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Subjects
Grades
Resource Type
Common Core: Standard
Common Core: ELA
Common Core: Math
CCLS  Math: F.BF.1.a
 Category
 Building Functions
 SubCategory
 Build A Function That Models A Relationship Between Two Quantities
 State Standard:
 Determine an explicit expression, a recursive process, or steps for calculation from a context.
35 Results

 Student Outcomes Students create exponential functions to model realworld situations. Students use logarithms to solve equations of the form f(t) = a ∙ bct for t. Students decide which type of model...

 Student Outcomes Students develop a general growth/decay rate formula in the context of compound interest. Students compute future values of investments with continually compounding interest rates.

 Topic D opens with a handson simulation and modeling activity in which students gather data and apply the analysis of Lesson 22 in Topic C to model it with an exponential function (ACED.2, FLE.5...

 Student Outcomes Students analyze data and realworld situations and find a function to use as a model. Students study properties of linear, quadratic, sinusoidal, and exponential functions.

 In Topic C, students graph logarithmic functions, identifying key features (FIF.4, FIF.7) and discover how the logarithmic properties are evidenced in the graphs of corresponding logarithmic...

 Student Outcomes Students solve simple exponential equations numerically.

 Student Outcomes Students write an exponential function that represents the amount of water in a tank after t seconds if the height of the water doubles every 10 seconds. Students discover Euler’s...

 Student Outcomes Students approximate the value of quantities that involve positive irrational exponents. Students extend the domain of the function f(x) =bx for positive real numbers b to all real...

 At the beginning of Topic B, students apply the properties of exponents to solve exponential equations numerically (FBF.1a) as a way to motivate the need for logarithms, which are first introduced...

 In Topic A, students both review what they already know about exponential expressions and functions with integer exponents, and extend the meaning of an exponential expression to allow for first...

 Tables, graphs, and equations all represent models. We use terms such as “symbolic” or “analytic” to refer specifically to the equation form of a function model; “descriptive model” refers to a...

 Topic A focuses on the skills inherent in the modeling process: representing graphs, data sets, or verbal descriptions using explicit expressions (FBF.A.1a) when presented in graphic form in Lesson...

 In Topic D, students apply and reinforce the concepts of the module as they examine and compare exponential, piecewise, and step functions in a realworld context (FIF.C.9). They create equations...

 In Topic A, students explore arithmetic and geometric sequences as an introduction to the formal notation of functions (FIF.A.1, FIF.A.2). They interpret arithmetic sequences as linear functions...

 Student Outcomes Students interpret the function and its graph and use them to answer questions related to the model, including calculating the rate of change over an interval, and always using an...

 Student Outcomes Students model functions described verbally in a given context using graphs, tables, or algebraic representations.

 Student Outcomes Students use linear, quadratic, and exponential functions to model data from tables, and choose the regression most appropriate to a given context. They use the correlation...

 Student Outcomes Students write equations to model data from tables, which can be represented with linear, quadratic, or exponential functions, including several from Lessons 4 and 5. They recognize...

 Student Outcomes Students recognize when a table of values represents an arithmetic or geometric sequence. Patterns are present in tables of values. They choose and define the parameter values for...

 Student Outcomes Students create a twovariable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. ...

 Student Outcomes Students make sense of a contextual situation that can be modeled with linear, quadratic, and exponential functions when presented as a word problem. They analyze a verbal...

 Student Outcomes From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for...

 Student Outcomes Students create piecewise and step functions that relate to reallife situations and use those functions to solve problems. Students interpret graphs of piecewise and step functions...

 Student Outcomes Students apply knowledge of exponential functions and transformations of functions to a contextual situation.