# ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra II Module 3, Topic C: Exponential and Logarithmic Functions and Their Graphs
URL: https://www.engageny.org/resource/algebra-ii-module-3-topic-c-overview
Description:

In Module 3, Topic C, students graph logarithmic functions, identifying key features (F-IF.4, F-IF.7) and discover how the logarithmic properties are evidenced in the graphs of corresponding logarithmic functions. The inverse relationship between an exponential function and its corresponding logarithmic function is made explicit (F-BF.3).  In the final lesson in Topic C, students synthesize what they know about linear, quadratic, sinusoidal, and exponential functions to determine which function is most appropriate to use to model a variety of real-world scenarios (F-BF.1a).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra II Module 3, Topic E: Geometric Series and Finance
URL: https://www.engageny.org/resource/algebra-ii-module-3-topic-e-overview
Description:

Module 3, 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 while developing and practicing the formula for the sum of a finite geometric series (A-SSE.4). Throughout this set of lessons, students study the mathematics behind car loans, credit card payments, savings plans, and mortgages, developing the needed formulas from summing a finite geometric series in each case. Key features of tables and graphs are used to answer questions about finances (F-IF.7e).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Precalculus and Advanced Topics Module 3, Topic B: Rational Functions and Composition of Functions
Description:

In Module 3, Topic B, students explore the 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 polynomial functions. A study of rational expressions shows that these expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression. Students apply these operations to simplify rational expressions and go on to graphing rational functions, identifying zeros and asymptotes, and analyzing end behavior.

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to Algebra I, Algebra II, and Algebra II with Trigonometry Alabama Courses of Study.

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra I Module 3, Topic C: Transformations of Functions
URL: https://www.engageny.org/resource/algebra-i-module-3-topic-c-overview
Description:

In Module 3, 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 algebraic solutions to equations in one variable, seeing them as f(x) = g(x) and recognizing that the intersection of the graphs of f(x) and g(x) are solutions to the original equation (A-REI.D.11). Students use the absolute value function and other piecewise functions to investigate transformations of functions and draw formal conclusions about the effects of a transformation on the function’s graph (F-IF.C.7, F-BF.B.3).

Subject: Mathematics (9 - 12)
Title: Algebra I Module 4, Topic C: Function Transformations and Modeling
URL: https://www.engageny.org/resource/algebra-i-module-4-topic-c-overview
Description:

In Module 4, 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) = cube root of x), to perform horizontal and vertical translations as well as shrinking and stretching (F-IF.C.7b, F-BF.B.3). They recognize the application of transformations in vertex form for a quadratic function and use it to expand their ability to efficiently sketch graphs of square and cube root functions. Students compare quadratic, square root, or cube root functions in context and represent each in different ways (verbally with a description, as a table of values, algebraically, or graphically). In the final two lessons, students examine real-world problems of quadratic relationships presented as a data set, a graph, a written relationship, or an equation. They choose the most useful form for writing the function and apply the techniques learned throughout the module to analyze and solve a given problem (A-CED.A.2), including calculating and interpreting the rate of change for the function over an interval (F-IF.B.6).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra II Module 1, Topic B: Factoring--Its Use and Its Obstacles
URL: https://www.engageny.org/resource/algebra-ii-module-1-topic-b-overview
Description:

Module 1, Topic B 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 real-world situations and develop fluency with creating equations and functions given a verbal description, visual representation, or graph. This topic concludes with a discussion of polynomial division with remainder, further strengthening the connection between the remainder, the factors and zeros of a polynomial equation, and graphs of polynomial functions.

Subject: Mathematics (9 - 12)
Title: Algebra II Module 2, Topic A: The Story of Trigonometry and Its Context
URL: https://www.engageny.org/resource/algebra-ii-module-2-topic-a-overview
Description:

In Module 2, Topic A, students develop an understanding of the six basic trigonometric functions as functions of the amount of rotation of a point on the unit circle (F-TF.A.1), and then translate that understanding to the trigonometric functions as functions on the real number line (F-TF.A.2). Students study graphs of the functions to discover properties of the trigonometric functions (F-IF.C.7e).

Subject: Mathematics (9 - 12)
Title: Algebra II Module 2, Topic B: Understanding Trigonometric Functions and Putting Them to Use
URL: https://www.engageny.org/resource/algebra-ii-module-2-topic-b-overview
Description:

Students will use trigonometric functions to model periodic phenomena (F-TF.B.5) by fitting sinusoidal functions to data (S-ID.B.6a). Students use the properties of the graphs of sinusoidal functions to help fit functions to data to solve problems in the context of the data (F-IF.C.7e).  We end the module with the study of trigonometric identities and how to prove them (F-TF.C.8).

ALEX Classroom Resources: 8