Hubble Diagram
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 IA82 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 
IA82, IA121, IB81, IB84, IB121, IVA81, IVA122, IVA123 
Simple Diagram: Distances 
IA121, IVA82 
Simple Diagram: Redshifts 
IVF81, IVF82, IVF85 
Simple Diagram: Making the Diagram 
IA121, IB81, IC86, IC87, IVA121, IVA124 
Simple Diagram: Another Hubble Diagram 
IA81, IA123, IB82, IB84, IC86, IC87 
Distances 
IA81, IA121, IB81, IB82, IC86, IC87, IIIA82, IVA81, IVF82 
Redshifts 
IA121, IIIA82, IIIA121, IVA81, IVA121, IVA123, IVA81, IVD85, IVD121,
IVD122, IVE124, IVE125, IVF81, IVF82, IVF123, IVF125 
Conclusion 
IA81, IA121, IA123, IB122, IC86, IIIA82, IVA122, IVA123, IVA124,
IVF125 
Standards
IA81. 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.
IA82. 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.
IA121. 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.
IA122. 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.
IA123. 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.
IB81. 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.
IB82. 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.
IB84. New ideas in science sometimes spring from unexpected findings,
and they usually lead to new investigations.
IB121. 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.
IB122. 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).
IC86. 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.
IC87. Accurate recordkeeping, openness, and replication are essential
for maintaining an investigator's credibility with other scientists and society.
IIIA82. 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.
IIIA121. 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.
IVA81. The sun is a mediumsized star located near the edge of a
diskshaped 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.
IVA82. 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.
IVA121. 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.
IVA122. 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.
IVA123. Increasingly sophisticated technology is used to learn about the
universe. Visual, radio, and xray 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.
IVA124. Mathematical models and computer simulations are used in studying
evidence from many sources in order to form a scientific account of the universe.
IVD85. 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.
IVD121. 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.
IVD122. 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.
IVE124. 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.
IVE125. 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.
IVF81. 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.
IVF82. 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.
IVF85. 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.
IVF123. 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."
IVF125. 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 IA82 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 
IA121, IIA83, IID81, IIC121, IVA81, IVA121, IVB121, VC82, VB122,
VI2, VIII2, IX3, X3 
Distances 
IA81, IA84, IB81, IC81, IA121, IB121, IC84, IC122, IIA125, IIC81, IIC121,
IVA121, IVB124, VI2, VIII4, IX3 
Redshifts 
IA81, IA82, IC81, ID81, IIB125, IIC123, IVA1201, IVB86, IVB124, VI2,
X2, X3 
Conclusion 
IA81, IA121, IB121, IB123, IIB82, IIB84, IIB125, IIC121, IIC123,
IID81, IID121, IVA121, IVB81, IVB86, IVB122, VB125, VI2, VIII2, IX3, X1,
X3 
Standards
Students should be able to:
IA81. Work flexibly with fractions, decimals, and percents to solve problems.
IA82. Compare and order fractions, decimals, and percents efficiently
and find their approximate locations on a number line.
IA84. Understand and use ratios and proportions to represent quantitative
relationships
IA121. Develop a deeper understanding of very large and very small numbers
and of various representations of them.
IB81. Understand the meaning and effects of arithmetic operations with fractions,
decimals, and integers.
IB121. Judge the effects of such operations as multiplication, division,
and computing powers and roots on the magnitudes of quantities.
IB123. Develop an understanding of permutations and combinations as
counting techniques.
IC81. 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.
IC84. Develop, analyze, and explain methods for solving problems involving
proportions, such as scaling and finding equivalent ratios.
IC122. Judge the reasonableness of numerical computations and their results.
IIA83. Identify functions as linear or nonlinear and contrast their
properties from tables, graphs, or equations.
IIA125. Understand and compare the properties of classes of functions,
including exponential, polynomial, rational, logarithmic, and periodic functions.
IIB82. Explore relationships between symbolic expressions and graphs
of lines, paying particular attention to the meaning of intercept and slope.
IIB84. Recognize and generate equivalent forms for simple
algebraic expressions and solve linear equations.
IIB125. Judge the meaning, utility, and reasonableness of the
results of symbol manipulations, including those carried out by technology.
IIC81. Model and solve contextualized problems using various
representations, such as graphs, tables, and equations.
IIC121. Identify essential quantitative relationships in a situation
and determine the class or classes of functions that might model those relationships.
IIC123. Draw reasonable conclusions about a situation being modeled.
IID81. Use graphs to analyze the nature of changes in
quantities in linear relationships.
IID121. Approximate and interpret rates of change from graphical
and numerical data.
IVA81. Understand both metric and customary systems of measurement.
IVA121. Make decisions about units and scales that are
appropriate for problem situations involving measurement.
IVB81. Use common benchmarks to select appropriate methods
for estimating measurements.
IVB86. Solve simple problems involving rates and derived measurements
for such attributes as velocity and density.
IVB121. Analyze precision, accuracy, and approximate error in
measurement situations.
IVB124. Use unit analysis to check measurement computations.
VB122. 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.
VB125. Identify trends in bivariate data and find functions that
model the data or transform the data so that they can be modeled.
VC82. Make conjectures about possible relationships between two
characteristics of a sample on the basis of scatterplots of the data and
approximate lines of fit.
VC83. Use conjectures to formulate new questions and plan new studies to
answer them.
VI2. Solve problems that arise in mathematics and other contexts.
VIII2. Communicate their mathematical thinking coherently and clearly
to peers, teachers, and others.
VIII4. Use the language of mathematics to express mathematical ideas
precisely.
IX3. Recognize and apply mathematics in contexts outside of mathematics.
X1. Create and use representations to organize, record, and communicate
mathematical ideas.
X2. Select, apply, and translate among mathematical
representations to solve problems.
X3. Use representations to model and interpret physical, social, and
mathematical phenomena.
