MAT-HS Targeted Standards (A) Concept: Algebra (REI) Domain: Reasoning with Equations and Inequalities Cluster: Understand solving equations as a process of reasoning and explain the reasoning
MAT-HS.A-REI.04.b Solve quadratic equations in one variable.
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.
Student Learning Targets:
Knowledge Targets
I can
I can
Reasoning Targets
I can explain why taking the square root of both sides of an equation can yield two solutions.
Skills (Performance) Targets
I can solve quadratic equations by using square roots.
I can solve quadratic equations by factoring.
I can solve quadratic equations by completing the square.
I can solve quadratic equations using the quadratic formula.
I can find the number of solutions of a quadratic equation.
Product Targets
I can
I can
Proficiency Scale
Score
Description
Sample Activity
4.0
In addition to achieving level 3.0 content, the student makes in-depth inferences and applications that go beyond what was taught
Use the method of completing the square to derive the quadratic formula.
Solve a quadratic equation that has a complex solution and write in the form a + bi
3.5
In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success.
3.0
The student can:
Solve quadratic equations by:
using square roots
factoring
using the quadratic formula
(include equations with zero, one, or two real-solutions)
The student exhibits no major errors or omissions.
Solve the quadratic equation by finding square roots.
3x2 - 12 = 0
Solve the quadratic equation by factoring.
x2 - 14x + 45 = 0
Use the Quadratic formula to solve the equation.
5x2 - 13x = -9
2.5
The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content).
2.0
There are no major errors or omissions regarding the simpler details and processes as the student:
However, the student exhibits major errors or omissions regarding the more complex ideas and processes.
x2 = 49
(4t + 1)(t - 2) = 0
Identify a, b, and c as it’s used in the quadratic formula x2 + 6x = - 5
1.5
The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content).
1.0
With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
-
0.5
With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content).