas. If the match
is not considered good enough, a new round of abstraction and manipulation may
begin. The actual thinking need not go through these processes in logical
order but may shift from one to another in any order.

The Nature Of Mathematics: Mathematics, Science, and Technology

Developments in mathematics often stimulate innovations in science and
technology.

The Nature Of Mathematics: Mathematics, Science, and Technology

Mathematical modeling aids in technological design by simulating how a
proposed system would theoretically behave.

The Physical Setting: The Universe

Mathematical models and computer simulations are used in studying evidence
from many sources in order to form a scientific account of the universe.