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 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...

 Algebra I Module 3: Linear and Exponential Functions In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module,...

 Algebra I Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs In this module students analyze and explain precisely the process of solving an equation. Through...

 Algebra I Module 5: A Synthesis of Modeling with Equations and Functions In Module 5, students synthesize what they have learned during the year about functions to select the correct function type in...

 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...

 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...

 Algebra II Module 1: Polynomial, Rational, and Radical Relationships Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of...

 Algebra I Module 4: Polynomial and Quadratic Expressions, Equations, and Functions In earlier modules, students analyze the process of solving equations and developing fluency in writing,...

 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.

 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 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 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 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 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 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)...

 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 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...