#### Math - 2017-18

The student, given rational, radical, or polynomial expressions, will

c)  write radical expressions as expressions containing rational exponents and vice versa;

Bloom's Level:  Apply

### BIG IDEAS

• I can design the track of a roller coaster, determine the sloped curve of an exit ramp, trace the free falling path of a skydiver, and understand the mechanics of controllers like autopilot, cruise control, and a living room thermostat.
• I will apply mathematical processes for basic operations to algebraic expressions and divide algebraic terms out of algebraic expressions.

### UNDERSTANDING THE STANDARD

• Computational skills applicable to numerical fractions also apply to rational expressions involving variables.
• Radical expressions can be written and simplified using rational exponents.
• A relationship exists among arithmetic complex fractions, algebraic complex fractions, and rational numbers.
• The complete factorization of polynomials has occurred when each factor is a prime polynomial.
• Pattern recognition can be used to determine complete factorization of a polynomial.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

All.1c1  Convert from radical notation to exponential notation, and vice versa.  Solve an equation containing a radical expression.

### KEY VOCABULARY

rational, radical, polynomial expression, simplify, variables, equation vs. expression, factor completely, rational exponents,  sum, difference,product, quotient,monomial, binomial, complex algebraic fraction, simple algebraic fraction, radical expression, radical notation, exponential notation, rationalizing, numerator, denominator, difference of squares, difference of cubes, sum of cubes, perfect square trinomial, integer, verify

Updated: Feb 09, 2018