Standards of Learning (SOL)

 
 Essential Knowledge and Skills
 
  • Model sums, differences, products, and quotients of polynomials with concrete objects and their related pictorial and symbolic representations. (b)
  • Determine sums and differences of polynomials. (b)
  • Determine products of polynomials.  The factors should be limited to five or fewer terms (i.e., (4+ 2)(3+ 5) represents four terms and 
    (+ 1)(2x2  + 3) represents five terms). (b)
  • Determine the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor. (b)
  • Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. (c)
  • Factor and verify algebraic factorizations of polynomials with a graphing utility. (c) 
 

Assessments

Resources

 
Vocabulary
Polynomials, exponent, base, power, law of exponents, operations, factoring, binomial, trinomial, one variable, first-degree, second-degree, simplify, ratios, integers, model, concrete objects, product, difference, sum, quotient, binomial divisor, divisor, coefficient, leading coefficient, factorization, prime polynomials, scientific notation
 

Vertical Articulation

Post Standard of Learning

AII.3            The student will solve absolute value linear equations and inequalities; quadratic equations over the set of complex numbers; equations containing rational algebraic expressions; and equations containing radical expressions.

 

AII.3            The student will solve

a)   absolute value linear equations and inequalities;

b)   quadratic equations over the set of complex numbers;     

c)   equations containing rational algebraic expressions; and

d)   equations containing radical expressions.

The student will investigate the passage of time and

a) tell time to the hour and half-hour, using analog and digital clocks; and

b) read and interpret a calendar.

The student will investigate the passage of time and

a) tell time to the hour and half-hour, using analog and digital clocks; and

b) read and interpret a calendar.

The student will investigate the passage of time and

a) tell time to the hour and half-hour, using analog and digital clocks; and

b) read and interpret a calendar.

Essential Questions

  • Can two algebraic expressions that appear to be different be equivalent?
  • How do you add, subtract, and multiply polynomials?
  • How can we use the polynomial operations addition, subtraction, and multiplication in practical situations?
  • How can you model sums and differences of polynomials with concrete objects, pictures, and symbols?
  • How can you model products and quotients of polynomials  with concrete objects , pictures, and symbols?
  • How can you determine sums and differences of polynomials?
  • How can you determine products of polynomials?
  • How can you determine the quotient of polynomials?
  • Why do we factor polynomials?
  • How do you determine if an expression has a greatest common factor?
  • What models can you use to factor first and second degree polynomials?
  • How do you factor completely first- and second-degree polynomials in one variable?
  • How can we identify a difference of squares?
  • What is the relationship between the factor of a polynomial and the graph of the polynomial?
  • How can you verify factors of a polynomial with a graph?