HSA-APR.D.6

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

 
34 Lesson(s)
   

Speed Dating Rationally

12th Grade Math » Unit: Rational Functions and Equations
12th Grade Math » Unit: Rational Functions and Equations
Tiffany Dawdy
Phoenix, AZ
Environment: Urban
 
Big Idea:

Efficiency and accuracy improves as students solve rational equations with their ‘date’ in this interactive and self-checking speed dating activity.

 
Favorites (15)
 
Resources (20)
 
Reflections (1)
speed dating
   

Proving Polynomial Identities

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

There are links between polynomials and geometry. Both branches of math use proof and a polynomial identity can be used to generate Pythagorean triples.

 
Favorites (5)
 
Resources (18)
 
Reflections (1)
pythagorean triplesresized
   

Review of Polynomial Roots and Complex Numbers

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Arithmetic with polynomials and complex numbers are performed in similar ways, but powers of i have a meaning distinct from powers of variables.

 
Favorites (2)
 
Resources (10)
waterfall trivia
   

The Remainder Theorem

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Any polynomial p(x) can be written as a product of (x – a) and some quotient q(x), plus the remainder p(a).

 
Favorites (3)
 
Resources (13)
 
Reflections (1)
remainder theorem exit
   

Rationally Synthetic

Algebra II » Unit: Algebraic Arithmetic
Algebra II » Unit: Algebraic Arithmetic
Merrie Rampy
Craigmont, ID
Environment: Rural
 
Big Idea:

Help your students connect the dots from long division to polynomial long division to synthetic division.

 
Favorites (3)
 
Resources (14)
 
Reflections (1)
synthetic
   

Quiz and Intro to Graphs of Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.

 
Favorites (3)
 
Resources (12)
 
Reflections (1)
quartic
   

Seeing Structure in Expressions - Factoring Higher Order Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Like quadratic expressions, some higher order polynomial expressions can be rewritten in factored form to reveal values that make the expression equal to zero.

 
Favorites (5)
 
Resources (25)
 
Reflections (2)
factoring quick poll
   

Polynomial Long Division and Solving Polynomial Equations

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Operations with polynomials are a lot like operations with integers.

 
Favorites (6)
 
Resources (22)
 
Reflections (1)
long
   

Polynomial Long Division

Algebra II » Unit: Higher-Degree Polynomials
Algebra II » Unit: Higher-Degree Polynomials
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Mastery of polynomial long division comes with practice and reflection on the nature of the algorithm.

 
Favorites (3)
 
Resources (10)
wordle
   

The Fundamental Theorem of Algebra and Imaginary Solutions

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

The degree of a polynomial equation tells us how many solutions to expect as long as we include both real and imaginary solutions.

 
Resources (14)
 
Reflections (1)
quadratic imaginary
   

The Remainder Theorem, Day 1 of 2

Algebra II » Unit: Higher-Degree Polynomials
Algebra II » Unit: Higher-Degree Polynomials
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Students make sense of the many connections between polynomial factors, zeros, and remainders from polynomial long division.

 
Favorites (3)
 
Resources (16)
 
Reflections (1)
remainders
   

Polynomial Long Division

Algebra II » Unit: Polynomial Functions
Algebra II » Unit: Polynomial Functions
Amelia Jamison
Caldwell, ID
Environment: Rural
 
Big Idea:

Connect students to the math they did in fifth grade with this lesson on polynomial long division.

 
Favorites (4)
 
Resources (28)
 
Reflections (1)
image polynomial long division
   

Arithmetic with Complex Numbers

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Imaginary numbers are used to represent quantities that have two parts; working with these numbers is similar to working with polynomial expressions.

 
Favorites (5)
 
Resources (23)
 
Reflections (2)
mandlebrot set
   

Synthetic Division

Algebra II » Unit: Polynomial Functions
Algebra II » Unit: Polynomial Functions
Amelia Jamison
Caldwell, ID
Environment: Rural
 
Big Idea:

Connect students to the math they did in fifth grade with this lesson on polynomial long division.

 
Favorites (2)
 
Resources (27)
image synthetic division
   

Performance Task - Representing Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

The graphs of polynomial functions can be transformed by altering the algebraic form in specific ways. These transformations have the same effect on all the function types studied in Algebra 2 and Precalculus.

 
Favorites (2)
 
Resources (15)
 
Reflections (1)
representing polynomials
Common Core Math
 
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