Ability to use appropriate vocabulary to categorize polynomials and rational expressions b. Interpret complicated See the skills and knowledge Example: When determining the of a student could identify the range as by observing that the denominator is always greater than or expressions by viewing one or that are stated in the Standard. equal to 1 and that the numerator is always equal to one and therefore more of their parts as a single the quotients are always . entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Example: When analyzing a student would realize that the range of Note: This is an overarching would be . This realization would come from observing that the product standard that has applications of a radical and a negative number would be less than or equal to zero. in multiple units and multiple courses. A.SSE.2 Use the structure of an Note: This is an overarching Recognize higher degree polynomials that are quadratic in nature and can therefore be solved using methods associated with solving quadratic expression to identify ways to standard that has applications in equations. rewrite it. For example, see x4 multiple units and multiple – Recognize that rational expressions can be written in different forms and y4 as (x2)2 (y2)2, thus courses. – that each form is useful for different reasons. recognizing it as a difference of Example: Considering. The second expression would be more squares that can be factored as Ability to use properties of useful when determining the zeros of the expression. (x2 y2)(x2 + y2). mathematics to alter the – structure of an expression Ability to select and then use an appropriate factoring technique Ability to factor expressions completely over complex numbers A.SSE.4 Derive the formula for Knowledge of the difference Sum of Finite Geometric Progression the sum of a finite geometric between an infinite and a The sum in geometric progression (also called geometric series) is by series (when the common ratio finite series Equation (1) is not 1), and use the formula to Ability to apply the formula for solve problems. For example, the sum of a finite geometric series : calculate mortgage payments. ★
Ability to use appropriate vocabulary to categorize polynomials and rational expressions 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. Note: This is an overarching standard that has applications in multiple units and multiple courses. See the skills and knowledge that are stated in the Standard. Example: When determining the of a student could identify the range as by observing that the denominator is always greater than or equal to 1 and that the numerator is always equal to one and therefore the quotients are always . Example: When analyzing a student would realize that the range of would be . This realization would come from observing that the product of a radical and a negative number would be less than or equal to zero. 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). Note: This is an overarching standard that has applications in multiple units and multiple courses. Ability to use properties of mathematics to alter the structure of an expression Ability to select and then use an appropriate factoring technique Ability to factor expressions completely over complex numbers Recognize higher degree polynomials that are quadratic in nature and can therefore be solved using methods associated with solving quadratic equations. Recognize that rational expressions can be written in different forms and that each form is useful for different reasons. Example: Considering. The second expression would be more useful when determining the zeros of the expression. 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. ★ Knowledge of the difference between an infinite and a finite series Ability to apply the formula for the sum of a finite geometric series : Sum of Finite Geometric Progression The sum in geometric progression (also called geometric series) is by Equation (1)
unitplan_polynomialrational_and_radical_relationships.docx