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Common Core: Standard
Common Core: ELA
Common Core: Math
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 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...

 Student Outcomes Students rewrite expressions involving radicals and rational exponents using the properties of exponents.

 Student Outcomes Students will calculate quantities that involve positive and negative rational exponents.

 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...

 Student Outcomes Students review place value and scientific notation. Students use scientific notation to compute with large numbers.

 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...

 Student Outcomes Students review and practice applying the properties of exponents for integer exponents. Students model a realworld scenario involving exponential growth and decay.

 Exponential and Logarithmic Functions In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions...

 Student Outcomes Students understand the Fundamental Theorem of Algebra; that all polynomial expressions factor into linear terms in the realm of complex numbers. Consequences, in particular, for...

 Student Outcomes Students solve quadratic equations with real coefficients that have complex solutions. Students extend polynomial identities to the complex numbers. Students note the difference...

 Student Outcomes Students solve quadratic equations with real coefficients that have complex solutions. They recognize when the quadratic formula gives complex solutions and write them as a + bi for...

 Student Outcomes Students define a complex number in the form a + bi, where a and b are real numbers and the imaginary unit i satisfies i 2 = −1. Students geometrically identify i as a multiplicand...

 Students extend their facility with solving polynomial equations to working with complex zeros. Complex numbers are introduced via their relationship with geometric transformations. The topic...

 Student Outcomes Students model a crosssection of a riverbed with a polynomial function and estimate fluid flow with their algebraic model.

 Student Outcomes Students learn to fit polynomial functions to data values.

 Student Outcomes Students transition between verbal, numerical, algebraic, and graphical thinking in analyzing applied polynomial problems.

 Student Outcomes Students transition between verbal, numerical, algebraic, and graphical thinking in analyzing applied polynomial problems.

 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...

 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...

 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...

 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...

 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...