• 9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

• 6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.
• 9-12: 4E/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.

• 3-5: 4F/E3. Light travels and tends to maintain its direction of motion until it interacts with an object or material. Light can be absorbed, redirected, bounced back, or allowed to pass through.
• 6-8: 4F/M4. Vibrations in materials set up wavelike disturbances that spread away from the source. Sound and earthquake waves are examples. These and other waves move at different speeds in different materials.
• 6-8: 4F/M6. Light acts like a wave in many ways. And waves can explain how light behaves.
• 6-8: 4F/M7. Wave behavior can be described in terms of how fast the disturbance spreads, and in terms of the distance between successive peaks of the disturbance (the wavelength).
• 6-8: 4F/M8. There are a great variety of electromagnetic waves: radio waves, microwaves, infrared waves, visible light, ultraviolet rays, X-rays, and gamma rays. These wavelengths vary from radio waves, the longest, to gamma rays, the shortest.
• 9-12: 4F/H6ab. Waves can superpose on one another, bend around corners, reflect off surfaces, be absorbed by materials they enter, and change direction when entering a new material. All these effects vary with wavelength.
• 9-12: 4F/H6c. The energy of waves (like any form of energy) can be changed into other forms of energy.

• A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

• F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
• F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^?
• F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.^?
• F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
• F-IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

• F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

From research in physics education, there is increasing awareness that students come into a physics class with firmly held beliefs that cannot be ignored.  These tutorials use hands-on activities and probing questions to draw out misconceptions and facilitate learning.  They are designed for cooperative learning groups, with complete sets of student activities and problems.  Accompanying solutions are to be distributed to groups before they leave class, thus giving immediate feedback.

• Physics First Teaching About Waves and Wave Energy Unit
• Conceptual Physics Teaching About Waves and Wave Energy Unit
• Algebra-Based Physics Teaching About Waves and Wave Energy Unit
• AP/Calculus-Based Physics Teaching About Waves and Wave Energy Unit