13 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### 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!