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
SI (metric) system
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.)
Accuracy versus precision
Significant figures (“sig figs”)
How to write a lab report
History of physics
[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
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” . 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)