The Colors of Stars
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 Colors project are listed below the table
Chapter 1:
Introduction and Exploration 
IA51, IA81,
IA121, IB123, IC86, IC87, IIIA52, IVA55 
Chapter 2:
Definition of Color 
IA83, IVA55,
IVA82, IVA121, IVA123, IVF81, IVF82, IVF85, IVF123 
Chapter 3:
Thermal Radiation, Temperature, and Observed Spectra 
IA121, IB51,
IB123, IC86, IIIA82, IVA121, IVD81, IVF81, IVF85 
Chapter 4:
ColorColor Diagrams and Thermal Sources 
IA121, IB81, IB121,
IB123, IC86, IC87, IIIA82, IVA55, IVF81, IVF85 
Chapter 5:
Conclusion/
Research Challenge 
IA81, IB82,
IB121, IB122, IB123, IC86, IC87, IIIA82, IVA81, IVA82,
IVA121, IVA123 
Standards
IA51. Results of similar scientific invesitgations 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.
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.
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.
IB51. 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.
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.
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).
IB123. 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.
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.
IIIA52. 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.
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.
IVA55. Stars are like the sun, some being smaller and some
larger, but so far away that they look like points of light.
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.
IVD81. All matter is made up of atoms, which are far too small
to see directly through a microscope. The atoms of any element are alike
but are different from atoms of other elements. Atoms may stick together
in welldefined molecules or may be packed together in large arrays.
Different arrangements of atoms into groups compose all substances.
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."
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 Colors in Astronomy
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.
Chapter 1:
Introduction and Exploration 
IA81, IA82, IB82, IC81,
IIC81, IIC123, VC83, VI2, VIII2, X1, X3 
Chapter 2:
Definition of Color 
IA81, IA84, IB81,
IB82, IB121, IC81, IC84, IC122, IIA82, IIA121, IIB121,
IIB125, IVA81, IVB124, VI2, IX3 
Chapter 3:
Thermal Radiation, Temperature and Observed Spectra 
IA81, IA121, IB81, IB121,
IC81, IC122, IIC81, IVA82, IVA121, IVB124,
VI2 
Chapter 4:
ColorColor Diagrams and Thermal Sources 
IA81, IA82, IA84, IB81,
IC84, IIA83, IIA126, IIC123, IVA82, IVB124,
VA82, VC82, 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.
IB82. Use the associative and commutative properties of
addition and multiplication and the distributive property of
multiplication over addition to simplify computations with integers,
fractions, and decimals.
IB121. Judge the effects of such operations as multiplication,
division, and computing powers and roots on the magnitudes of quantities.
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.
IIA82. Relate and compare different forms of representation for
a relationship.
IIA83. Identify functions as linear or nonlinear and contrast
their properties from tables, graphs, or equations.
IIA123. Analyze functions of one variable by investigating
rates of change, intercepts, zeros, asymptotes, and local and global
behavior.
IIA125. Understand and compare the properties of classes of
functions, including exponential, polynomial, rational, logarithmic, and
periodic functions.
IIA126. Interpret representations of functions of two
variables.
IIB121. Understand the meaning of equivalent forms of
expressions, equations, inequalities, and relations.
IIB123. Use symbolic algebra to represent and explain
mathematical relationships.
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.
IVA82. Understand relationships among units and convert from
one unit to another within the same system.
IVB124. Use unit analysis to check measurement computations.
VA82. Select, create, and use appropriate graphical
representations of data, including histograms, box plots, and scatterplots.
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.
IX3. Recognize and apply mathematics in contexts outside of
mathematics.
X1. Create and use representations to organize, record, and
communicate mathematical ideas.
X3. Use representations to model and interpret physical,
social, and mathematical phenomena.
