• High School Mathematics Algebra I Part I Unit 4


    Subject: Mathematics
    Course: Algebra I Part I
    Timeline: 6-10 Days
    Unit 4 Title: Linear Equations and Inequalities

    Unit Overview: 
     
    This unit emphasizes connecting multiple representations of linear functions given a problem context, table, model, graph and/or equation. Connections are continuously made between these representations so that students become fluent in relating functions expressed both algebraically and geometrically.  Graphing calculators are emphasized heavily in this unit to better connect the algebraic and geometric contexts of a function.  A function is described as a special type of relation and is identified as such in both a table and a graph.  Relations and functions are introduced by requiring students to analyze shapes of graphs that describe a situation but which do not include numbers.  Definitions and applications of domain and range are embedded throughout the unit and are identified using a problem context, ordered pairs, a graph, and/or a table. Students will investigate relationships among quantities using graphs, and will also use mathematics to represent real-world situations.  By working with functions through multiple representations, students explore the idea of change, including changes in speed, altitude, distance, volume, time and other variable quantities.  
     
    This unit consists of four lessons, some of which may take more than one classroom period.
    (Note: Formalizing the concept of slope (including its calculation) in the context of a situation, table, or graph is addressed in Unit 3). 

    Unit Objectives:
     
    By the end of Unit 4, all students will be able to:
    • represent a pattern both algebraically and graphically
    • identify the domain and range of a relation and determine if a relation is a function using a table or graph as well as determining if the relation is continuous or discrete
    • make, interpret and graph a linear function given a problem situation or any other representation of the function
    • move fluently between all representations, i.e. from a context, to a table, to a model, to a graph and to an equation
    • be proficient in using a graphing calculator to: graph a line given an equation, access the table for that equation, input a set of points into a table in order to graph the points, and visually determine domain and range. 

    Focus Standards:
     
    PA.CCSS.Math.Eligible Content.A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern 
    algebraically and graphically.
    PA.CCSS.Math.Eligible Content.A1.2.1.1.2 Determine whether a relation is a function given a set of points on a graph.
    PA.CCSS.Math.Eligible Content.A1.2.1.1.3 Identify the domain and range of a relation (represented as ordered pairs,
    a graph, or a table.)
    PA.CCSS.Math.Eligible Content.A1.2.1.2.1 Create, interpret and or use the equation, graph, or table of a linear function.
    PA.CCSS.Math.Eligible Content.A1.2.1.2.2 Translate from one representation of a linear function to another. 

    Mathematical Practice Standards:
     
    #1 Make sense of problems and persevere in solving them.
     
    Students use the concepts and skills that they previously learned about functions and modeling in order to solve new problems by demonstrating their reasoning strategies, growth, and perseverance as independent problem solvers.
     
    #3 Construct viable arguments and critique the reasoning of others.  
     
    To formulize the concepts of relations and functions, students construct viable arguments using techniques such as working backward, using trial and error, or exploring the process of elimination while working together and critiquing the reasoning of others.
     
    #8 Modeling with mathematics.
     
    Students learn to write and evaluate a function rule by using a model to help visualize a real-world situation.  They also learn to analyze the situation mathematically, draw conclusions, and interpret the results in the context of the situation.

    Assessments:
     

    Formative assessments are included for each lesson. There is a final unit exam, with Honors and retake versions included.


    Differentiation:
     
    Each lesson has differentiation options for each portion of the lesson. Additional differentiation options are listed with directions and student masters in the Teacher’s Guide.

    Academic Language:
     
    Continuous graph
    Dependent variable
    Discrete graph
    Domain
    Function and function notation
     
    Independent variable
    Linear function
    Nonlinear function
    Range
    Relation