# 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 H-R Diagram project.

The list below shows all Project 2061 benchmarks met by the H-R diagram project. 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.

The H-R Diagram unit meets the following Project 2061 Benchmarks:

IA12-1, IC8-6, IIIB8-1, IVA8-1, IVA8-2, IVA12-1, IVA12-3.

### Benchmarks

**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 very simple to extremely complex, but scientists operate on the belief that the rules can be discovered by careful, systematic study.

**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.

**IIIB8-1**. Design usually requires taking constraints into account. Some constraints, such as gravity or the properties of materials to be used, are unaviodable. Other constraints, including economic, political, social, ethical, and aesthetic ones, limit choices.

**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.

**IVA12-3**. 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.

## 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 standards for students completing grade 2, grade 5, grade 8, and grade 12. The table below shows which standards are met by the H-R Diagram project.

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 standard 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. The standards met by the H-R Diagram project are:

IA8-1, IA8-4, IA8-5, IA12-1, IB12-1, IC8-1, IC12-2, IIA12-5, IIC8-1, IIC12-3, IVA8-2, IVA12-1, IVB12-4, VA8-2, VB8-2, VC8-2, VC8-3, VI-2, VIII-2, IX-3, X-3.

### Standards

Students should be able to:

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

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

**IA8-5**. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.

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

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

**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.

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

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

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

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

**IVA8-2**. Understand relationships among units and convert from one unit to another within the same system.

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

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

**VA8-2**. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

**VB8-2**. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

**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.

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

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