Foundations of Algebra 2 Unit 3 Polynomials

BY THE END OF THIS UNIT:

CORE CONTENT

Cluster Title: Polynomial Operations
Standard A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Concepts and Skills to Master
• Add, subtract, and multiply polynomials
• Rules of Exponents

SUPPORTS FOR TEACHERS

Critical Background Knowledge
·  Distributive Property
·  Combining Like Terms
·  Classifying/Recognizing Polynomials
·  Formulas for perimeter, area and volume of geometric shapes
Academic Vocabulary
Distributive, Polynomials, Base, Exponent, Coefficient
Suggested Instructional Strategies
·  Start by ensuring students understand the basic rules of exponents and combining like terms
·  Apply these rules as students add, subtract, and multiply polynomials
·  Include real-world and geometric examples / Resources
Textbook Correlation: 1-3, 6-1 Concept Byte, Algebra 1 Resources
Add and Subtract Polynomials Discovery Education Video
Multiply Polynomials Discovery Education Video
Sample Formative Assessment Tasks
Skill-based task
1. (2x2 + 3) + 4(x – 2)
2. (3x3 – 4x2 + 1) – (2x + 4)
3. (2x + 1)(x – 7) / Problem Task
1) A rectangle has sides whose lengths are represented by the expressions
(x + 5) and (x2 – 2x + 9). What expressions represent the area and perimeter of the rectangle?

CORE CONTENT

Cluster Title: Interpreting Functions
Standard A-SSE.2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4as (x2)2 –(y2)2, thus recognizing it as a difference of squares.
Concepts and Skills to Master
• Factoring Polynomials by Greatest Common Factor
• Factoring Trinomials with and without leading coefficients
• Factoring a Difference of Squares

SUPPORTS FOR TEACHERS

Critical Background Knowledge
• Rules for Exponents
•Multiplying Polynomials
Academic Vocabulary
Factoring, Trinomials, Greatest Common Factor, Coefficient
Suggested Instructional Strategies
·  Be sure to relate factoring to multiplying polynomials (factoring determines what multiplies to equal the polynomial)
·  Create factoring foldables/graphic organizers
·  For students needing additional help, use Algebra Tiles
·  For quadratics where a ≠ 1, teach by multiplying ac and grouping (explained on pg. 231) / Resources
·  Textbook Correlation: 4-4
·  4-4 Think About a Plan (Teacher Resource)
·  Factoring Notes Organizer
·  Factoring Game – to be played in groups, collaborative learning
Sample Formative Assessment Tasks
Skill-based task
1) Factor: x2 – 36
2) Factor: 6x2y + 9xyz – 18y2z
3) Factor: x2 – 4x – 32
4) Factor: 3x2 – 11x – 20 / Problem Task
Pearson 4 – 4 Think About a Plan

CORE CONTENT

Cluster Title: Interpreting Functions
Standard A-APR.3.Identify zeroes of polynomials when suitable factorizations are available, and use the zeroes to construct a rough graph of the function defined by the polynomial.
Concepts and Skills to Master
• Finding zeroes of quadratics graphically
• Transfer graphs of quadratic functions from the calculator to graph paper, labeling axes as needed to make sense

SUPPORTS FOR TEACHERS

Critical Background Knowledge
• Graphing calculator techniques using table feature to identify zeroes; • Recognizing x-intercepts; • Factoring
Academic Vocabulary
Zeroes, Roots, Intercepts
Suggested Instructional Strategies
·  In Foundations, we will focus on finding the solutions to quadratic equations graphically and understanding those graphs on the calculator and in proportion on graph paper.
·  Also review the concepts of roots and zeroes being the x-intercepts of the graph, where y = 0.
·  Explain the concept of “no real solutions” when no x-intercepts exist.
·  Discuss the real-world implications of the solutions to quadratic equations (where the ball hits the ground, etc.) / Resources
·  Textbook Correlation: 4-5
·  Finding Roots by Graphing Discovery Education Video
Sample Formative Assessment Tasks
Skill-based task
Solve the following equations:
1) x2 + 9x = 36
2) 3x2 + 8x + 2 = 0
3) 4x2 – 25 = 0 / Problem Task
1) Textbook pg. 248 #11

CORE CONTENT

Cluster Title: Number and Quantity
Standard: N-CN.7 Solve quadratic equations with real coefficients that have complex rational solutions.
Concepts and Skills to Master
·  Use the quadratic formula to solve quadratics with rational solutions

SUPPORTS FOR TEACHERS

Critical Background Knowledge
·  Order of Operations; Simplifying Radicals – from prior lessons
Academic Vocabulary
Roots, Quadratic Formula, Rational Solutions
Suggested Instructional Strategies
• Solve a quadratic equation by graphing (ex.
y = x2 – 4x – 5).
• Then, show how the quadratic formula can solve the equation to get the same solutions.
• Use your discretion for how in-depth to get in deriving the quadratic formula (explained on pg. 260). / Resources
·  Textbook Correlation: 4-7
• Enrichment 4-7: Quadratic Formula Relationship to Factoring
• Regents Prep Quadratic Formula Examples
Sample Formative Assessment Tasks
Skill-based task:
Solve by quadratic formula:
1) x2 – 9x – 52 = 0
2) 4x2 + 15x = 3 / Problem Task:
Pg. 265 #18 – 19

Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order

not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.