MA19.PRE.20

Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.20

Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a clear-cut solution. Construct a viable argument to justify a solution method. Include equations that may involve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric functions, and their inverses.

Unpacked Content

Knowledge

Students know:
  • How to solve equations using a reasoning process centered around inverse operations and order of operations

Skills

Students are able to:
  • Solve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric equations (including their inverses) using multiple solution strategies and explain each step in the solution path.
  • Construct a viable argument to justify a chosen solution path used to solve a linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric equation (including their inverses).
  • Compare the steps in each and determine which solution path is most efficient, given an equation with multiple solution paths.
  • Explain when an equation has no solution or infinitely many solutions.

Understanding

Students understand that:
  • The process of solving equations is a reasoning process to determine a solution that satisfies the equation rather than a procedural list of steps.
  • An equation has no solution because there is no value that can maintain equivalency and an equation has infinitely many solutions because all values used for the variable create a true equivalency statement

Vocabulary

  • equivalence
  • viable

Aligned Learning Resources

Recognizing Quadratic Functions
Finding Components of Quadratic Functions - Overview Video
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