Standards Map

Mathematics > Course Model Algebra I (Traditional Pathway) > Creating Equations
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Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Creating Equations

Cluster - Create equations that describe numbers or relationships.

[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.

Resources:

Predecessor Standards:

  • 8.EE.C.7
    Solve linear equations in one variable.
  • 8.EE.C.7.a
    Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
  • 8.EE.C.7.b
    Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
  • 8.EE.C.8
    Analyze and solve pairs of simultaneous linear equations.
  • 8.EE.C.8.a
    Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
  • 8.EE.C.8.b
    Solve systems of two linear equations in two variables algebraically (using substitution and elimination strategies), and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
  • 8.EE.C.8.c
    Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.A-SSE.A.1
    Interpret expressions that represent a quantity in terms of its context.*
  • AI.A-SSE.A.1.a
    Interpret parts of an expression, such as terms, factors, and coefficients.
  • AI.A-SSE.A.1.b
    Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)t as the product of P and a factor not depending on P.
  • AI.A-REI.A.1
    Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solution method.
  • AI.A-REI.B.3
    Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • AI.A-REI.B.3.a
    Solve linear equations and inequalities in one variable involving absolute value.
  • HS.ESS.1.4
    Use Kepler’s laws to predict the motion of orbiting objects in the solar system. Describe how orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system. Clarification Statements: Kepler’s laws apply to human-made satellites as well as planets, moons, and other objects. Calculations involving Kepler’s laws of orbital motions should not deal with more than two bodies, nor involve calculus.
  • 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.2.4
    Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and predict the effects of gravitational and electrostatic forces between objects. Clarification Statement: Emphasis is on the relative changes when distance, mass or charge, or both are changed. State Assessment Boundaries: State assessment will be limited to systems with two objects. Permittivity of free space is 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.4.4
    Calculate and describe the ability of a hydraulic system to multiply distance, multiply force, and effect directional change. Clarification Statement: Emphasis is on the ratio of piston sizes (cross-sectional area) as represented in Pascal’s law.