Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
: Within this benchmark, the expectation is to solve by factoring techniques, taking square roots, the quadratic formula and completing the square.
| Name |
Description |
| Solving Quadratic Equations by Completing the square | Students will model the process of completing the square (leading coefficient of 1) with algebra tiles, and then practice solving equations using the completing the square method. This lesson provides a discovery opportunity to conceptually see why the process of squaring half of the b value is considered completing the square. |
| Solving Quadratics - Exploring Different Methods | Students will explore how different methods find the solutions (roots) to quadratic equations including, factoring, graphing, and the quadratic formula. |
| Radical Mathematical | In this lesson students will solve radical equations, showing how extraneous solutions may arise. Students will solve radical equations that model real-world relationships. |
| Where did the answers go? Oh, they're imaginary! | In this lesson, students will solve quadratic equations with imaginary (complex) solutions and be facilitated in the discovery of the Fundamental Theorem of Algebra. |
| The Quadratic Quandary | Students will sort various quadratic equations by the method they would use for solving (ie. factoring, quadratic formula). Then as a class they justify their placements and eventually discover that there are many ways to solve and that some make sense in different situations, however there is no real "correct" method for each equation type. |
