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Mathematics > Course Model Algebra I (Traditional Pathway) > Reasoning with Equations and Inequalities
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Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Reasoning with Equations and Inequalities

Cluster - Understand solving equations as a process of reasoning and explain the reasonin

[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.

Resources:

Predecessor Standards:

  • 6.EE.B.5
    Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
  • 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.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • 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.A-REI.B.3
    Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • AI.A-REI.B.4.a
    Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
  • AI.A-REI.B.4.b
    Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the solutions of a quadratic equation results in non-real solutions and write them as a ± bi for real numbers a and b.
  • AII.A-REI.A.2
    Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.