Big Idea:

Big Idea 3

Expressions with exponents can be written in multiple, equivalent ways.

1 week

Evidence of Understanding

  • compare and contrast exponential functions with other functions that contain exponents
    • describe similarities and differences between power and exponential models
      • compare graphs of power functions and exponential functions (focus on y = x2 and y = 2x, y = x3 and y = 3x, and y =x and y = ½x)
      • possible extension: notice similarities between x2 and 2x and use that to anticipate and describe possible similarities between √x and the inverse of 2x
    • generate and justify a function rule from a table, sequence, graph, or situation
      • determine when a power, exponential, or neither function model is appropriate
         
  • investigate and transform expressions containing exponents into equivalent forms
    • rewrite expressions using exponent properties am ● an = am + n (product), (am)n = amn (power), a0 = 1 (zero),am/an = am -  n(quotient), and a-m = 1/am
      • explore and describe the commutativity of exponent rules
      • prove expressions with different bases are equivalent (Example: 643 = 86 = 49 = 218)
    • explain the relationship between a rational exponent and its equivalent radical form
      • connect the definition of a square root or cube root to its equivalent exponent
    • convert between expressions with radicals and expressions with rational exponents
       
  • analyze and evaluate expressions or equations using properties of exponents
    • identify equations or expressions that can be rewritten with common bases to solve problems
      • Example: solve 32x = 27x + 1 by rewriting as 32x = (33)x + 1or solve (1/16)x+ 13 = 77 by simplifying and rewriting as (2-4)x = 26
    • evaluate expressions and solve equations using radicals or rational exponents
      • Example: Evaluate 813/2 or 7(1284) or Solve (5x - 2)5/3 - 1 = 31
      • apply properties of exponents and common bases to evaluate without a calculator
      • use rational exponents to determine an unknown base rate

Develop conceptual understanding:

power function, exponential function, exponent properties, commutative, base, exponent, rational exponent, radical form, square root, cube root  

Supporting terms to communicate:

function, dependent, independent, input, output, domain, range, integer, rational number, equation, expression  

Core Resource
A core resource supports multiple days of instruction.
  • Expressions with exponents
    Students classify sequences as linear, exponential, or other based on the characteristics of the sequence.
    Resource:
    Expressions with exponents

    Students classify sequences as linear, exponential, or other based on the characteristics of the sequence.

Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.