Alaska: Seeing Structure in Expressions Math Standards

INTERPRET EXPRESSIONS THAT REPRESENT A QUANTITY IN TERMS OF ITS CONTEXT.

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

USE THE STRUCTURE OF AN EXPRESSION TO IDENTIFY WAYS TO REWRITE IT. FOR EXAMPLE, SEE X^4 – Y^4 AS (X^2)^2 – (Y^2)^2, THUS RECOGNIZING IT AS A DIFFERENCE OF SQUARES THAT CAN BE FACTORED AS (X^2 – Y^2)(X^2 + Y^2).

CHOOSE AND PRODUCE AN EQUIVALENT FORM OF AN EXPRESSION TO REVEAL AND EXPLAIN PROPERTIES OF THE QUANTITY REPRESENTED BY THE EXPRESSION.

• A-SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines. For example, x^2 + 4x +3 = (x +3)(x +1).
• A-SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. For example, x^2 + 4x + 3 = (x + 2)^2 -1.
• A-SSE.3.c Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

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.