# ALEX Resources

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 Lesson Plans (2) Classroom Resources (6)

ALEX Lesson Plans
Subject: Mathematics (9 - 12)
Title: Building Functions: Composition of Functions
Description:

This lesson provides a review of evaluating functions and finding function rules as well as an introduction to the composition of functions. The review is accomplished through the use of an online exploration using a function machine. The idea of a function machine is also used to explain the composition of functions. Instruction is provided in finding the composition using several different representations of functions (input/output tables, graphs, and function rules).

This lesson results from the ALEX Resource Gap Project.

Subject: Mathematics (9 - 12)
Title: It's All in the Family
Description:

Students will be motivated to learn how to build new linear functions from existing linear functions.  Students will bring pictures of themselves and their parents from home to personally involve them in the lesson.  Students will learn to use the patterns inherent in functions to quickly and accurately graph linear functions.  This lesson will only deal with vertical shifts and the steepness of the line.  Horizontal shifts will be dealt with in future lessons. In addtion, in future lessons  students will transfer this knowledge to also graph exponential, quadratic, and absolute value functions.

This is a College- and Career-Ready Standards showcase lesson plan.

ALEX Classroom Resources
Subject: Mathematics (9 - 12)
Title: Algebra II Module 3, Topic A: Real Numbers
URL: https://www.engageny.org/resource/algebra-ii-module-3-topic-a-overview
Description:

In Module 3, 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 rational and then irrational exponents (N-RN.1). Students practice applying properties of exponents to expressions with non-integer exponents (N-RN.2). Students use the average rate of change and repeated reasoning to discover Euler’s number, e (F-IF.6).

Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Algebra II Module 3, Topic B: Logarithms
URL: https://www.engageny.org/resource/algebra-ii-module-3-topic-b-overview
Description:

At the beginning of Module 3, Topic B, students apply the properties of exponents to solve exponential equations numerically (F-BF.1a) as a way to motivate the need for logarithms, which are first introduced by the more intuitive name “WhatPower." In the intermediate lessons, students discover the logarithmic properties by creating and examining logarithmic tables and answering sets of directed questions. In the final lessons in Topic B, they solve logarithmic equations by applying the inverse relationship between exponents and logarithms (F-LE.4).

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 D: Using Logarithms in Modeling Situtation
URL: https://www.engageny.org/resource/algebra-ii-module-3-topic-d-overview
Description:

Module 3, Topic D opens with a hands-on 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 (A-CED.2, F-LE.5). Students use logarithms to solve exponential equations analytically and express the solution as a logarithm (F-LE.4). Students study the relationship between exponential growth and decay and geometric series (F-IF.3), and students must use properties of exponents to interpret expressions for exponential functions (F-IF.8b). Armed with a more thorough understanding of exponential functions and equations, students revisit the topic of Newton’s Law of Cooling that was introduced in Algebra I (F-BF.1b).

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