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Common Core: Standard
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 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...

 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...

 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...

 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...

 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 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...

 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 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...

 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...

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

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