Topic: Seeing Structure in Expressions |
Common Core Mathematics 9-12 |
| Cluster Interpret the structure of expressions |
| | Grade 9-12 |
| | | A.SSE.1. | 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. |
| | | A.SSE.2. | 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}). |
| Cluster Write expressions in equivalent forms to solve problems |
| | Grade 9-12 |
| | | 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 1.15^{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%. |
| | | 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. |