• 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.

• 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.

• 6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
• 9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.

• 6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.
• 6-8: 11B/M4. Simulations are often useful in modeling events and processes.

• 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

• A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

• 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.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• 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.

• F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
• F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
• F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
• F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^?

• RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11—12 texts and topics.

• RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.

• RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

This module integrates a Java simulation, related lessons, physics background information, and explicit help in using every tool available in the simulation. It features a block suspended on a frictionless spring. Students can change the spring constant, mass of the block, and amplitude. Tools include a vector display and real-time graphs of potential and kinetic energy, position, velocity, and mechanical energy.

• Physics First Simple Harmonic Motion Unit
• Conceptual Physics Simple Harmonic Motion Unit
• Algebra-Based Physics Simple Harmonic Motion Unit
• AP/Calculus-Based Physics Simple Harmonic Motion Unit

Looking for a scaffolded simulation on SHM that has a lesson plan, background information, and explicit help for students? This module, developed by the University of Calgary Physics Department, brings it all together in one convenient location. It features a mass on a frictionless spring. You can adjust the spring constant, add/subtract mass, and change amplitude. The tools include a vector display, kinetic/potential energy bar graphs, and real-time graphs of position, velocity, and mechanical energy.

• Physics First Teaching About Oscillation Unit
• Conceptual Physics Teaching About Oscillation Unit
• Algebra-Based Physics Teaching About Oscillation Unit
• AP/Calculus-Based Physics Teaching About Oscillation Unit