Project 2061 Benchmarks
Nature of Science - Physical World
By the End of Grade 2
The sun can be seen only in the daytime, but the moon can be seen sometimes at night and sometimes during the day. The sun, moon, and stars all appear to move slowly across the sky. 4A/P2
By the End of Grade 5
- The patterns of stars in the sky stay the same, although they appear to move across the sky nightly, and different stars can be seen in different seasons. 4A/E1
- Telescopes magnify the appearance of some distant objects in the sky, including the moon and the planets. The number of stars that can be seen through telescopes is dramatically greater than can be seen by the unaided eye. 4A/E2
- Planets change their positions against the background of stars. 4A/E3
- The earth is one of several planets that orbit the sun, and the moon orbits around the earth. 4A/E4
- Stars are like the sun, some being smaller and some larger, but so far away that they look like points of light. 4A/E5
- A large light source at a great distance looks like a small light source that is much closer. 4A/E6
By the End of Grade 8
- The sun is a medium-sized star located near the edge of a disc-shaped galaxy of stars, part of which can be seen as a glowing band of light that spans the sky on a very clear night. 4A/M1a
- The sun is many thousands of times closer to the earth than any other star. Light from the sun takes a few minutes to reach the earth, but light from the next nearest star takes a few years to arrive. The trip to that star would take the fastest rocket thousands of years. 4A/M2abc
By the End of Grade 12
- Increasingly sophisticated technology is used to learn about the universe. Visual, radio, and X-ray telescopes collect information from across the entire spectrum of electromagnetic waves; computers handle data and complicated computations to interpret them; space probes send back data and materials from remote parts of the solar system; and accelerators give subatomic particles energies that simulate conditions in the stars and in the early history of the universe before stars formed. 4A/H3
- Mathematical models and computer simulations are used in studying evidence from many sources in order to form a scientific account of the universe. 4A/H4
Nature of Technology - Technology and Science
By the End of Grade 2
- 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. 3A/P1
- 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. 3A/P2
By the End of Grade 5
- Technology enables scientists and others to observe things that are too small or too far away to be seen otherwise and to study the motion of objects that are moving very rapidly or are hardly moving at all. 3A/E2
- 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. 3A/E3
- 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. 3A/E4
By the End of Grade 8
- 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. 3A/M1
- 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. 3A/M2
By the End of Grade 12
- Technological problems and advances 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. 3A/H1*
- Mathematics, creativity, logic, and originality are all needed to improve technology. 3A/H2
- Technology usually affects society more directly than science does because technology solves practical problems and serves human needs (and also creates new problems and needs). 3A/H3a*
- One way science affects society is by stimulating and satisfying people's curiosity and enlarging or challenging their views of what the world is like. 3A/H3b*
Mathematical World - Symbolic Relationships
By the End of Grade 2
- Similar patterns may show up in many places in nature and in the things people make. 9B/P1
By the End of Grade 5
- Tables and graphs can show how values of one quantity are related to values of another. 9B/E2
By the End of Grade 8
- 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, increase or decrease in steps, or do something different from any of these. 9B/M3*
By the End of Grade 12
- 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. 9B/H3
- Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another. 9B/H4
- 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 by more than one, and sometimes not at all. 9B/H5