[A.SSE.] Seeing Structure In Expressions

Objectives

Interpret the structure of expressions. [Linear, exponential, and quadratic]

• A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

  • A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.

  • A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r)n as the product of P and a factor not depending on P.

  • A.SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ – y⁴ as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

Write expressions in equivalent forms to solve problems.

• A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

  • • A.SSE.3a Factor a quadratic expression to reveal the zeros of the function it defines.

    • A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

    • A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.