# Correlations

## Correlations to Project 2061 Benchmarks in Science Education

The Project 2061 Benchmarks in Science Education is a report, originally published in 1993 by the American Association for the Advancement of Science (AAAS), that listed what students should know about scientific literacy. The report listed facts and concepts about science and the scientific process that all students should know at different grade levels.

The report is divided and subdivided into different content areas. Within each subarea, the report lists benchmarks for students completing grade 2, grade 5, grade 8, and grade 12. The table below shows which benchmarks are met by which sections of the Hubble Diagram project.

The left column lists the sections of the project. The right column lists all benchmarks that are at least partially discussed by that section. Content headings are listed as Roman numerals, subheadings as letters, grade levels by numbers, and specific points by numbers after the hyphen. For example, benchmark IA8-2 means the second benchmark for eighth grade students in the first content area, first subarea. All benchmarks met by the Hubble project are listed below the table.

Introduction |
IA8-2, IA12-1, IB8-1, IB8-4, IB12-1, IVA8-1, IVA12-2, IVA12-3 |

Simple Diagram: Distances |
IA12-1, IVA8-2 |

Simple Diagram: Redshifts |
IVF8-1, IVF8-2, IVF8-5 |

Simple Diagram: Making the Diagram |
IA12-1, IB8-1, IC8-6, IC8-7, IVA12-1, IVA12-4 |

Simple Diagram: Another Hubble Diagram |
IA8-1, IA12-3, IB8-2, IB8-4, IC8-6, IC8-7 |

Distances |
IA8-1, IA12-1, IB8-1, IB8-2, IC8-6, IC8-7, IIIA8-2, IVA8-1, IVF8-2 |

Redshifts |
IA12-1, IIIA8-2, IIIA12-1, IVA8-1, IVA12-1, IVA12-3, IVA8-1, IVD8-5, IVD12-1, IVD12-2, IVE12-4, IVE12-5, IVF8-1, IVF8-2, IVF12-3, IVF12-5 |

Conclusion |
IA8-1, IA12-1, IA12-3, IB12-2, IC8-6, IIIA8-2, IVA12-2, IVA12-3, IVA12-4, IVF12-5 |

### Standards

**IA8-1**. 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.

**IA8-2**. 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.

**IA12-1**. Scientists assume that the universe is a vast single system in which the basic rules are the same everywhere. The rules may range from the very simple to the extremely complex, but scientists operate on the belief that the rules can be discovered by careful, systematic study.

**IA12-2**. 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.

**IA12-3**. 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.

**IB8-1**. 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.

**IB8-2**. 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.

**IB8-4**. New ideas in science sometimes spring from unexpected findings, and they usually lead to new investigations.

**IB12-1**. 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.

**IB12-2**. 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).

**IC8-6**. 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.

**IC8-7**. Accurate record-keeping, openness, and replication are essential for maintaining an investigator’s credibility with other scientists and society.

**IIIA8-2**. Technology is essential to science for such purposes as access to outer space and other remote locations, sample collection and treatments, measurement, data collection and storage, computation, and communication of information.

**IIIA12-1**. Technological problems often create a demand for new scientific knowledge, and new technologies make it possible for scientists to extend their research in new ways or to undertake entirely new lines of research. The very availability of new technology itself often sparks scientific advances.

**IVA8-1**. The sun is a medium-sized star located near the edge of a disk-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. The universe contains many billions of galaxies, and each galaxy contains many billions of stars. To the naked eye, even the closest of these galaxies is no more than a dim, fuzzy spot.

**IVA8-2**. 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. Some distant galaxies are so far away that their light takes several billion years to reach the earth. People on earth, therefore see them as they were that long ago in the past.

**IVA12-1**. The stars differ from each other in size, temperature, and age, but they appear to be made up of the same elements that are found on the earth and to behave according to the same physical principles. Unlike the sun, most stars are in systems of two or more stars orbiting around one another.

**IVA12-2**. On the basis of scientific evidence, the universe is estimated to be over ten billion years old. The current theory is that its entire contents expanded explosively from a hot, dense, chaotic mass. Stars condensed by gravity out of clouds of molecules of the lightest elements until nuclear fusion of the light elements into heavier ones began to occur. Fusion released great amounts of energy over millions of years. Eventually, some stars exploded, producing clouds of heavy elements from which other stars and planets could later condense. The process of star formation and destruction continues.

**IVA12-3**. 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 an avalanche of data and increasingly complicated computations to interpret them; space probes send back data and materials from the 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.

**IVA12-4**. Mathematical models and computer simulations are used in studying evidence from many sources in order to form a scientific account of the universe.

**IVD8-5**. Scientific ideas about elements were borrowed from some Greek philosophers of 2,000 years earlier, who believed that everything was made from four basic substances: air, earth, fire, and water. It was the combinations of these “elements” in different proportions that gave other substances their observable properties. The Greeks were wrong about those four, but now over 100 different elements have been identifies, some rare and some plentiful, out of which everything is made. Because most elements tend to combine with others, few elements are found in their pure form.

**IVD12-1**. Atoms are made of a positive nucleus surrounded by negative electrons. An atom’s electron configuration, particularly the outermost electrons, determines how the atom can interact with other atoms. Atoms form bonds to other atoms by transferring or sharing electrons.

**IVD12-2**. The nucleus, a tiny fraction of the volume of an atom, is composed of protons and neutrons, each almost two thousand times heavier than an electron. The number of positive protons in the nucleus determines what an atom’s electron configuration can be and so defines the element. In a neutral atom, the number of electrons equals the number of protons. But an atom may acquire an unbalanced charge by gaining or losing electrons.

**IVE12-4**. Different energy levels are associated with different configurations of atoms and molecules. Some changes of configuration require an input of energy whereas others release energy.

**IVE12-5**. When energy of an isolated atom or molecule changes, it does so in a definite jump from one value to another, with no possible values in between. The change in energy occurs when radiation is absorbed or emitted, so the radiation also has distinct energy values. As a result, the light emitted or absorbed by separate atoms or molecules (as in a gas) can be used to identify what the substance is.

**IVF8-1**. Light from the sun is made up of a mixture of many different colors of light, even though to the eye the light looks almost white> Other things that give off or reflect light have a different mix of colors.

**IVF8-2**. Something can be “seen” when light waves emitted or reflected by it enter the eye – just as something can be “heard” when sound waves from it enter the ear.

**IVF8-5**. Human eyes respond to only a narrow range of wavelengths of electromagnetic radiation – visible light. Differences of wavelength within that range are perceived as differences in color.

**IVF12-3**. Accelerating electric charges produce electromagnetic waves around them. A great variety of radiations are electromagnetic waves: radio waves, microwaves, radiant heat, visible light, ultraviolet radiation, x rays, and gamma rays. These wavelengths vary from radio waves, the longest, to gamma rays, the shortest. In empty space, all electromagnetic waves move at the same speed – the “speed of light.”

**IVF12-5**. The observed wavelength of a wave depends upon the relative motion of the source and the observer. If either is moving toward the other, the observed wavelength is shorter; if either is moving away, the wavelength is longer. Because the light seen from almost all distant galaxies has longer wavelengths than comparable light here on earth, astronomers believe that the whole universe is expanding.

## Correlations to NCTM Principles and Standards for School Mathematics

*Principles and Standards for School Mathematics* was released in 2000 by the National Council of Teachers of Mathematics. The standards, a collaboration between education researchers and school mathematics teachers, lists what concepts students should understand, and what skills they should possess, at different stages of their mathematics education.

The report is divided and subdivided into ten different content areas. Within the first six areas, the report lists benchmarks for students completing grade 2, grade 5, grade 8, and grade 12. The table below shows which standards are met by which sections of the Hubble Diagram project.

The left column lists the sections of the project. The right column lists all standards that are at least partially discussed by that section. Content headings are listed as Roman numerals, subheadings as letters, grade levels as numbers, and specific points by numbers after the hyphen. For example, standard IA8-2 means the second benchmark for eighth grade students in the first content area, first subarea. Content areas VI through X, which concern skill processes in mathematics, are not divided into subareas or grade levels. All standards met by the Hubble diagram project are listed below the table.

A Simple Diagram |
IA12-1, IIA8-3, IID8-1, IIC12-1, IVA8-1, IVA12-1, IVB12-1, VC8-2, VB12-2, VI-2, VIII-2, IX-3, X-3 |

Distances |
IA8-1, IA8-4, IB8-1, IC8-1, IA12-1, IB12-1, IC8-4, IC12-2, IIA12-5, IIC8-1, IIC12-1, IVA12-1, IVB12-4, VI-2, VIII-4, IX-3 |

Redshifts |
IA8-1, IA8-2, IC8-1, ID8-1, IIB12-5, IIC12-3, IVA1201, IVB8-6, IVB12-4, VI-2, X-2, X-3 |

Conclusion |
IA8-1, IA12-1, IB12-1, IB12-3, IIB8-2, IIB8-4, IIB12-5, IIC12-1, IIC12-3, IID8-1, IID12-1, IVA12-1, IVB8-1, IVB8-6, IVB12-2, VB12-5, VI-2, VIII-2, IX-3, X-1, |

### Standards

Students should be able to:

**IA8-1**. Work flexibly with fractions, decimals, and percents to solve problems.

**IA8-2**. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line.

**IA8-4**. Understand and use ratios and proportions to represent quantitative relationships

**IA12-1**. Develop a deeper understanding of very large and very small numbers and of various representations of them.

**IB8-1**. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

**IB12-1**. Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.

**IB12-3**. Develop an understanding of permutations and combinations as counting techniques.

**IC8-1**. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods.

**IC8-4**. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

**IC12-2**. Judge the reasonableness of numerical computations and their results.

**IIA8-3**. Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.

**IIA12-5**. Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.

**IIB8-2**. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

**IIB8-4**. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.

**IIB12-5**. Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

**IIC8-1**. Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

**IIC12-1**. Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model those relationships.

**IIC12-3**. Draw reasonable conclusions about a situation being modeled.

**IID8-1**. Use graphs to analyze the nature of changes in quantities in linear relationships.

**IID12-1**. Approximate and interpret rates of change from graphical and numerical data.

**IVA8-1**. Understand both metric and customary systems of measurement.

**IVA12-1**. Make decisions about units and scales that are appropriate for problem situations involving measurement.

**IVB8-1**. Use common benchmarks to select appropriate methods for estimating measurements.

**IVB8-6**. Solve simple problems involving rates and derived measurements for such attributes as velocity and density.

**IVB12-1**. Analyze precision, accuracy, and approximate error in measurement situations.

**IVB12-4**. Use unit analysis to check measurement computations.

**VB12-2**. For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlations coefficients using technological tools.

**VB12-5**. Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.

**VC8-2**. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

**VC8-3**. Use conjectures to formulate new questions and plan new studies to answer them.

**VI-2**. Solve problems that arise in mathematics and other contexts.

**VIII-2**. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

**VIII-4**. Use the language of mathematics to express mathematical ideas precisely.

**IX-3**. Recognize and apply mathematics in contexts outside of mathematics.

**X-1**. Create and use representations to organize, record, and communicate mathematical ideas.

**X-2**. Select, apply, and translate among mathematical representations to solve problems.

**X-3**. Use representations to model and interpret physical, social, and mathematical phenomena.