Standards Map

Mathematics > Course Model Algebra I (Traditional Pathway) > Linear, Quadratic, and Exponential Models
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Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Linear, Quadratic, and Exponential Models

Cluster - Construct and compare linear, quadratic, and exponential models and solve problems.

[AI.F-LE.A.1.b] - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*

Resources:

    Predecessor Standards:

    • 7.RP.A.3
      Use proportional relationships to solve multi-step ratio, rate, and percent problems. For example: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.
    • 8.F.A.3
      Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
    • 8.F.B.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.

    Successor Standards:

    No Successor Standards found.

    Same Level Standards:

    • AI.F-BF.A.2
      Write arithmetic and geometric sequences both recursively and with an explicit formula them to model situations, and translate between the two forms.*
    • AI.F-LE.A.1.a
      Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.*
    • AI.F-LE.A.1.c
      Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*
    • 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.2.2
      Use mathematical representations to show that the total momentum of a system of interacting objects is conserved when there is no net force on the system. Clarification Statement: Emphasis is on the qualitative meaning of the conservation of momentum and the quantitative understanding of the conservation of linear momentum in interactions involving elastic and inelastic collisions between two objects in one dimension.
    • HS.PHY.2.3
      Apply scientific principles of motion and momentum to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision.* Clarification Statement: Both qualitative evaluations and algebraic manipulations may be used.
    • 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.2.10
      Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations. Clarification Statements: Predictions of changes in motion can be made numerically, graphically, and algebraically using basic equations for velocity, constant acceleration, and Newton’s first and second laws. Forces can include contact forces, including friction, and forces acting at a distance, such as gravity and magnetic forces.