This learning progression focuses on Solving Quadratic Equations using multiple methods including by inspection, taking square roots, completing the square, the quadratic formula, and factoring. This learning progression would be taught in a high school Algebra I class, consisting of mostly freshmen. In the first lesson students will be learning these methods and when to use each one of the methods, and thought the next two lessons they will be reviewing all of these methods and getting more practice on them during the activities planned for each of the following two lessons.
CCSS Content Standards:
CCSS.MATH.CONTENT.HSA.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.
CCSS.MATH.CONTENT.HSA.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 quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
CCSS Mathematical Practice Standards:
CCSS.MATH.PRACTICE.MP1
Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP5
Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP8
Look for and express regularity in repeated reasoning.
The learning progression is attached here: