HSA-APR.D.6
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- HSA-APR.D.6Rewrite 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.
- HSA-APR.D.7(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
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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
Big Idea:
Efficiency and accuracy improves as students solve rational equations with their ‘date’ in this interactive and self-checking speed dating activity.
Standards:
Favorites
(16)
Resources
(20)
Reflections
(1)
Proving Polynomial Identities
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
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.
Standards:
Favorites
(7)
Resources
(18)
Reflections
(1)
Review of Polynomial Roots and Complex Numbers
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
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.
Standards:
Favorites
(2)
Resources
(10)
The Remainder Theorem
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
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).
Standards:
Favorites
(5)
Resources
(13)
Reflections
(1)
Rationally Synthetic
Algebra II »
Unit: Algebraic Arithmetic
Algebra II »
Unit: Algebraic Arithmetic
Big Idea:
Help your students connect the dots from long division to polynomial long division to synthetic division.
Standards:
Favorites
(5)
Resources
(14)
Reflections
(1)
Quiz and Intro to Graphs of Polynomials
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.
Standards:
Favorites
(3)
Resources
(12)
Reflections
(1)
Seeing Structure in Expressions - Factoring Higher Order Polynomials
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
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.
Standards:
Favorites
(6)
Resources
(25)
Reflections
(2)
Polynomial Long Division and Solving Polynomial Equations
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Operations with polynomials are a lot like operations with integers.
Standards:
Favorites
(7)
Resources
(22)
Reflections
(1)
Polynomial Long Division
Algebra II »
Unit: Higher-Degree Polynomials
Algebra II »
Unit: Higher-Degree Polynomials
Big Idea:
Mastery of polynomial long division comes with practice and reflection on the nature of the algorithm.
Standards:
Favorites
(3)
Resources
(10)
The Fundamental Theorem of Algebra and Imaginary Solutions
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
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.
Standards:
Resources
(14)
Reflections
(1)
The Remainder Theorem, Day 1 of 2
Algebra II »
Unit: Higher-Degree Polynomials
Algebra II »
Unit: Higher-Degree Polynomials
Big Idea:
Students make sense of the many connections between polynomial factors, zeros, and remainders from polynomial long division.
Standards:
Favorites
(3)
Resources
(16)
Reflections
(1)
Polynomial Long Division
Algebra II »
Unit: Polynomial Functions
Algebra II »
Unit: Polynomial Functions
Big Idea:
Connect students to the math they did in fifth grade with this lesson on polynomial long division.
Standards:
Favorites
(9)
Resources
(28)
Reflections
(1)
Arithmetic with Complex Numbers
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
Big Idea:
Imaginary numbers are used to represent quantities that have two parts; working with these numbers is similar to working with polynomial expressions.
Standards:
Favorites
(5)
Resources
(23)
Reflections
(2)
Big Idea:
Connect students to the math they did in fifth grade with this lesson on polynomial long division.
Standards:
Favorites
(4)
Resources
(27)
Performance Task - Representing Polynomials
Algebra II »
Unit: Polynomial Theorems and Graphs
Algebra II »
Unit: Polynomial Theorems and Graphs
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.
Standards:
Favorites
(2)
Resources
(15)
Reflections
(1)
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