Science
Technology
Engineering
Mathematics





Goals and Objectives 
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Curriculum 
Blueprint for Learning 
Classroom Resources 

Benchmarks for
Integrated
Curriculum 
35 BENCHMARKS 
A. Systems
By the end of 5th grade, students should know
that:
1.
In something that consists of many parts, the
parts usually influence one another.
2.
Something may not work as well (or at all) if a
part of it is missing, broken, worn out,
mismatched, or misconnected. 
B. Models
By the end of 5th grade, students should know
that:
1.
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.
2.
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. 
C. Constancy and Change
By the end of 5th grade, students should know
that:
1.
Some features of things may stay the same even
when other features change.
2.
Things change in steady, repetitive, or
irregular ways or sometimes in more than one way
at the same time. 
D. Scale
By the end of 5th grade, students should know
that:
1.
Almost anything has limits on how big or small
it can be.
2.
Finding out what the biggest and the smallest
possible values of something are is often as
revealing as knowing what the usual value is.

C. Mathematical Inquiry
By the end of 5th grade, students should know
that:
1.
Numbers and shapes and operations on them help
to describe and predict things about the world
around us.
2.
In using mathematics, choices have to be made
about what operations will give the best
results. 
A. Technology and Science
By the end of 5th grade, students should know
that:
1.
Throughout all of history, people everywhere
have invented and used tools.
2.
In earlier times, the accumulated information
and techniques of each generation of workers
were taught on the job directly to the next
generation of workers. Today, the knowledge base
for technology can be found as well in libraries
of print and electronic resources and is often
taught in the classroom.
3.
Measuring instruments can be used to gather
accurate information for making scientific
comparisons of objects and events and for
designing and constructing things that will work
properly.
4.
Technology extends the ability of people to
change the world: to cut, shape, or put together
materials; to move things from one place to
another; and to reach farther with their hands,
voices, senses, and minds. 

68 BENCHMARKS 
A. Patterns and Relationships
By the end of 8th grade, students should know
that:
1.
Usually there is no one right way to solve a
mathematical problem; different methods have
different advantages and disadvantages.
2.
Logical connections can be found between
different parts of mathematics. 
B. Mathematics, Science, and Technology
By the end of 8th grade, students should know
that:
1.
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. 
C. Mathematical Inquiry
By the end of 8th grade, students should know
that:
1.
Mathematicians often represent things with
abstract ideas, such as numbers or perfectly
straight lines, and then work with those ideas
alone.
2.
When mathematicians use logical rules to work
with representations of things, the results may
or may not be valid for the things themselves. 
A. Systems
By the end of 8th grade, students should know
that:
1.
A system can include processes as well as
things.
2.
Thinking about things as systems means looking
for how every part relates to others.
3.
Any system is usually connected to other
systems, both internally and externally. 
B. Models
By the end of 8th grade, students should know
that:
1.
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.
2.
Mathematical models can be displayed on a
computer and then modified to see what happens.
3.
Different models can be used to represent the
same thing. 
C. Constancy and Change
By the end of 8th grade, students should know
that:
1.
Physical and biological systems tend to change
until they become stable and then remain that
way unless their surroundings change.
2.
A system may stay the same because nothing is
happening or because things are happening but
exactly counterbalance one another.
3.
Many systems contain feedback mechanisms that
serve to keep changes within specified limits.
4.
Symbolic equations can be used to summarize how
the quantity of something changes over time or
in response to other changes.
5.
Symmetry (or the lack of it) may determine
properties of many objects, from molecules and
crystals to organisms and designed structures.
6.
Cycles, such as the seasons or body temperature,
can be described by their cycle length or
frequency, what their highest and lowest values
are, and when these values occur. 
D. Scale
By the end of 8th grade, students should know
that:
1.
Properties of systems that depend on volume,
such as capacity and weight, change out of
proportion to properties that depend on area,
such as strength or surface processes.
2.
As the complexity of any system increases,
gaining an understanding of it depends
increasingly on summaries, such as averages and
ranges, and on descriptions of typical examples
of that system. 
A. Technology and Science
By the end of 8th grade, students should know
that:
1.
In earlier times, the accumulated information
and techniques of each generation of workers
were taught on the job directly to the next
generation of workers.
2.
Technology is essential to science for such
purposes as access to outer space and other
remote locations, sample collection and
treatment, measurement, data collection and
storage, computation, and communication of
information.
3.
Engineers, architects, and others who engage in
design and technology use scientific knowledge
to solve practical problems. 

912 BENCHMARKS 
A. Systems
By the end of 12th grade, students should know
that:
1.
A system usually has some properties that are
different from those of its parts, but appear
because of the interaction of those parts.
2.
Understanding how things work and designing
solutions to problems of almost any kind can be
facilitated by systems analysis.
3.
The successful operation of a designed system
usually involves feedback.
4.
Even in some very simple systems, it may not
always be possible to predict accurately the
result of changing some part or connection. 
B. Models
By the end of 12th grade, students should know
that:
1.
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.
2.
Computers have greatly improved the power and
use of mathematical models by performing
computations that are very long, very
complicated, or repetitive.
3.
The usefulness of a model can be tested by
comparing its predictions to actual observations
in the real world. 
C. Constancy and Change
By the end of 12th grade, students should know
that:
1.
A system in equilibrium may return to the same
state of equilibrium if the disturbances it
experiences are small.
2.
Along with the theory of atoms, the concept of
the conservation of matter led to revolutionary
advances in chemical science.
3.
Things can change in detail but remain the same
in general (the players change, but the team
remains; cells are replaced, but the organism
remains).
4.
Graphs and equations are useful (and often
equivalent) ways for depicting and analyzing
patterns of change.
5.
In many physical, biological, and social
systems, changes in one direction tend to
produce opposing (but somewhat delayed)
influences, leading to repetitive cycles of
behavior.
6.
In evolutionary change, the present arises from
the materials and forms of the past, more or
less gradually, and in ways that can be
explained.
7.
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. 
D. Scale
By the end of 12th grade, students should know
that:
1.
Representing large numbers in terms of powers of
ten makes it easier to think about them and to
compare things that are greatly different.
2.
Because different properties are not affected to
the same degree by changes in scale, large
changes in scale typically change the way that
things work in physical, biological, or social
systems.
3.
As the number of parts of a system increases,
the number of possible interactions between
pairs of parts increases much more rapidly. 
A. Patterns and Relationships
By the end of 12th grade, students should know
that:
1.
Mathematics is the study of any patterns or
relationships, whereas natural science is
concerned only with those patterns that are
relevant to the observable world.
2.
As in other sciences, simplicity is one of the
highest values in mathematics.
3.
Theories and applications in mathematical work
influence each other.
4.
New mathematics continues to be invented, and
connections between different parts of
mathematics continue to be found. 
B. Mathematics, Science, and Technology
By the end of 12th grade, students should know
that:
1.
Mathematical modeling aids in technological
design by simulating how a proposed system would
theoretically behave.
2.
Mathematics and science as enterprises share
many values and features: belief in order,
ideals of honesty and openness, the importance
of criticism by colleagues, and the essential
role played by imagination.
3.
Mathematics provides a precise language for
science and technology—to describe objects and
events, to characterize relationships between
variables, and to argue logically.
4.
Developments in science or technology often
stimulate innovations in mathematics by
presenting new kinds of problems to be solved.
5.
Developments in mathematics often stimulate
innovations in science and technology. 
C. Mathematical Inquiry
By the end of 12th grade, students should know
that:
1.
Some work in mathematics is much like a game
mathematicians choose an interesting set of
rules and then play according to those rules to
see what can happen.
2.
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. 
A. Technology and Science
By the end of 12th grade, students should know
that:
1.
Technological problems often create a demand for
new scientific knowledge, and new technologies
make it possible for scientists to extend their
research in new ways or to undertake entirely
new lines of research.
2.
Mathematics, creativity, logic and originality
are all needed to improve technology.
3.
Technology usually affects society more directly
than science because it solves practical
problems and serves human needs (and may create
new problems and needs). 

NATIONAL SCIENCE EDUCATION STANDARDS 
From
Chapter 6, download all of the
standards for K4, 58 and 912 related to this topic.
Enter below. 
Go to NSES… 
K4 STANDARDS 
CONTENT STANDARD A:
As a result of activities in grades K4, all students
should develop
·
Abilities
necessary to do scientific inquiry
·
Understanding about scientific inquiry

58 STANDARDS 
CONTENT STANDARD A:
As a result of activities in grades 58, all students
should develop
·
Abilities
necessary to do scientific inquiry
·
Understandings about scientific inquiry

912 STANDARDS 
CONTENT STANDARD A: As a
result of activities in grades 912, all students should
develop
·
Abilities
necessary to do scientific inquiry
·
Understandings about scientific inquiry
PROGRAM STANDARD A:
All elements of the K12 science program must be
consistent with the other National Science Education
Standards and
with one another and developed within and across grade
levels to meet a clearly stated set of goals.
·
In an
effective science program, a set of clear goals and
expectations for students must be used to guide the
design, implementation, and assessment of all elements
of the science program.
·
Curriculum
frameworks should be used to guide the selection and
development of units and courses of study.
·
Teaching
practices need to be consistent with the goals and
curriculum frameworks.
·
Assessment
policies and practices should be aligned with the goals,
student expectations, and curriculum frameworks.
·
Support
systems and formal and informal expectations of teachers
must be aligned with the goals, student expectations and
curriculum frameworks.
·
Responsibility needs to be clearly defined for
determining, supporting, maintaining, and upgrading all
elements of the science program.

CONTENT CLARIFICATION BUILDER
Related Content Knowledge 
SCIENCE FOR ALL AMERICANS 
 Science for All
Americans is based on the belief that the
scienceliterate person is one who is aware that
science, mathematics, and technology are
interdependent human enterprises with strengths
and limitations; understands key concepts and
principles of science; is familiar with the
natural world and recognizes both its diversity
and unity; and uses scientific knowledge and
scientific ways of thinking for individual and
social purposes.
Some important themes pervade science,
mathematics, and technology and appear over and over
again, whether we are looking at an ancient
civilization, the human body, or a comet. They are ideas
that transcend disciplinary boundaries and prove
fruitful in explanation, in theory, in observation, and
in design.
It is the union of science, mathematics, and
technology that forms the scientific endeavor and that
makes it so successful. Although each of these human
enterprises has a character and history of its own, each
is dependent on and reinforces the others

Science provides
mathematics with interesting problems to
investigate, and mathematics provides science with
powerful tools to use in analyzing data. Often,
abstract patterns that have been studied for their
own sake by mathematicians have turned out much
later to be very useful in science. Science and
mathematics are both trying to discover general
patterns and relationships, and in this sense they
are part of the same endeavor.

Mathematics is the
chief language of science. The symbolic language of
mathematics has turned out to be extremely valuable
for expressing scientific ideas unambiguously.

Mathematics and
science have many features in common. These include
a belief in understandable order; an interplay of
imagination and rigorous logic; ideals of honesty
and openness; the critical importance of peer
criticism; the value placed on being the first to
make a key discovery; being international in scope;
and even, with the development of powerful
electronic computers, being able to use technology
to open up new fields of investigation.

Mathematics and
technology have also developed a fruitful
relationship with each other. The mathematics of
connections and logical chains, for example, has
contributed greatly to the design of computer
hardware and programming techniques. Mathematics
also contributes more generally to engineering, as
in describing complex systems whose behavior can
then be simulated by computer. In those simulations,
design features and operating conditions can be
varied as a means of finding optimum designs. For
its part, computer technology has opened up whole
new areas in mathematics, even in the very nature of
proof, and it also continues to help solve
previously daunting problems.
2.

Go to SFAA… 
BENCHMARKS FOR SCIENCE LITERACY
(ESSAY) 
1. Which Benchmarks address the topic you targeted for
instruction?
COMMON THEMES
2 Some powerful
ideas often used by mathematicians, scientists, and
engineers are not the intellectual property of any one
field or discipline. Indeed, notions of system, scale,
change and constancy, and models have important
applications in business and finance, education, law,
government and politics, and other domains, as well as
in mathematics, science, and technology. These common
themes are really ways of thinking rather than theories
or discoveries. (Energy also represents a prominent tool
for thinking in science and technology, but because it
is part of the content of science, it is not included
here as a theme.) Science for All Americans recommends
what all students should know about those themes, and
the benchmarks in the four sections below suggest how
student understanding of them should grow over the
school years. Although the context of both Science for
All Americans and Benchmarks is mainly science,
mathematics, and technology, other contexts are
identified here to emphasize the general usefulness of
these themes.
3. Copy and paste the information below and remove any
unrelated material. 
GRADES: 
Go to Benchmarks… 
> Go to History Standards… 

MATHEMATICS 
Data Analysis and Probability
Instructional programs from prekindergarten
through grade 12 should enable all students to

formulate questions that can be addressed
with data and collect, organize, and display
relevant data to answer them;

select and use appropriate statistical
methods to analyze data;

develop and evaluate inferences and
predictions that are based on data;

understand and apply basic concepts of
probability.

Connections
Instructional programs from prekindergarten
through grade 12 should enable all students to

recognize and use connections among
mathematical ideas;

understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole;

recognize and apply mathematics in contexts
outside of mathematics.

What are the Mathematics Standards that a student could
meet by completing t
his unit? 
> Go to Mathematics Standards… 




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