• Course Description

    Algebra I provides a bridge from the study of patterns and relationships in previous grades to the study of functions, algebraic relationships, and the development of advanced mathematical reasoning skills. This course will help prepare today’s students for tomorrow’s world by involving students in exploring and discovering math concepts, connecting algebra to the real world and to other subjects, and by integrating technology as a problem-solving tool.

    Grade Level(s): 8-12th, Duration 1 Year

    Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards  

    Essential Questions

    • What is the purpose of developing an expression?
    • How do you use equations and inequalities to communicate your ideas and solve problems?
    • How can writing equations and inequalities make solving real-world problems more efficient?
    • How can you represent and describe functions?
    • What do the features of the graph reveal about the problem situation?
    • How can we model two variable data and use models to make predictions?
    • What is the meaning of a solution to a system of linear equations in the context of the problem?
    • How is the solution to the system represented algebraically and graphically?
    • How can given data representations be interpreted?

    Enduring Understandings/Big Ideas

    • Students will understand that expressions are powerful tools for exploring reasoning about and representing situations.
    • Students will understand that symbols, such as numbers and variables, can be used and can be manipulated using different processes and operations to represent real-life quantities and their relationships.
    • Students will understand that equations are dynamic tools for problem solving, communicating, and expressing ideas and concepts.
    • Students will understand that equations and inequalities are used to understand how quantities are related.
    • Students will understand that functions can be represented in multiple ways.
    • Students will understand that functions show the relationships between variables.
    • Students will understand that a system of equations may not have only one solution.
    • Students will understand that systems can be solved using a graph, table, or equations. On some occasions and in some contexts one solution method may be more efficient or informative than another.
    • Students will understand that visual displays of categorical and quantitative data should be examined to identify general shape, center, and spread.

    Course-Level Scope & Sequence (Units &/or Skills)

    Unit 1: Expressions

    Students will be able to

    • Identify the parts of an expression such as terms, factors, coefficients
    • Explain the meaning of the parts of an expression within the context of a problem
    • Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context.
    • Add or multiply two rational numbers
    • Use ratios and rates as a way to understand problems and to guide the solution to multi-step problems
    • Convert units and rates.

    Unit 2: Equations and Inequalities

    Students will be able to

    • Create their own equation or inequality to represent and solve a unique real-world situation
    • Graph solutions for unique real world situations
    • Solve linear equations and inequalities
    • Justify each step of solving an equation
    • Construct a viable argument to justify a solution to an equation
    • Construct a viable argument to justify a solution to inequality
    • Check solutions for appropriateness

    Unit 3: Introduction to Functions

    Students will be able to

    • Identify the domain and range of a function
    • Identify whether a relation is a function
    • Relate the practical domain of a function with its real-world meaning
    • Graph equations that represent functions
    • Identify the patterns that describe linear and nonlinear functions
    • Relate the domain of a function to its graph

    Unit 4: Linear Functions

    Students will be able to

    • Identify key features in graphs and tables of linear functions.
    • Relate the domain of a function with its real-world meaning of linear functions
    • Calculate the rate of change or slope of a linear function using ordered pairs, tables of values and graphs
    • Graph a linear function from an equation or table
    • Compare the key features of linear functions
    • Create a linear equation to represent the relationship between two quantities
    • Create a linear function that models our given data
    • Create an equation when given a transformation(s) from a parent function (y=x2)
    • Summarize the transformation from a parent function (y=x2)
    • Identify the effect of vertical translations of linear functions
    • Solve a function for the dependent variable and write the inverse of a function by interchanging the values of the dependent
      and independent variable
    • Describe whether the real-world situation has a linear pattern of change
    • Explain that linear functions change at the same rate over time
    • Use technology to model and compare linear functions
    • Construct linear functions, including arithmetic sequences, given a graph , a description of a relationship, or two input - output pairs
    • Asses the fit of a function by plotting and analyzing residuals
    • Create a scatter plot from two quantitative variables
    • Create and analyze a residual plot to determine whether the function is an appropriate fit
    • Create and use a model of best fit to solve problems
    • Describe how the independent and dependent variables are related
    • Fit a function to data and use that function to solve problems
    • Identify linear functions based on graphs and tables
    • Interpret the parameters in a linear function
    • Describe the correlation using the correlation coefficient.

    Unit 5: Absolute Value Functions

    Students will be able to

    • Explain the meaning of the parts of an absolute value expression
    • Justify each step of solving an absolute value equation
    • Identify key features in graphs and tables of absolute value functions
    • Graph a function from an equation or table
    • Compare and contrast absolute value functions with linear functions
    • Classify the equation's absolute value and determine the number of solutions
    • Write an absolute value equation from a graph
    • Describe how changing parameters affect the graph of an absolute value function.

    Unit 6: Systems of Linear Equations and Inequalities

    Students will be able to

    • Identify solutions to a system of linear inequalities in two variables using technology
    • Solve systems of equations graphically
    • Solve systems of equations using substitution and elimination
    • Justify using a solution method for solving a system of linear equations or inequalities
    • Write and use a system of equations and/or inequalities to solve a real world problem
    • Find the constraints of the problem that uses equations or inequalities
    • Graph the solutions to a linear inequality in two variables using technology
    • Explain in the context of a real world problem why a solution may have no, one or infinite solutions.

    Unit 7: Statistics and Probability

    Students will be able to

    • Calculate the basic probability of an event
    • Calculate & interpret the joint probability of two events occurring in sequence
    • Calculate & interpret conditional probability

    Unit 8: Exponential Functions

    Students will be able to

    • Describe the pattern in geometric sequences
    • Represent geometric sequences both recursively and with an explicit formula
    • Distinguish between situations that can be modeled with exponential and linear functions
    • Construct exponential functions including geometric sequences, given a graph, a description of a relationship, or ordered pairs
    • Identify exponential functions based on graphs and tables
    • Interpret exponential functions that arise in applications
    • Sketch and describe exponential functions showing the key features
    • Translate exponential functions with a focus on vertical translations
    • Interpret the parameters of an exponential function in terms of context
    • Connect geometric sequences to exponential functions
    • Compare the key features of linear and exponential functions
    • Graph an exponential function from an equation or table
    • Write and use recursive formulas for geometric sequences
    • Model exponential growth and decay
    • Interpret exponential functions that arise in applications
    • Graph exponential functions using translations
    • Interpret parameter changes in applications.

    Unit 9: Polynomials

    Students will be able to

    • Multiply polynomials
    • Name polynomials using number of terms and degrees.
    • Add and subtract polynomials
    • Factor polynomials using the greatest common factor

    Unit 10: Quadratic Functions

    Students will be able to

    • Identify patterns in quadratic rate of change
    • Model quadratic functions using technology
    • Apply transformations to quadratic functions
    • Determine if situations are modeled by quadratic functions
    • Analyze quadratic functions using multiple representations
    • Graph quadratic functions
    • Solve quadratic functions using graphs, tables of values, square roots, completing the square, factoring, and quadratic formula
    • Determine intercepts; intervals where the function is increasing, decreasing, positive, or negative, relative maxima and minima, and symmetries for quadratic functions
    • Determine the practical domain for quadratic functions
    • Compare quadratic functions to linear and exponential functions
    • Factor and complete the square in a quadratic function to show zeros, extreme values and symmetry of the graph, and interpret these in terms of a context.
    • Describe how the coefficients a, b, and c effect the graph of a quadratic function
    • Compare quadratic growth to linear and exponential growth
    • Create quadratic equations using one variable and two variables and use them in a contextual situation to solve problems
    • Transform quadratic equations written in standard form to vertex form
    • Derive the quadratic formula by completing the square
    • Create an equation when given a transformation(s) from a parent function (y=x2)
    • Identify the effect of the coefficients, a, b, and c, on a quadratic functions.
    • Summarize the transformation from a parent function (y=x2)
    • Translate quadratic graphs vertically, horizontally, and by a scale factor
    • Use the parent graph (y=x2) of a quadratic function to translate the graph
    • Design a real-world situation that can be modeled by a given function
    • Identify key features in graphs and tables including: intercepts; intervals where the functions is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior
    • Relate the practical domain of a function with its real-world meaning
    • Graph simple quadratic functions using a table and more complex quadratic functions using technology
    • Analyze the intercepts and vertex of quadratic functions
    • Compare and contrast two quadratic functions each expressed in a different forms (standard and vertex)
    • Justify that exponential functions increase more rapidly than linear and quadratic functions
    • Sketch a graph showing the key features of a quadratic equation from a description of the relationship
    • Identify a non-constant rate of change in a quadratic function
    • Create dot plots, histograms and box plots
    • Compare the shape of two or more data sets, measures of center and spread
    • Analyze the effect of outliers on a data set including shape, measures of center and spread
    • Create a quadratic function that models given data
    • Transform a quadratic equation written in standard form to an equation in vertex form (x - p)2 = q by completing the square
    • Derive the quadratic formula by completing the square on the standard form of a quadratic equation
    • Solve quadratic equations in one variable by simple inspection, taking the square root, factoring, and completing the square
    • Understand why taking the square root of both sides of an equation yields two solutions
    • Students should solve by factoring, completing the square, and using the quadratic formula
    • Solve quadratic equations by inspection, factoring, taking the square root, completing the square, and by using the quadratic formula
    • Relate the practical domain of a function with its real-world meaning

    Unit 11: Modeling with Nonlinear Functions (Piecewise, Radical, Inverse)

    • Students will be able to
    • Solve systems with technology that include exponential functions and linear functions
    • Summarize the transformation from a parent function (y=x2)
    • Define an inverse function
    • Solve a function for the dependent variable and write the inverse of a function by interchanging the values of the dependent and independent variable
    • Solve and graph an inverse function
    • Compare and contrast absolute value, step and piecewise-defined functions with linear and exponential functions
    • Graph a function from an equation or a table
    • Write an equation when given a transformation of a parent function.

    Course Resources & Materials: District and teacher-made materials

    Date Last Revised/Approved: 2013