Project 2061 Benchmarks for Science Literacy

Rhode Island uses the Project 2061 Benchmarks for Science Literacy for their standards.

The STANDARDS CORRELATION chart suggests which Project 2061 Benchmarks for Science Literacy you can cover using PASSPORT TO WEATHER AND CLIMATE in your classroom. We hope you will discover additional standards you can use. These are the ones our Instructional Materials Development team felt most directly related to the activities contained in PASSPORT TO WEATHER AND CLIMATE.

For additional Project 2061 Benchmarks for Science Literacy you can cover see the STANDARDS CORRELATION chart for the following PASSPORT TO KNOWLEDGE projects:

PASSPORT TO ANTARCTICA

PASSPORT TO THE RAINFOREST

PASSPORT TO THE SOLAR SYSTEM

LIVE FROM MARS 2001/2002

PASSPORT TO THE UNIVERSE

Kindergarten through Grade 2,   Grades 3-5,   Grades 6-8,   Grades 9-12

Kindergarten through Grade 2

The Nature of Science
A. The Scientific World View

By the end of the 2nd grade, students should know that:

 

When a science investigation is done the way it was done before, we expect to get a very similar result.

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Science investigations generally work the same way in different places.

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B. Scientific Inquiry

By the end of the 2nd grade, students should know that:

 

People can often learn about things around them by just observing those things carefully, but sometimes they can learn more by doing something to the things and noting what happens.

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Tools such as thermometers, magnifiers, rulers, or balances often give more information about things than can be obtained by just observing things without their help.

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Describing things as accurately as possible is important in science because it enables people to compare their observations with those of others.

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When people give different descriptions of the same thing, it is usually a good idea to make some fresh observations instead of just arguing about who is right.

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C. The Scientific Enterprise

By the end of the 2nd grade, students should know that:

 

Everybody can do science and invent things and ideas.

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In doing science, it is often helpful to work with a team and to share findings with others. All team members should reach their own individual conclusions, however, about what the findings mean.

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A lot can be learned about plants and animals by observing them closely, but care must be taken to know the needs of living things and how to provide for them in the classroom.

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The Nature of Mathematics
A. Patterns and Relationships

By the end of the 2nd grade, students should know that:

 

Cirles, squares, triangles, and other shapes can be found in things in nature and in things that people build.

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Patterns can be made by putting different shapes together or taking them apart.

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Things move, or can be made to move, along straight, curved, circular, back-and-forth, and jagged paths.

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Numbers can be used to count any collection of things.

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B. Mathematics, Science, and Technology

By the end of the 2nd grade, students should know that:

 

No benchmarks for this level.

 


C. Mathematical Inquiry

By the end of the 2nd grade, students should know that:

 

Numbers and shapes can be used to tell about things.

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The Nature of Technology
A. Technology and Science

By the end of the 2nd grade, students should know that:

 

Tools are used to do things better or more easily and to do some things that could not otherwise be done at all. In technology, tools are used to observe, measure, and make things.

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When trying to build something or to get something to work better, it usually helps to follow directions if there are any or to ask someone who has done it before for suggestions.

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B. Design and Systems

By the end of the 2nd grade, students should know that:

 

People may not be able to actually make or do everything that they can design.

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C. Issues in Technology

By the end of the 2nd grade, students should know that:

 

People, alone or in groups, are always inventing new ways to solve problems and get work done. The tools and ways of doing things that people have invented affect all aspects of life.

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When a group of people wants to build something or try something new, they should try to figure out ahead of time how it might affect other people.

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B. The Earth

By the end of the 2nd grade, students should know that:

 

Some events in nature have a repeating pattern. The weather changes some from day to day, but things such as temperature and rain (or snow) tend to be high, low, or medium in the same months every year.

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Water can be a liquid or a solid and can go back and forth from one form to the other. If water is turned into ice and then the ice is allowed to melt, the amount of water is the same as it was before freezing.

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E. Energy Transformations

By the end of the 2nd grade, students should know that:

 

The sun warms the land, air, and water.

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8. The Designed World
D. Communication

By the end of the 2nd grade, students should know that:

 

Information can be sent and received in many different ways. Some allow answering back and some do not. Each way has advantages and disadvantages.

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Devices can be used to send and receive messages quickly and clearly.

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E. Information Processing

By the end of the 2nd grade, students should know that:

 

There are different ways to store things so they can be easily found later.

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Letters and numbers can be used to put things in a useful order.

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9. The Mathematical World
A. Numbers

By the end of the 2nd grade, students should know that:

 

Numbers can be used to count things, place them in order, or name them.

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Sometimes in sharing or measuring there is a need to use numbers between whole numbers.

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It is possible (and often useful) to estimate quantities without knowing them exactly.

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Simple graphs can help to tell about observations.

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B. Symbolic Relationships

By the end of the 2nd grade, students should know that:

 

Similar patterns may show up in many places in nature and in the things people make.

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Sometimes changing one thing causes changes in something else. In some situations, changing the same thing in the same way usually has the same result.

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C. Shapes

By the end of the 2nd grade, students should know that:

 

Shapes such as circles, squares, and triangles can be used to describe many things that can be seen.

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D. Uncertainty

By the end of the 2nd grade, students should know that:

 

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.

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Often a person can find out about a group of things by studying just a few of them.

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E. Reasoning

By the end of the 2nd grade, students should know that:

 

People are more likely to believe your ideas if you can give good reasons for them.

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11. Common Themes
A. Systems

By the end of the 2nd grade, students should know that:

 

Most things are made of parts.

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Something may not work if some of its parts are missing.

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When parts are put together, they can do things that they couldn't do by themselves.

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B. Models

By the end of the 2nd grade, students should know that:

 

Many of the toys children play with are like real things only in some ways. They are not the same size, are missing many details, or are not able to do all of the same things.

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A model of something is different from the real thing but can be used to learn something about the real thing.

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One way to describe something is to say how it is like something else.

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C. Constancy and Change

By the end of the 2nd grade, students should know that:

 

Things change in some ways and stay the same in some ways.

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People can keep track of some things, seeing where they come from and where they go.

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Things can change in different ways, such as in size, weight, color, and movement. Some small changes can be detected by taking measurements.

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Some changes are so slow or so fast that they are hard to see.

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D. Scale

By the end of the 2nd grade, students should know that:

 

Things in nature and things people make have very different sizes, weights, ages, and speeds.

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12. Habits of Mind
A. Values and Attitudes

By the end of the 2nd grade, students should know that:

 

Raise questions about the world around them and be willing to seek answers to some of them by making careful observations and trying things out.

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B. Computation and Estimation

By the end of the 2nd grade, students should know that:

 

Use whole numbers and simple, everyday fractions in ordering, counting, identifying, measuring, and describing things and experiences.

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Readily give the sums and differences of single-digit numbers in familiar contexts where the operation makes sense to them and they can judge the reasonableness of the answer.

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Give rough estimates of numerical answers to problems before doing them formally.

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Explain to other students how they go about solving numerical problems.

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Make quantitative estimates of familiar lengths, weights, and time intervals and check them by measurements.

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C. Manipulation and Observation

By the end of the 2nd grade, students should know that:

 

Use hammers, screwdrivers, clamps, rulers, scissors, and hand lenses, and operate ordinary audio equipment.

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Assemble, describe, take apart and reassemble constructions using interlocking blocks, erector sets, and the like.

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Make something out of paper, cardboard, wood, plastic, metal, or existing objects that can actually be used to perform a task.

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Measure the length in whole units of objects having straight edges.

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D. Communication Skills

By the end of the 2nd grade, students should know that:

 

Describe and compare things in terms of number, shape, texture, size, weight, color, and motion.

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Draw pictures that correctly portray at least some features of the thing being described.

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E. Critical-Response Skills

By the end of the 2nd grade, students should know that:

 

Ask "How do you know?" in appropriate situations and attempt reasonable answers when others ask them the same question.

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Grades 3 through 5

The Nature of Science
A. The Scientific World View

By the end of the 5th grade, students should know that:

 

Results of similar scientific investigations seldom turn out exactly the same. Sometimes this is because of unexpected differences in the things being investigated, sometimes because of unrealized differences in the methods used or in the circumstances in which the investigation is carried out, and sometimes just because of uncertainties in observations. It is not always easy to tell which.

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B. Scientific Inquiry

By the end of the 5th grade, students should know that:

 

Scientific investigations may take many different forms, including observing what things are like or what is happening somewhere, collecting specimens for analysis, and doing experiments. Investigations can focus on physical, biological, and social questions.

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Results of scientific investigations are seldom exactly the same, but if the differences are large, it is important to try to figure out why. One reason for following directions carefully and for keeping records of one's work is to provide information on what might have caused the differences.

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Scientists' explanations about what happens in the world come partly from what they observe, partly from what they think. Sometimes scientists have different explanations for the same set of observations. That usually leads to their making more observations to resolve the differences.

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Scientists do not pay much attention to claims about how something they know about works unless the claims are backed up with evidence that can be confirmed and with a logical argument.

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C. The Scientific Enterprise

By the end of the 5th grade, students should know that:

 

Science is an adventure that people everywhere can take part in, as they have for many centuries.

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Clear communication is an essential part of doing science. It enables scientists to inform others about their work, expose their ideas to criticism by other scientists, and stay informed about scientific discoveries around the world.

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Doing science involves many different kinds of work and engages men and women of all ages and backgrounds.

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The Nature of Mathematics
A. Patterns and Relationships

By the end of the 5th grade, students should know that:

 

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 pratical problems, sometimes because they are interesting in themselves.

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Mathematical ideas can be represented concretely, graphically, and symbolically.

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B. Mathematics, Science, and Technology

By the end of the 5th grade, students should know that:

 

No benchmarks for this level.

 


C. Mathematical Inquiry

By the end of the 5th grade, students should know that:

 

Numbers and shapes-and operations on them-help to describe and predict things about the world around us.

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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.

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The Nature of Technology
A. Technology and Science

By the end of the 5th grade, students should know that:

 

Throughout all of history, people everywhere have invented and used tools. Most tools of today are different from those of the past but many are modifications of very ancient tools.

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Technology enables scientists and others to observe things that are too small or too far away to be seen without them and to study the motion of objects that are moving very rapidly or are hardly moving at all

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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.

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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. The changes may be for survival needs such as food, shelter, and defense, for communication and transportation, or to gain knowledge and express ideas.

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B. Design and Systems

By the end of the 5th grade, students should know that:

 

There is no perfect design. Designs that are best in one respect (safety or ease of use, for example) may be inferior in other ways (cost or appearance). Usually some features must be sacrificed to get others. How such trade-offs are received depends upon which features are emphasized and which are down-played.

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Even a good design may fail. Sometimes steps can be taken ahead of time to reduce the likelihood of failure, but it cannot be entirely eliminated.

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The solution to one problem may create other problems.

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C. Issues in Technology

By the end of the 5th grade, students should know that:

 

Technology has been part of life on the earth since the advent of the human species. Like language, ritual, commerce, and the arts, technology is an intrinsic part of human culture, and it both shapes society and is shaped by it. The technology available to people greatly influences what their lives are like.

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Any invention is likely to lead to other inventions. Once an invention exists, people are likely to think up ways of using it that were never imagined at first.

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Transportation, communications, nutrition, sanitation, health care, entertainment, and other technologies give large numbers of people today the goods and services that once were luxuries enjoyed only by the wealthy. These benefits are not equally available to everyone.

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Scientific laws, engineering principles, properties of materials, and construction techniques must be taken into account in designing engineering solutions to problems. Other factors, such as cost, safety, appearance, environmental impact, and what will happen if the solution fails also must be considered.

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Technologies often have drawbacks as well as benefits. A technology that helps some people or organisms may hurt others—either deliberately (as weapons can) or inadvertently (as pesticides can). When harm occurs or seems likely, choices have to be made or new solutions found.

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Because of their ability to invent tools and processes, people have an enormous effect on the lives of other living things.

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8. The Designed World
D. Communication

By the end of the 5th grade, students should know that:

 

People have always tried to communicate with one another. Signed and spoken language was one of the first inventions. Early forms of recording messages used markings on materials such as wood or stone.

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Communication involves coding and decoding information. In any language, both the sender and the receiver have to know the same code, which means that secret codes can be used to keep communication private.

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People have invented devices, such as paper and ink, engraved plastic disks, and magnetic tapes, for recording information. These devices enable great amounts of information to be stored and retrieved—and be sent to one or many other people or places.

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Communication technologies make it possible to send and receive information more and more reliably, quickly, and cheaply over long distances.

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E. Information Processing

By the end of the 5th grade, students should know that:

 

Computers are controlled partly by how they are wired and partly by special instructions called programs that are entered into a computer's memory. Some programs stay permanently in the machine but most are coded on disks and transferred into and out of the computer to suit the user.

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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.

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Mistakes can occur when people enter programs or data into a computer. Computers themselves can make errors in information processing because of defects in their hardware or software.

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F. Health Technology

By the end of the 5th grade, students should know that:

 

There are normal ranges for body measurements—including temperature, heart rate, and what is in the blood and urine—that help to tell when people are well. Tools, such as thermometers and x-ray machines, provide us clues about what is happening inside the body.

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Technology has made it possible to repair and sometimes replace some body parts.

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9. The Mathematical World
A. Numbers

By the end of the 5th grade, students should know that:

 

The meaning of numerals in many-digit numbers depends on their positions.

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In some situations, "0" means none of something, but in others it may be just the label of some point on a scale.

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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).

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

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B. Symbolic Relationships

By the end of the 5th grade, students should know that:

 

Mathematical statements using symbols may be true only when the symbols are replaced by certain numbers.

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Tables and graphs can show how values of one quantity are related to values of another.

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C. Shapes

By the end of the 5th grade, students should know that:

 

Length can be thought of as unit lengths joined together, area as a collection of unit squares, and volume as a set of unit cubes.

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If 0 and 1 are located on a line, any other number can be depicted as a position on the line.

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Graphical display of numbers may make it possible to spot patterns that are not otherwise obvious, such as comparative size and trends.

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Many objects can be described in terms of simple plane figures and solids. Shapes can be compared in terms of concepts such as parallel and perpendicular, congruence and similarity, and symmetry. Symmetry can be found by reflection, turns, or slides.

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Areas of irregular shapes can be found by dividing them into squares and triangles.

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

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D. Uncertainty

By the end of the 5th grade, students should know that:

 

Some predictions can be based on what is known about the past, assuming that conditions are pretty much the same now.

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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.

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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.

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Spreading data out on a number line helps to see what the extremes are, where they pile up, and where the gaps are. A summary of data includes where the middle is and how much spread is around it.

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A small part of something may be special in some way and not give an accurate picture of the whole. How much a portion of something can help to estimate what the whole is like depends on how the portion is chosen. There is a danger of choosing only the data that show what is expected by the person doing the choosing.

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Events can be described in terms of being more or less likely, impossible, or certain.

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E. Reasoning

By the end of the 5th grade, students should know that:

 

One way to make sense of something is to think how it is like something more familiar.

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Reasoning can be distorted by strong feelings.

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11. Common Themes
A. Systems

By the end of the 5th grade, students should know that:

 

In something that consists of many parts, the parts usually influence one another.

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Something may not work as well (or at all) if a part of it is missing, broken, worn out, mismatched, or misconnected.

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B. Models

By the end of the 5th grade, students should know that:

 

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.

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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.

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C. Constancy and Change

By the end of the 5th grade, students should know that:

 

Some features of things may stay the same even when other features change. Some patterns look the same when they are shifted over, or turned, or reflected, or seen from different directions.

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Things change in steady, repetitive, or irregular ways-or sometimes in more than one way at the same time. Often the best way to tell which kinds of change are happening is to make a table or graph of measurements.

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D. Scale

By the end of the 5th grade, students should know that:

 

Almost anything has limits on how big or small it can be.

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Finding out what the biggest and the smallest possible values of something are is often as revealing as knowing what the usual value is.

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12. Habits of Mind
A. Values and Attitudes

By the end of the 5th grade, students should know that:

 

Keep records of their investigations and observations and not change the records later.

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Offer reasons for their findings and consider reasons suggested by others.

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B. Computation and Estimation

By the end of the 5th grade, students should know that:

 

Add, subtract, multiply, and divide whole numbers mentally, on paper, and with a calculator.

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Use fractions and decimals, translating when necessary between decimals and commonly encountered fractions—halves, thirds, fourths, fifths, tenths, and hundredths (but not sixths, sevenths, etc.).

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Judge whether measurements and computations of quantities such as length, area, volume, weight, or time are reasonable in a familiar context by comparing them to typical values.

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State the purpose of each step in a calculation.

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Read and follow step-by-step instructions in a calculator or computer manual when learning new procedures.

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C. Manipulation and Observation

By the end of the 5th grade, students should know that:

 

Choose appropriate common materials for making simple mechanical constructions and repairing things.

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Measure and mix dry and liquid materials (in the kitchen, garage, or laboratory) in prescribed amounts, exercising reasonable safety.

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Keep a notebook that describes observations made, carefully distinguishes actual observations from ideas and speculations about what was observed, and is understandable weeks or months later.

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Use calculators to determine area and volume from linear dimensions, aggregate amounts of area, volume, weight, time, and cost, and find the difference between two quantities of anything.

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Make safe electrical connections with various plugs, sockets, and terminals.

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D. Communication Skills

By the end of the 5th grade, students should know that:

 

Write instructions that others can follow in carrying out a procedure.

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Make sketches to aid in explaining procedures or ideas.

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Use numerical data in describing and comparing objects and events.

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E. Critical-Response Skills

By the end of the 5th grade, students should know that:

 

Buttress their statements with facts found in books, articles, and databases, and identify the sources used and expect others to do the same.

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Recognize when comparisons might not be fair because some conditions are not kept the same.

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Seek better reasons for believing something than "Everybody knows that . . ." or "I just know" and discount such reasons when given by others.

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Grades 6 through 8

The Nature of Science
A. The Scientific World View

By the end of the 8th grade, students should know that:

 

When similar investigations give different results, the scientific challenge is to judge whether the differences are trivial or significant, and it often takes further studies to decide. Even with similar results, scientists may wait until an investigation has been repeated many times before accepting the results as correct.

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Scientific knowledge is subject to modification as new information challenges prevailing theories and as a new theory leads to looking at old observations in a new way.

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Some scientific knowledge is very old and yet is still applicable today.

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Some matters cannot be examined usefully in a scientific way. Among them are matters that by their nature cannot be tested objectively and those that are essentially matters of morality. Science can sometimes be used to inform ethical decisions by identifying the likely consequences of particular actions but cannot be used to establish that some action is either moral or immoral.

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B. Scientific Inquiry

By the end of the 8th grade, students should know that:

 

Scientists differ greatly in what phenomena they study and how they go about their work. Although there is no fixed set of steps that all scientists follow, scientific investigations usually involve the collection of relevant evidence, the use of logical reasoning, and the application of imagination in devising hypotheses and explanations to make sense of the collected evidence.

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If more than one variable changes at the same time in an experiment, the outcome of the experiment may not be clearly attributable to any one of the variables. It may not always be possible to prevent outside variables from influencing the outcome of an investigation (or even to identify all of the variables), but collaboration among investigators can often lead to research designs that are able to deal with such situations.

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What people expect to observe often affects what they actually do observe. Strong beliefs about what should happen in particular circumstances can prevent them from detecting other results. Scientists know about this danger to objectivity and take steps to try and avoid it when designing investigations and examining data. One safeguard is to have different investigators conduct independent studies of the same questions.

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New ideas in science sometimes spring from unexpected findings, and they usually lead to new investigations.

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C. The Scientific Enterprise

By the end of the 8th grade, students should know that:

 

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

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Until recently, women and racial minorities, because of restrictions on their education and employment opportunities, were essentially left out of much of the formal work of the science establishment; the remarkable few who overcame those obstacles were even then likely to have their work disregarded by the science establishment.

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No matter who does science and mathematics or invents things, or when or where they do it, the knowledge and technology that result can eventually become available to everyone in the world.

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Scientists are employed by colleges and universities, business and industry, hospitals, and many government agencies. Their places of work include offices, classrooms, laboratories, farms, factories, and natural field settings ranging from space to the ocean floor.

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In research involving human subjects, the ethics of science require that potential subjects be fully informed about the risks and benefits associated with the research and of their right to refuse to participate. Science ethics also demand that scientists must not knowingly subject coworkers, students, the neighborhood, or the community to health or property risks without their prior knowledge and consent. Because animals cannot make informed choices, special care must be taken in using them in scientific research.

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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.

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Accurate record-keeping, openness, and replication are essential for maintaining an investigator's credibility with other scientists and society.

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The Nature of Mathematics
A. Patterns and Relationships

By the end of the 8th grade, students should know that:

 

Usually there is no one right way to solve a mathematical problem; different methods have different advantages and disadvantages.

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Logical connections can be found between different parts of mathematics.

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B. Mathematics, Science, and Technology

By the end of the 8th grade, students should know that:

 

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.

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C. Mathematical Inquiry

By the end of the 8th grade, students should know that:

 

Mathematicians often represent things with abstract ideas, such as numbers or perfectly straight lines, and then work with those ideas alone. The "things" from which they abstract can be ideas themselves (for example, a proposition about "all equal-sided triangles" or "all odd numbers").

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When mathematicians use logical rules to work with representations of things, the results may or may not be valid for the things themselves. Using mathematics to solve a problem requires choosing what mathematics to use; probably making some simplifying assumptions, estimates, or approximations; doing computations; and then checking to see whether the answer makes sense. If an answer does not seem to make enough sense for its intended purpose, then any of these steps might have been inappropriate.

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The Nature of Technology
A. Technology and Science

By the end of the 8th grade, students should know that:

 

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.

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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.

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Engineers, architects, and others who engage in design and technology use scientific knowledge to solve practical problems. But they usually have to take human values and limitations into account as well.

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B. Design and Systems

By the end of the 8th grade, students should know that:

 

Design usually requires taking constraints into account. Some constraints, such as gravity or the properties of the materials to be used, are unavoidable. Other constraints, including economic, political, social, ethical, and aesthetic ones, limit choices.

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All technologies have effects other than those intended by the design, some of which may have been predictable and some not. In either case, these side effects may turn out to be unacceptable to some of the population and therefore lead to conflict between groups.

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Almost all control systems have inputs, outputs, and feedback. The essence of control is comparing information about what is happening to what people want to happen and then making appropriate adjustments. This procedure requires sensing information, processing it, and making changes. In almost all modern machines, microprocessors serve as centers of performance control.

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Systems fail because they have faulty or poorly matched parts, are used in ways that exceed what was intended by the design, or were poorly designed to begin with. The most common ways to prevent failure are pretesting parts and procedures, overdesign, and redundancy.

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C. Issues in Technology

By the end of the 8th grade, students should know that:

 

The human ability to shape the future comes from a capacity for generating knowledge and developing new technologies—and for communicating ideas to others.

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Technology cannot always provide successful solutions for problems or fulfill every human need.

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Throughout history, people have carried out impressive technological feats, some of which would be hard to duplicate today even with modern tools. The purposes served by these achievements have sometimes been practical, sometimes ceremonial.

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Technology has strongly influenced the course of history and continues to do so. It is largely responsible for the great revolutions in agriculture, manufacturing, sanitation and medicine, warfare, transportation, information processing, and communications that have radically changed how people live.

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New technologies increase some risks and decrease others. Some of the same technologies that have improved the length and quality of life for many people have also brought new risks.

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Rarely are technology issues simple and one-sided. Relevant facts alone, even when known and available, usually do not settle matters entirely in favor of one side or another. That is because the contending groups may have different values and priorities. They may stand to gain or lose in different degrees, or may make very different predictions about what the future consequences of the proposed action will be.

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Societies influence what aspects of technology are developed and how these are used. People control technology (as well as science) and are responsible for its effects.

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B. The Earth

By the end of the 8th grade, students should know that:

 

Because the earth turns daily on an axis that is tilted relative to the plane of the earth's yearly orbit around the sun, sunlight falls more intensely on different parts of the earth during the year. The difference in heating of the earth's surface produces the planet's seasons and weather patterns.

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Climates have sometimes changed abruptly in the past as a result of changes in the earth's crust, such as volcanic eruptions or impacts of huge rocks from space. Even relatively small changes in atmospheric or ocean content can have widespread effects on climate if the change lasts long enough.

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The cycling of water in and out of the atmosphere plays an important role in determining climatic patterns. Water evaporates from the surface of the earth, rises and cools, condenses into rain or snow, and falls again to the surface. The water falling on land collects in rivers and lakes, soil, and porous layers of rock, and much of it flows back into the ocean.

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Fresh water, limited in supply, is essential for life and also for most industrial processes. Rivers, lakes, and groundwater can be depleted or polluted, becoming unavailable or unsuitable for life.

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Heat energy carried by ocean currents has a strong influence on climate around the world.

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Some minerals are very rare and some exist in great quantities, but-for practical purposes-the ability to recover them is just as important as their abundance. As minerals are depleted, obtaining them becomes more difficult. Recycling and the development of substitutes can reduce the rate of depletion but may also be costly.

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E. Energy Transformations

By the end of the 8th grade, students should know that:

 

Energy cannot be created or destroyed, but only changed from one form into another.

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Most of what goes on in the universe-from exploding stars and biological growth to the operation of machines and the motion of people-involves some form of energy being transformed into another. Energy in the form of heat is almost always one of the products of an energy transformation.

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Heat can be transferred through materials by the collisions of atoms or across space by radiation. If the material is fluid, currents will be set up in it that aid the transfer of heat.

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Energy appears in different forms. Heat energy is in the disorderly motion of molecules; chemical energy is in the arrangement of atoms; mechanical energy is in moving bodies or in elastically distorted shapes; gravitational energy is in the separation of mutually attracting masses.

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8. The Designed World
C. Energy Sources and Use

By the end of the 8th grade, students should know that:

 

Energy can change from one form to another, although in the process some energy is always converted to heat. Some systems transform energy with less loss of heat than others.

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Different ways of obtaining, transforming, and distributing energy have different environmental consequences.

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In many instances, manufacturing and other technological activities are performed at a site close to an energy source. Some forms of energy are transported easily, others are not.

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Electrical energy can be produced from a variety of energy sources and can be transformed into almost any other form of energy. Moreover, electricity is used to distribute energy quickly and conveniently to distant locations.

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Energy from the sun (and the wind and water energy derived from it) is available indefinitely. Because the flow of energy is weak and variable, very large collection systems are needed. Other sources don't renew or renew only slowly.

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Different parts of the world have different amounts and kinds of energy resources to use and use them for different purposes.

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D. Communication

By the end of the 8th grade, students should know that:

 

Errors can occur in coding, transmitting, or decoding information, and some means of checking for accuracy is needed. Repeating the message is a frequently used method.

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Information can be carried by many media, including sound, light, and objects. In this century, the ability to code information as electric currents in wires, electromagnetic waves in space, and light in glass fibers has made communication millions of times faster than is possible by mail or sound.

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E. Information Processing

By the end of the 8th grade, students should know that:

 

Most computers use digital codes containing only two symbols, 0 and 1, to perform all operations. Continuous signals (analog) must be transformed into digital codes before they can be processed by a computer.

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What use can be made of a large collection of information depends upon how it is organized. One of the values of computers is that they are able, on command, to reorganize information in a variety of ways, thereby enabling people to make more and better uses of the collection.

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Computer control of mechanical systems can be much quicker than human control. In situations where events happen faster than people can react, there is little choice but to rely on computers. Most complex systems still require human oversight, however, to make certain kinds of judgments about the readiness of the parts of the system (including the computers) and the system as a whole to operate properly, to react to unexpected failures, and to evaluate how well the system is serving its intended purposes.

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An increasing number of people work at jobs that involve processing or distributing information. Because computers can do these tasks faster and more reliably, they have become standard tools both in the workplace and at home.

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9. The Mathematical World
A. Numbers

By the end of the 8th grade, students should know that:

 

There have been systems for writing numbers other than the Arabic system of place values based on tens. The very old Roman numerals are now used only for dates, clock faces, or ordering chapters in a book. Numbers based on 60 are still used for describing time and angles.

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A number line can be extended on the other side of zero to represent negative numbers. Negative numbers allow subtraction of a bigger number from a smaller number to make sense, and are often used when something can be measured on either side of some reference point (time, ground level, temperature, budget).

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Numbers can be written in different forms, depending on how they are being used. How fractions or decimals based on measured quantities should be written depends on how precise the measurements are and how precise an answer is needed.

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The operations + and - are inverses of each other-one undoes what the other does; likewise x and ÷ .

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The expression a/b can mean different things: a parts of size 1/b each, a divided by b, or a compared to b.

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Numbers can be represented by using sequences of only two symbols (such as 1 and 0, on and off); computers work this way.

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Computations (as on calculators) can give more digits than make sense or are useful.

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B. Symbolic Relationships

By the end of the 8th grade, students should know that:

 

An equation containing a variable may be true for just one value of the variable.

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Mathematical statements can be used to describe how one quantity changes when another changes. Rates of change can be computed from differences in magnitudes and vice versa.

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Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease indefinitely, increase or decrease in steps, or do something different from any of these.

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C. Shapes

By the end of the 8th grade, students should know that:

 

Some shapes have special properties: triangular shapes tend to make structures rigid, and round shapes give the least possible boundary for a given amount of interior area. Shapes can match exactly or have the same shape in different sizes.

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Lines can be parallel, perpendicular, or oblique.

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Shapes on a sphere like the earth cannot be depicted on a flat surface without some distortion.

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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.

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It takes two numbers to locate a point on a map or any other flat surface. The numbers may be two perpendicular distances from a point, or an angle and a distance from a point.

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

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D. Uncertainty

By the end of the 8th grade, students should know that:

 

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.

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Probabilities are ratios and can be expressed as fractions, percentages, or odds.

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The mean, median, and mode tell different things about the middle of a data set.

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Comparison of data from two groups should involve comparing both their middles and the spreads around them.

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The larger a well-chosen 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.

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E. Reasoning

By the end of the 8th grade, students should know that:

 

Some aspects of reasoning have fairly rigid rules for what makes sense; other aspects don't. If people have rules that always hold, and good information about a particular situation, then logic can help them to figure out what is true about it. This kind of reasoning requires care in the use of key words such as if, and, not, or, all, and some. Reasoning by similarities can suggest ideas but can't prove them one way or the other.

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Practical reasoning, such as diagnosing or troubleshooting almost anything, may require many-step, branching logic. Because computers can keep track of complicated logic, as well as a lot of information, they are useful in a lot of problem-solving situations.

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Sometimes people invent a general rule to explain how something works by summarizing observations. But people tend to overgeneralize, imagining general rules on the basis of only a few observations.

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People are using incorrect logic when they make a statement such as "If A is true, then B is true; but A isn't true, therefore B isn't true either."

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A single example can never prove that something is always true, but sometimes a single example can prove that something is not always true.

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An analogy has some likenesses to but also some differences from the real thing.

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10. Historical Perspectives
A. Displacing the Earth from the Center of the Universe

By the end of the 8th grade, students should know that:

 

The motion of an object is always judged with respect to some other object or point and so the idea of absolute motion or rest is misleading.

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Telescopes reveal that there are many more stars in the night sky than are evident to the unaided eye, the surface of the moon has many craters and mountains, the sun has dark spots, and Jupiter and some other planets have their own moons.

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11. Common Themes
A. Systems

By the end of the 8th grade, students should know that:

 

A system can include processes as well as things.

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Thinking about things as systems means looking for how every part relates to others. The output from one part of a system (which can include material, energy, or information) can become the input to other parts. Such feedback can serve to control what goes on in the system as a whole.

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Any system is usually connected to other systems, both internally and externally. Thus a system may be thought of as containing subsystems and as being a subsystem of a larger system.

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B. Models

By the end of the 8th grade, students should know that:

 

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.

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

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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.

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C. Constancy and Change

By the end of the 8th grade, students should know that:

 

Physical and biological systems tend to change until they become stable and then remain that way unless their surroundings change.

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A system may stay the same because nothing is happening or because things are happening but exactly counterbalance one another.

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Many systems contain feedback mechanisms that serve to keep changes within specified limits.

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Symbolic equations can be used to summarize how the quantity of something changes over time or in response to other changes.

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Symmetry (or the lack of it) may determine properties of many objects, from molecules and crystals to organisms and designed structures.

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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. Different cycles range from many thousands of years down to less than a billionth of a second.

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D. Scale

By the end of the 8th grade, students should know that:

 

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.

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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.

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12. Habits of Mind
A. Values and Attitudes

By the end of the 8th grade, students should know that:

 

Know why it is important in science to keep honest, clear, and accurate records.

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Know that hypotheses are valuable, even if they turn out not to be true, if they lead to fruitful investigations.

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Know that often different explanations can be given for the same evidence, and it is not always possible to tell which one is correct.

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B. Computation and Estimation

By the end of the 8th grade, students should know that:

 

Find what percentage one number is of another and figure any percentage of any number.

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Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals, and percents.

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Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids.

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Find the mean and median of a set of data.

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

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Insert instructions into computer spreadsheet cells to program arithmetic calculations.

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Determine what unit (such as seconds, square inches, or dollars per tankful) an answer should be expressed in from the units of the inputs to the calculation, and be able to convert compound units (such as yen per dollar into dollar per yen, or miles per hour into feet per second).

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Decide what degree of precision is adequate and round off the result of calculator operations to enough significant figures to reasonably reflect those of the inputs.

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Express numbers like 100, 1,000, and 1,000,000 as powers of 10.

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Estimate probabilities of outcomes in familiar situations, on the basis of history or the number of possible outcomes.

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C. Manipulation and Observation

By the end of the 8th grade, students should know that:

 

Use calculators to compare amounts proportionally.

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Use computers to store and retrieve information in topical, alphabetical, numerical, and key-word files, and create simple files of their own devising.

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Read analog and digital meters on instruments used to make direct measurements of length, volume, weight, elapsed time, rates, and temperature, and choose appropriate units for reporting various magnitudes.

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Use cameras and tape recorders for capturing information.

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Inspect, disassemble, and reassemble simple mechanical devices and describe what the various parts are for; estimate what the effect that making a change in one part of a system is likely to have on the system as a whole.

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D. Communication Skills

By the end of the 8th grade, students should know that:

 

Organize information in simple tables and graphs and identify relationships they reveal.

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Read simple tables and graphs produced by others and describe in words what they show.

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Locate information in reference books, back issues of newspapers and magazines, compact disks, and computer databases.

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Understand writing that incorporates circle charts, bar and line graphs, two-way data tables, diagrams, and symbols.

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Find and describe locations on maps with rectangular and polar coordinates.

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E. Critical-Response Skills

By the end of the 8th grade, students should know that:

 

Question claims based on vague attributions (such as "Leading doctors say...") or on statements made by celebrities or others outside the area of their particular expertise.

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Compare consumer products and consider reasonable personal trade-offs among them on the basis of features, performance, durability, and cost.

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Be skeptical of arguments based on very small samples of data, biased samples, or samples for which there was no control sample.

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Be aware that there may be more than one good way to interpret a given set of findings.

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Notice and criticize the reasoning in arguments in which (1) fact and opinion are intermingled or the conclusions do not follow logically from the evidence given, (2) an analogy is not apt, (3) no mention is made of whether the control groups are very much like the experimental group, or (4) all members of a group (such as teenagers or chemists) are implied to have nearly identical characteristics that differ from those of other groups.

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Grades 9 through 12

The Nature of Science
A. The Scientific World View

By the end of the 12th grade, students should know that:

 

Scientists assume that the universe is a vast single system in which the basic rules are the same everywhere. The rules may range from very simple to extremely complex, but scientists operate on the belief that the rules can be discovered by careful, systematic study.

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From time to time, major shifts occur in the scientific view of how the world works. More often, however, the changes that take place in the body of scientific knowledge are small modifications of prior knowledge. Change and continuity are persistent features of science.

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No matter how well one theory fits observations, a new theory might fit them just as well or better, or might fit a wider range of observations. In science, the testing, revising, and occasional discarding of theories, new and old, never ends. This ongoing process leads to an increasingly better understanding of how things work in the world but not to absolute truth. Evidence for the value of this approach is given by the improving ability of scientists to offer reliable explanations and make accurate predictions.

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B. Scientific Inquiry

By the end of the 12th grade, students should know that:

 

Investigations are conducted for different reasons, including to explore new phenomena, to check on previous results, to test how well a theory predicts, and to compare different theories.

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Hypotheses are widely used in science for choosing what data to pay attention to and what additional data to seek, and for guiding the interpretation of the data (both new and previously available).

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Sometimes, scientists can control conditions in order to obtain evidence. When that is not possible for practical or ethical reasons, they try to observe as wide a range of natural occurrences as possible to be able to discern patterns.

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There are different traditions in science about what is investigated and how, but they all have in common certain basic beliefs about the value of evidence, logic, and good arguments. And there is agreement that progress in all fields of science depends on intelligence, hard work, imagination, and even chance.

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Scientists in any one research group tend to see things alike, so even groups of scientists may have trouble being entirely objective about their methods and findings. For that reason, scientific teams are expected to seek out the possible sources of bias in the design of their investigations and in their data analysis. Checking each other's results and explanations helps, but that is no guarantee against bias.

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In the short run, new ideas that do not mesh well with mainstream ideas in science often encounter vigorous criticism. In the long run, theories are judged by how they fit with other theories, the range of observations they explain, how well they explain observations, and how effective they are in predicting new findings.

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New ideas in science are limited by the context in which they are conceived; are often rejected by the scientific establishment; sometimes spring from unexpected findings; and usually grow slowly, through contributions from many investigators.

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C. The Scientific Enterprise

By the end of the 12th grade, students should know that:

 

The early Egyptian, Greek, Chinese, Hindu, and Arabic cultures are responsible for many scientific and mathematical ideas and technological inventions.

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Modern science is based on traditions of thought that came together in Europe about 500 years ago. People from all cultures now contribute to that tradition.

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Progress in science and invention depends heavily on what else is happening in society, and history often depends on scientific and technological developments.

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Science disciplines differ from one another in what is studied, techniques used, and outcomes sought, but they share a common purpose and philosophy, and all are part of the same scientific enterprise. Although each discipline provides a conceptual structure for organizing and pursuing knowledge, many problems are studied by scientists using information and skills from many disciplines. Disciplines do not have fixed boundaries, and it happens that new scientific disciplines are being formed where existing ones meet and that some subdisciplines spin off to become new disciplines in their own right.

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Current ethics in science hold that research involving human subjects may be conducted only with the informed consent of the subjects, even if this constraint limits some kinds of potentially important research or influences the results. When it comes to participation in research that could pose risks to society, most scientists believe that a decision to participate or not is a matter of personal ethics rather than professional ethics.

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Scientists can bring information, insights, and analytical skills to bear on matters of public concern. Acting in their areas of expertise, scientists can help people understand the likely causes of events and estimate their possible effects. Outside their areas of expertise, however, scientists should enjoy no special credibility. And where their own personal, institutional, or community interests are at stake, scientists as a group can be expected to be no less biased than other groups are about their perceived interests.

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The strongly held traditions of science, including its commitment to peer review and publication, serve to keep the vast majority of scientists well within the bounds of ethical professional behavior. Deliberate deceit is rare and likely to be exposed sooner or later by the scientific enterprise itself. When violations of these scientific ethical traditions are discovered, they are strongly condemned by the scientific community, and the violators then have difficulty regaining the respect of other scientists.

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Funding influences the direction of science by virtue of the decisions that are made on which research to support. Research funding comes from various federal government agencies, industry, and private foundations.

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The Nature of Mathematics
A. Patterns and Relationships

By the end of the 12th grade, students should know that:

 

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. Although mathematics began long ago in practical problems, it soon focused on abstractions from the material world, and then on even more abstract relationships among those abstractions.

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As in other sciences, simplicity is one of the highest values in mathematics. Some mathematicians try to identify the smallest set of rules from which many other propositions can be logically derived.

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Theories and applications in mathematical work influence each other. Sometimes a practical problem leads to the development of new mathematical theories; often mathematics developed for its own sake turns out to have practical applications.

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New mathematics continues to be invented, and connections between different parts of mathematics continue to be found.

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B. Mathematics, Science, and Technology

By the end of the 12th grade, students should know that:

 

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

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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.

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Mathematics provides a precise language for science and technology-to describe objects and events, to characterize relationships between variables, and to argue logically.

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Developments in science or technology often stimulate innovations in mathematics by presenting new kinds of problems to be solved. In particular, the development of computer technology (which itself relies on mathematics) has generated new kinds of problems and methods of work in mathematics.

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Developments in mathematics often stimulate innovations in science and technology.

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C. Mathematical Inquiry

By the end of the 12th grade, students should know that:

 

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. The more interesting the results, the better. The only limit on the set of rules is that they should not contradict one another.

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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.

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The Nature of Technology
A. Technology and Science

By the end of the 12th grade, students should know that:

 

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. The very availability of new technology itself often sparks scientific advances.

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Mathematics, creativity, logic and originality are all needed to improve technology.

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Technology usually affects society more directly than science because it solves pratical problems and serves human needs (and may create new problems and needs). In contrast, science affects society mainly by stimulating and satisfying people's curiosity and occasionally by enlarging or challenging their views of what the world is like.

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B. Design and Systems

By the end of the 12th grade, students should know that:

 

In designing a device or process, thought should be given to how it will be manufactured, operated, maintained, replaced, and disposed of and who will sell, operate, and take care of it. The costs associated with these functions may introduce yet more constraints on the design.

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The value of any given technology may be different for different groups of people and at different points in time.

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Complex systems have layers of controls. Some controls operate particular parts of the system and some control other controls. Even fully automatic systems require human control at some point.

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Risk analysis is used to minimize the likelihood of unwanted side effects of a new technology. The public perception of risk may depend, however, on psychological factors as well as scientific ones.

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The more parts and connections a system has, the more ways it can go wrong. Complex systems usually have components to detect, back up, bypass, or compensate for minor failures.

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To reduce the chance of system failure, performance testing is often conducted using small-scale models, computer simulations, analogous systems, or just the parts of the system thought to be least reliable.

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C. Issues in Technology

By the end of the 12th grade, students should know that:

 

Social and economic forces strongly influence which technologies will be developed and used. Which will prevail is affected by many factors, such as personal values, consumer acceptance, patent laws, the availability of risk capital, the federal budget, local and national regulations, media attention, economic competition, and tax incentives.

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Technological knowledge is not always as freely shared as scientific knowledge unrelated to technology. Some scientists and engineers are comfortable working in situations in which some secrecy is required, but others prefer not to do so. It is generally regarded as a matter of individual choice and ethics, not one of professional ethics.

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In deciding on proposals to introduce new technologies or to curtail existing ones, some key questions arise concerning alternatives, risks, costs, and benefits. What alternative ways are there to achieve the same ends, and how do the alternatives compare to the plan being put forward? Who benefits and who suffers? What are the financial and social costs, do they change over time, and who bears them? What are the risks associated with using (or not using) the new technology, how serious are they, and who is in jeopardy? What human, material, and energy resources will be needed to build, install, operate, maintain, and replace the new technology, and where will they come from? How will the new technology and its waste products be disposed of and at what costs?

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The human species has a major impact on other species in many ways: reducing the amount of the earth's surface available to those other species, interfering with their food sources, changing the temperature and chemical composition of their habitats, introducing foreign species into their ecosystems, and altering organisms directly through selective breeding and genetic engineering.

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Human inventiveness has brought new risks as well as improvements to human existence.

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B. The Earth

By the end of the 12th grade, students should know that:

 

Life is adapted to conditions on the earth, including the force of gravity that enables the planet to retain an adequate atmosphere, and an intensity of radiation from the sun that allows water to cycle between liquid and vapor.

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Weather (in the short run) and climate (in the long run) involve the transfer of energy in and out of the atmosphere. Solar radiation heats the land masses, oceans, and air. Transfer of heat energy at the boundaries between the atmosphere, the land masses, and the oceans results in layers of different temperatures and densities in both the ocean and atmosphere. The action of gravitational force on regions of different densities causes them to rise or fall-and such circulation, influenced by the rotation of the earth, produces winds and ocean currents.

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C. Processes that Shape the Earth

By the end of the 12th grade, students should know that:

 

Plants alter the earth's atmosphere by removing carbon dioxide from it, using the carbon to make sugars and releasing oxygen. This process is responsible for the oxygen content of the air.

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The formation, weathering, sedimentation, and reformation of rock constitute a continuing "rock cycle" in which the total amount of material stays the same as its forms change.

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8. The Designed World
D. Communication

By the end of the 12th grade, students should know that:

 

Almost any information can be transformed into electrical signals. A weak electrical signal can be used to shape a stronger one, which can control other signals of light, sound, mechanical devices, or radio waves.

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The quality of communication is determined by the strength of the signal in relation to the noise that tends to obscure it. Communication errors can be reduced by boosting and focusing signals, shielding the signal from internal and external noise, and repeating information, but all of these increase costs. Digital coding of information (using only 1's and 0's) makes possible more reliable transmission of information.

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As technologies that provide privacy in communication improve, so do those for invading privacy.

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E. Information Processing

By the end of the 12th grade, students should know that:

 

Computer modeling explores the logical consequences of a set of instructions and a set of data. The instructions and data input of a computer model try to represent the real world so the computer can show what would actually happen. In this way, computers assist people in making decisions by simulating the consequences of different possible decisions.

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Redundancy can reduce errors in storing or processing information but increases costs.

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Miniaturization of information-processing hardware can increase processing speed and portability, reduce energy use, and lower cost. Miniaturization is made possible through higher-purity materials and more precise fabrication technology.

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9. The Mathematical World
A. Numbers

By the end of the 12th grade, students should know that:

 

Comparison of numbers of very different size can be made approximately by expressing them as nearest powers of 10.

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Numbers can be written with bases different from ten (which people probably use because of their 10 fingers). The simplest base, 2, uses just two symbols (1 and 0, or on and off).

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When calculations are made with measurements, a small error in the measurements may lead to a large error in the results.

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The effects of uncertainties in measurements on a computed result can be estimated.

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B. Symbolic Relationships

By the end of the 12th grade, students should know that:

 

In some cases, the more of something there is, the more rapidly it may change (as the number of births is proportional to the size of the population). In other cases, the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting).

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Symbolic statements can be manipulated by rules of mathematical logic to produce other statements of the same relationship, which may show some interesting aspect more clearly. Symbolic statements can be combined to look for values of variables that will satisfy all of them at the same time.

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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.

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Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

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When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes more than one, and sometimes maybe not at all.

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The reasonableness of the result of a computation can be estimated from what the inputs and operations are.

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C. Shapes

By the end of the 12th grade, students should know that:

 

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

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There are formulas for calculating the surface areas and volumes of regular shapes. When the linear size of a shape changes by some factor, its area and volume change disproportionately: area in proportion to the square of the factor, and volume in proportion to its cube. Properties of an object that depend on its area or volume also change disproportionately.

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Geometric shapes and relationships can be described in terms of symbols and numbers-and vice versa. For example, the position of any point on a surface can be specified by two numbers; a graph represents all the values that satisfy an equation; and if two equations have to be satisfied at the same time, the values that satisfy them both will be found where their graphs intersect.

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Different ways to map a curved surface (like the earth's) onto a flat surface have different advantages.

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D. Uncertainty

By the end of the 12th grade, students should know that:

 

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.

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When people estimate a statistic, they may also be able to say how far off the estimate might be.

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The middle of a data distribution may be misleading-when the data are not distributed symmetrically, or when there are extreme high or low values, or when the distribution is not reasonably smooth.

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The way data are displayed can make a big difference in how they are interpreted.

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Both percentages and actual numbers have to be taken into account in comparing different groups; using either category by itself could be misleading.

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Considering whether two variables are correlated requires inspecting their distributions, such as in two-way tables or scatterplots. A believable correlation between two variables doesn't mean that either one causes the other; perhaps some other variable causes them both or the correlation might be attributable to chance alone. A true correlation means that differences in one variable imply differences in the other when all other things are equal.

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The larger a well-chosen sample of a population is, the better it estimates population summary statistics. For a well-chosen sample, the size of the sample is much more important than the size of the population. To avoid intentional or unintentional bias, samples are usually selected by some random system.

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A physical or mathematical model can be used to estimate the probability of real-world events.

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E. Reasoning

By the end of the 12th grade, students should know that:

 

To be convincing, an argument needs to have both true statements and valid connections among them. Formal logic is mostly about connections among statements, not about whether they are true. People sometimes use poor logic even if they begin with true statements, and sometimes they use logic that begins with untrue statements.

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Logic requires a clear distinction among reasons: A reason may be sufficient to get a result, but perhaps is not the only way to get there; or, a reason may be necessary to get the result, but it may not be enough by itself; some reasons may be both sufficient and necessary.

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Wherever a general rule comes from, logic can be used in testing how well it works. Proving a generalization to be false (just one exception will do) is easier than proving it to be true (for all possible cases). Logic may be of limited help in finding solutions to problems if one isn't sure that general rules always hold or that particular information is correct; most often, one has to deal with probabilities rather than certainties.

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Once a person believes in a general rule, he or she may be more likely to notice cases that agree with it and to ignore cases that don't. To avoid biased observations, scientific studies sometimes use observers who don't know what the results are "supposed" to be.

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Very complex logical arguments can be made from a lot of small logical steps. Computers are particularly good at working with complex logic but not all logical problems can be solved by computers. High-speed computers can examine the validity of some logical propositions for a very large number of cases, although that may not be a perfect proof.

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11. Common Themes
A. Systems

By the end of the 12th grade, students should know that:

 

A system usually has some properties that are different from those of its parts, but appear because of the interaction of those parts.

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Understanding how things work and designing solutions to problems of almost any kind can be facilitated by systems analysis. In defining a system, it is important to specify its boundaries and subsystems, indicate its relation to other systems, and identify what its input and its output are expected to be.

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The successful operation of a designed system usually involves feedback. The feedback of output from some parts of a system to input of other parts can be used to encourage what is going on in a system, discourage it, or reduce its discrepancy from some desired value. The stability of a system can be greater when it includes appropriate feedback mechanisms.

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Even in some very simple systems, it may not always be possible to predict accurately the result of changing some part or connection.

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B. Models

By the end of the 12th grade, students should know that:

 

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.

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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.

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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.

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C. Constancy and Change

By the end of the 12th grade, students should know that:

 

A system in equilibrium may return to the same state of equilibrium if the disturbances it experiences are small. But large disturbances may cause it to escape that equilibrium and eventually settle into some other state of equilibrium.

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Along with the theory of atoms, the concept of the conservation of matter led to revolutionary advances in chemical science. The concept of conservation of energy is at the heart of advances in fields as diverse as the study of nuclear particles and the study of the origin of the universe.

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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). Sometimes counterbalancing changes are necessary for a thing to retain its essential constancy in the presence of changing conditions.

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Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change.

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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.

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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.

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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.

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D. Scale

By the end of the 12th grade, students should know that:

 

Representing large numbers in terms of powers of ten makes it easier to think about them and to compare things that are greatly different.

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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.

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As the number of parts of a system increases, the number of possible interactions between pairs of parts increases much more rapidly.

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12. Habits of Mind
A. Values and Attitudes

By the end of the 12th grade, students should know that:

 

Know why curiosity, honesty, openness, and skepticism are so highly regarded in science and how they are incorporated into the way science is carried out; exhibit those traits in their own lives and value them in others.

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View science and technology thoughtfully, being neither categorically antagonistic nor uncritically positive.

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B. Computation and Estimation

By the end of the 12th grade, students should know that:

 

Use ratios and proportions, including constant rates, in appropriate problems.

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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.

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Make up and write out simple algorithms for solving problems that take several steps.

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Use computer spreadsheet, graphing, and database programs to assist in quantitative analysis.

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Compare data for two groups by representing their averages and spreads graphically.

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Express and compare very small and very large numbers using powers-of-ten notation.

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Trace the source of any large disparity between an estimate and the calculated answer.

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Recall immediately the relations among 10, 100, 1000, 1 million, and 1 billion (knowing, for example, that 1 million is a thousand thousands).

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Consider the possible effects of measurement errors on calculations.

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C. Manipulation and Observation

By the end of the 12th grade, students should know that:

 

Learn quickly the proper use of new instruments by following instructions in manuals or by taking instructions from an experienced user.

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Use computers for producing tables and graphs and for making spreadsheet calculations.

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Troubleshoot common mechanical and electrical systems, checking for possible causes of malfunction, and decide on that basis whether to make a change or get advice from an expert before proceeding.

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Use power tools safely to shape, smooth, and join wood, plastic, and soft metal.

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D. Communication Skills

By the end of the 12th grade, students should know that:

 

Make and interpret scale drawings.

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Write clear, step-by-step instructions for conducting investigations, operating something, or following a procedure.

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Choose appropriate summary statistics to describe group differences, always indicating the spread of the data as well as the data's central tendencies.

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Describe spatial relationships in geometric terms such as perpendicular, parallel, tangent, similar, congruent, and symmetrical.

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Use and correctly interpret relational terms such as if . . . then . . . , and, or, sufficient, necessary, some, every, not, correlates with, and causes.

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Participate in group discussions on scientific topics by restating or summarizing accurately what others have said, asking for clarification or elaboration, and expressing alternative positions.

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Use tables, charts, and graphs in making arguments and claims in oral and written presentations.

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E. Critical-Response Skills

By the end of the 12th grade, students should know that:

 

Notice and criticize arguments based on the faulty, incomplete, or misleading use of numbers, such as in instances when (1) average results are reported, but not the amount of variation around the average, (2) a percentage or fraction is given, but not the total sample size (as in "9 out of 10 dentists recommend..."), (3) absolute and proportional quantities are mixed (as in "3,400 more robberies in our city last year, whereas other cities had an increase of less than 1%), or (4) results are reported with overstated precision (as in representing 13 out of 19 students as 68.42%).

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Check graphs to see that they do not misrepresent results by using inappropriate scales or by failing to specify the axes clearly.

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Wonder how likely it is that some event of interest might have occurred just by chance.

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Insist that the critical assumptions behind any line of reasoning be made explicit so that the validity of the position being taken-whether one's own or that of others-can be judged.

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Be aware, when considering claims, that when people try to prove a point, they may select only the data that support it and ignore any that would contradict it.

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Suggest alternative ways of explaining data and criticize arguments in which data, explanations, or conclusions are represented as the only ones worth consideration, with no mention of other possibilities. Similarly, suggest alternative trade-offs in decisions and designs and criticize those in which major trade-offs are not acknowledged.

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