### 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.

## Calculators

This should go without saying, but you are responsible for learning how to use your calculator. Be able to enter numbers in standard and scientific notation, and have the calculator perform operations on them.

one can purchase scientific calculators for less than $10

## Isolating a variable

## SI (metric) system

https://kaiserscience.wordpress.com/physics/introductory-skills/metric-system/

## Dimensional analysis

Dimensional analysis : KaiserScience

## Scientific notation

Scientific notation worksheets

MathMol: How to write in scientific notation

Scientific Notation Primer: Regents Prep website

## Size and scale

The size and scale of the universe lesson, from Scale of the Universe app – htwins.net

Worksheets: The size and scale of the universe

## Accuracy versus precision

## Significant figures (“sig figs”)

Significant figures (KaiserScience)

Counting sig figs (ScienceGeek.net)

## How to write a lab report

## Graphing

Data needs an interpretation to have meaning

## Critical thinking

Learning requires the ability to think independently and critically.

Why does science even matter in the first place?

You’re Not Going to Believe What I’m Going To Tell You

the Scientific method (and nope, its not a simple recipe)

What is philosophy? Using systematic, reasoned thinking to analyze questions

Understanding what we read: Close Reading Strategies

## History of physics

Mesopotamian science and astronomy

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)

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

## Math is the language of physics

### Math is the language 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

## 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)