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Mathematics > Course Model Mathematics II (Integrated Pathway) > Seeing Structure in Expressions
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Seeing Structure in Expressions

Cluster - Interpret the structure of quadratic and exponential expressions.

[MII.A-SSE.A.2] - Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2) – 3).

Resources:


  • Expression
    A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a).

Predecessor Standards:

  • 7.EE.A.1
    Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x +1) and -3(x – 5/3) = -3x + 5.
  • 8.EE.A.1
    Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3-5 = 3-3 = 1/33 = 1/27.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.A-SSE.B.3.a
    Factor a quadratic expression to reveal the zeros of the function it defines.
  • MII.A-SSE.B.3.c
    Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15t can be rewritten as (1.15 1/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
  • MIII.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • MIII.A-SSE.B.4
    Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.* For example, calculate mortgage payments.
  • MIII.A-APR.B.3
    Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
  • MIII.A-APR.C.4
    Provide polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.
  • MIII.A-APR.C.5
    (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
  • MIII.A-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.
  • MIII.A-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.
  • PC.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • PC.A-APR.C.5
    (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
  • PC.A-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.
  • AQR.A-APR.C.5
    (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.