Mathematics » High School: Algebra » Seeing Structure in Expressions

Standards in this domain:

Interpret the structure of expressions.

  • A-SSE.1. Interpret expressions that represent a quantity in terms of its context.
    • Interpret parts of an expression, such as terms, factors, and coefficients.
    • 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. Factor a quadratic expression to reveal the zeros of the function it defines.
    • b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
    • c. 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%.
  • A-SSE.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.