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Introductory skills


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High school students are expected to have learned certain math skills by the end of grade 8; they will use these math skills in this course. Additional math skills are introduced throughout the year.

Isolating a variable

How to isolate a variable

SI (metric) system


Metric system table

Dimensional analysis

Dimensional analysis : KaiserScience

Fun with dimensional analysis – read the introduction, and look at examples 1 and 2.  They are explained very well. (Examples after that have typos, so ignore those.)

Scientific notation

MathMol: How to write in scientific notation

Scientific Notation Primer: Regents Prep website

Accuracy versus precision

Accuracy and precision

Significant figures (“sig figs”)

Significant figures (KaiserScience)

Counting sig figs (ScienceGeek.net)

How to write a lab report

Lab report

History of physics

Mesopotamian science and astronomy

Aristotle’s laws of motion

Early views of the solar system

Medieval views of the solar system

Modern view of the solar system

Early quantum theory: The end of the era of classical physics

Scaling laws

Scaling and biophysics (on our website)

Size and scale of giant monsters (on our website)

Areas and volumes

Godzilla versus the scaling laws of physics

Scaling: Why Galileo knew that giants don’t exist

The Biology (and scaling laws) of B-movie monsters

[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

– Galileo, Opere Il Saggiatore p. 171

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Science and Engineering Practices: 5. Using Mathematics and Computational Thinking:
Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m 3, acre-feet, etc.).

National Council of Teachers of Mathematics
Students need to develop an understanding of metric units and their relationships, as well as fluency in applying the metric system to real-world situations. Because some non-metric units of measure are common in particular contexts, students need to develop familiarity with multiple systems of measure, including metric and customary systems and their relationships.

National Science Teachers Association
The efficiency and effectiveness of the metric system has long been evident to scientists, engineers, and educators. Because the metric system is used in all industrial nations except the United States, it is the position of the National Science Teachers Association that the International System of Units (SI) and its language be incorporated as an integral part of the education of children at all levels of their schooling.

Next Gen Science Standards HS-PS2 Motion and Stability

Crosscutting Concepts: Different patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena. (HS-PS2-4)

A Framework for K-12 Science Education

Scale, proportion, and quantity. In considering phenomena, it is critical to recognize what is relevant at different measures of size, time, and energy and to recognize how changes in scale, proportion, or quantity affect a system’s structure or performance….

The understanding of relative magnitude is only a starting point. As noted in Benchmarks for Science Literacy, “The large idea is that the way in which things work may change with scale. Different aspects of nature change at different rates with changes in scale, and so the relationships among them change, too” [4]. Appropriate understanding of scale relationships is critical as well to engineering—no structure could be conceived, much less constructed, without the engineer’s precise sense of scale.

  • Dimension 2, Crosscutting Concepts, A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
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