Mathematics | Course : Model Algebra I (Traditional Pathway)
Domain - Reasoning with Equations and Inequalities
Cluster - Solve equations and inequalities in one variable.
[AI.A-REI.B.3.a] - Solve linear equations and inequalities in one variable involving absolute value.
- Absolute value
The absolute value of a real number is its (non-negative) distance from 0 on a number line. - Linear equation
Any equation that can be written in the form Ax + By + C = 0 where A and B cannot both be 0. The graph of such an equation is a line. - Variable
A quantity that can change or that may take on different values. Refers to the letter or symbol representing such a quantity in an expression, equation, inequality, or matrix.
[AI.A-CED.A.4] -
Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (Properties of equality).* For example, rearrange Ohm’s law R=V2/P to solve for voltage, V. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt.
[AI.F-BF.B.4.a] -
Solve an equation of the form f(x) = c for a linear function f that has an inverse and write an expression for the inverse.
[HS.CHEM.2.8] -
Use kinetic molecular theory to compare the strengths of electrostatic forces and the prevalence of interactions that occur between molecules in solids, liquids, and gases. Use the combined gas law to determine changes in pressure, volume, and temperature in gases.
[HS.PHY.2.1] -
Analyze data to support the claim that Newton’s second law of motion is a mathematical model describing change in motion (the acceleration) of objects when acted on by a net force. Clarification Statements: Examples of data could include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object rolling down a ramp, and a moving object being pulled by a constant force. Forces can include contact forces, including friction, and forces acting at a distance, such as gravity and magnetic forces.
State Assessment Boundary: Variable forces are not expected in state assessment.
[HS.PHY.2.9] -
Evaluate simple series and parallel circuits to predict changes to voltage, current, or resistance when simple changes are made to a circuit.
Clarification Statements: Predictions of changes can be represented numerically, graphically, or algebraically using Ohm’s law. Simple changes to a circuit may include adding a component, changing the resistance of a load, and adding a parallel path, in circuits with batteries and common loads. Simple circuits can be represented in schematic diagrams. State Assessment Boundary: Use of measurement devices and predictions of changes in power are not expected in state assessment.
[HS.PHY.3.2] -
Develop and use a model to illustrate that energy at the macroscopic scale can be accounted for as either motions of particles and objects or energy stored in fields. Clarification Statements: Examples of phenomena at the macroscopic scale could include evaporation and condensation, the conversion of kinetic energy to thermal energy, the gravitational potential energy stored due to position of an object above the earth, and the stored energy (electrical potential) of a charged object’s position within an electrical field. Examples of models could include diagrams, drawings, descriptions, and computer simulations.
[HS.PHY.3.4] -
Provide evidence that when two objects of different temperature are in thermal contact within a closed system, the transfer of thermal energy from higher-temperature objects to lower-temperature objects results in thermal equilibrium, or a more uniform energy distribution among the objects and that temperature changes necessary to achieve thermal equilibrium depend on the specific heat values of the two substances.
Clarification Statement: Energy changes should be described both quantitatively in a single phase (Q = mcΔT) and conceptually either in a single phase or during a phase change.
[HS.PHY.4.1] -
Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium. Clarification Statements: Emphasis is on relationships when waves travel within a medium, and comparisons when a wave travels in different media. Examples of situations to consider could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the Earth. Relationships include v = λf, T = 1/f, and the qualitative comparison of the speed of a transverse (including electromagnetic) or longitudinal mechanical wave in a solid, liquid, gas, or vacuum. State Assessment Boundary: Transitions between two media are not expected in state assessment.
[HS.ETS.2.3] -
Compare the costs and benefits of custom versus mass production based on qualities of the desired product, the cost of each unit to produce, and the number of units needed.