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
