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 Student Outcomes Students reduce rational expressions to lowest terms. Students determine the domain of rational functions.

 Student Outcomes Students understand that rational expressions form a system analogous to the rational numbers, closed underaddition, subtraction, multiplication, and division by a nonzero rational...

 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...

 Student Outcomes Students observe patterns in the coefficients of the terms in binomial expansions. They formalize their observations and explore the mathematical basis for them. Students use the...

 Student Outcomes Students discover patterns in the expansion of binomials, leading to the understanding of the binomial theorem. Students use Pascal’s triangle to find the coefficients of binomial...

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Student Outcomes Students represent complicated systems of equations, including 4×4 and 5×5 systems of equations, using matrix equations in the form Ax = b, where A represents the coefficient matrix...

 Student Outcomes Students will represent systems of three or more simultaneous equations as a linear transformation in the form Ax = b, where A represents the linear transformation, x represents the...

 Student Outcomes Students will represent systems of equations as linear transformations of the form Lx = b, using matrix notation. Students will discover that the systems of equations written in the...

 Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...

 Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via highdimensional matrices. Matrix...

 Student Outcomes Students use geometric series to calculate how much money should be saved each month to have 1 million in assets within a specified amount of time.

 Student Outcomes Students model the scenario of buying a house. Students recognize that a mortgage is mathematically equivalent to car loans studied in Lesson 30 and apply the present value of...

 Student Outcomes Students will compare payment strategies for a decreasing credit card balance. Students will apply the sum of a finite geometric series formula to a decreasing balance on a credit...

 Student Outcomes Students use the sum of a finite geometric series formula to develop a formula to calculate a payment plan for a car loan and use that calculation to derive the present value of an...

 Student Outcomes Students derive the sum of a finite geometric series formula. Students apply the sum of a finite geometric series formula to a structured savings plan.

 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...

 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.

 Student Outcomes Students apply properties of logarithms to solve exponential equations. Students relate solutions to f(x) = g(x) to the intersection point(s) on the graphs of y = f(x) and y = g(x)...

 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 solve simple exponential equations numerically.

 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...