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22 Results

 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...

 In Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and...

 Topic A introduces polynomial expressions. In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is...

 In Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex...

 Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form, (x) = a(x  h)2 + k in Topic B. The strategy known as completing the square is...

 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...

 This topic focuses on factoring polynomials and the advantages of factored form of a polynomial to both solve equations and sketch graphs of polynomial functions. Students solve problems involving...

 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 C, students explore the families of functions that are related to the parent functions, specifically for quadratic (f(x) = x2), square root (f(x) = the square root of x), and cube root (f(x...

 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 this topic, students develop an understanding of the six basic trigonometric functions as functions of the amount of rotation of a point on the unit circle (FTF.A.1), and then translate that...

 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...

 Students will use trigonometric functions to model periodic phenomena (FTF.B.5) by fitting sinusoidal functions to data (SID.B.6a). Students use the properties of the graphs of sinusoidal...

 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...

 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...

 Topic E is a culminating series of lessons driven by MP.4, Modeling with Mathematics. Students apply what they have learned about mathematical models and exponential growth to financial literacy...

 Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is...

 The graphs of the trigonometric functions are revisited in Topic C. Students visualize these graphs with the aid of the appropriate software and briefly recall how changing various parameters of a...

 In this topic, students extend their understanding of probability, building on work from Grade 11. The multiplication rule for independent events introduced in Grade 11 is generalized to a rule that...

 In Topic B, students explore composition of functions in depth and notice that a composition of a polynomial function with the function f(x) = 1/x gives functions that can be written as ratios of...

 In Topic C students study inverse functions, being careful to understand when inverse functions do and do not exist, working to restrict the domain of a function to produce an invertible function. ...