Download Sample Only - Working Copy Unwrapping CCSS Mathematics

Unwrapping CCSS Mathematics Example – High School
A.REI.4. Solve quadratic equations in one variable.
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.
b. Solve quadratic equations by inspection (e.g., for x 2  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.
Concepts:
Need to know about quadratic equations in one variable
Vocabulary
 Quadratic equation

Forms of quadratic equations
 x2  p; x2  25



x2  bx  c; x2  4x  25
ax2  bx  c  0; x 2  8x  6  0
( x  h) 2  4 p 
( x  p)2  q; ( x  3) 2  25

Methods of solution
 Inspection
 Square roots
 Complete the square
 Quadratic formula
 Factor
2/22/2012 11:03 AM
Document1
Note: This example is used in conjunction with another file: Unwrapping the Math Standards
Types of solutions (quadratic formula)
 Real
 Complex
Skills:
Be Able to Do
Solve quadratic equations in one variable
Use the method - completing the square
Derive the quadratic formula
Solve by inspection ( x 2  25 )
Solve by taking square roots
Solve by completing the square
Future uses, conics, trig functions, zeros, etc.
Solve by using quadratic formula
How to derive it.
Solve by factoring
Lots of hints, patterns, and effective practice.
Recognize that QF may give complex solutions (using the
quadratic formula)
Target: only as it applies to QF at this point.
Write complex solutions as a  bi (using quadratic formula)
Target: only as it applies to QF at this point.
Big Ideas
1. Quadratic equations can be written in various forms.
2. There are various methods we can use to solve quadratic equations.
3. The quadratic formula can be derived by manipulating the form ( x  p)2  q
2/22/2012 11:03 AM
Document1

b 2
b2
c
(
x

)

(
) 

2
2a
4a
a

Note: This example is used in conjunction with another file: Unwrapping the Math Standards
Essential Questions
1.
2.
3.
4.
What is a quadratic equation?
How can algebra be used to solve quadratic equations?
How many solutions can quadratic equations have?
How can we decide which method to use to solve quadratic equations?
Topics or
Context:
Lessons, Activities, Units of Instruction
Quadratic equation unit - solving
 Text – 9.1-9.7
 TRP practice problems
Teach each method, but make sure to connect them.
…..
Strategies/Activities
 Completing the Square Notes – Prepare for
Completing the Square
 Peer teaching – Solving by completing the
square
 …
 Peer teaching =Factoring quadratics form
Since completing the square is kind of tricky, use the
peer teaching (with effective notes) to practice.
Prepare for it FIRST by reviewing prior skills.
x 2  bx  c

Peer teaching =Factoring quadratics form
ax 2  bx  c

…..
Assessments
 HW
 Activities
 Practice test
 Unit tests

2/22/2012 11:03 AM
Document1
Make sure instruction, HW, activities, and assessments
are all connected and coherent.
Note: This example is used in conjunction with another file: Unwrapping the Math Standards