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 In this installment of the video professional development series, there are two videos for small groups of educators to learn from the Common Core in practice. The first video does not include...

 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 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...

 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...

 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...

 In Topic D, students are formally introduced to the modeling cycle (see page 61 of the CCLS) through problems that can be solved by creating equations and inequalities in one variable, systems of...

 Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Topic C, instead of just...

 In middle school, students applied the properties of operations to add, subtract, factor, and expand expressions (6.EE.3, 6.EE.4, 7.EE.1, 8.EE.1). Now, in Topic B, students use the structure of...

 In Topic A, students explore the main functions that they will work with in Grade 9: linear, quadratic, and exponential. The goal is to introduce students to these functions by having them make...

 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 Students recognize linear, quadratic, and exponential functions when presented as a data set or sequence, and formulate a model based on the data.

 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 compare two different quadratic, square root, or cube root functions represented as graphs, tables, or equations. They interpret, contextualize and abstract various...

 Student Outcomes Students graph simple quadratic equations of the form y = a(x  h)2 + k (completedsquare or vertex form), recognizing that (h,k) represents the vertex of the graph and use a graph...

 Student Outcomes Students use the quadratic formula to solve quadratic equations that cannot be easily factored. Students understand that the discriminant, b2  4ac, can be used to determine whether...

 Student Outcomes Students derive the quadratic formula by completing the square for a general quadratic equation in standard form, ax2 + bx + c = 0, and use it to verify the solutions for equations...