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

### Logarithms can be written in multiple, equivalent ways.

1 week

Evidence of Understanding

• create exponential models and use them to solve problems (focus on base 2, 10, and e)
• create a function rule from a situation, graph, or a table of values
• recognize when to convert between exponential and logarithmic form and justify reasoning
• Example: some problems should be converted, like 3x - 10 =19 or log4(3x) = 3, but other problems do not require conversion to be solved, like 92x - 1 = 81 or log927= x
• convert an exponential model to a logarithm to solve for an unknown
• evaluate the logarithm using technology
• analyze a situation to consider viable and nonviable domain and range values
• interpret inputs or outputs of a function in terms of the situation it models
• compare end behavior of the exponential function with the limits of the situation
• Example: continuous exponential functions have no limits on the domain but in a situation there may be limits to how much the outputs can grow or decay
• generate an explicit or recursive rule for a sequence and use it to solve problems
• create a situation that could be represented by a given sequence
• recognize when the domain or range of a function relationship is discrete and generate a sequence that best represents corresponding outputs for a situation
• Example: Billy measures the height of a ball, dropped from 3 meters, that rebounds to 75% of its original height after each bounce.
• determine the sum of a finite set of terms in a situation
• write arithmetic and geometric sequences using summation notation and use summation notation to solve problems
• expand a series written with summation notation and use the expanded form to solve for specific inputs or outputs in a situation
• create a situation that best models a given series written in summation notation

Develop conceptual understanding:

summation notation, sigma notation

Supporting terms to communicate:

function, input, output, domain, range, discrete, end behavior, asymptote, intercept, initial value, rate of change, growth, decay, logarithm, exponential, base, e, natural base, natural log, arithmetic, geometric

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
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. COMING SOON!