This class introduces students to fundamental algebraic skills such as: operations, algebraic expressions, solving equations, graphing, linear, quadratic, and exponential functions, and statistics. Students engage with relevant mathematical contexts to make math meaningful.
Unit 1 invites students to use tables, graphs, visuals, and equations to describe mathematical relationships. Students focus on equations and graphs in Unit 2 as they solve one- and two-variable equations and inequalities. They also revisit forms of linear equations when solving two-variable equations, which connects to equations of lines of best fit in Unit 3. Unit 3 also supports students in visualizing and analyzing one-variable and two-variable data.
Unit 4 introduces features of functions that students will attend to in later units (e.g., domain and range, key features). Unit 5 revisits the work of Unit 2 as students solve systems of linear equations and inequalities. Unit 6 deepens the work that students started with exponential functions in Unit 1, incorporating the language about functions from Unit 4. Unit 7 is the first of two units about quadratics, and focuses on the forms and key features of quadratic functions. The final unit of Algebra 1 (Unit 8) introduces several strategies for moving between forms of quadratic equations (e.g., factoring, completing the square, quadratic formula) to help highlight features of interest.
As students encounter challenging problems, and practice asking for help and a willingness to learn from others, they build the social emotional learning competencies of self-management, self awareness, relationship skills, and social awareness.
Grade Level(s): 8th Grade, 9th Grade
Related Priority Standards (State &/or National): K-12 Mathematics Missouri Learning Standards
Course Essential Questions:
- How can we represent values using variables?
- How can a real-world situation be translated into an algebraic equation?
- What strategies can be used to solve and graph equations and inequalities?
- How can you use functions to model and interpret real-world situations?
- How can trends in data be analyzed using linear functions?
- How can systems of equations be used to represent situations and solve problems?
- What are real world models of exponential growth and decay?
- How does understanding how to find the vertex of a quadratic function help in making decisions in real-life applications?
Course Enduring Understandings, Goals & Objectives
- Students will understand that patterns and relationships can be represented with graphs, tables, and equations.
- Students will understand that functions are a mathematical way to describe relationships between two quantities that vary.
- Students will understand that linear equations can be used to represent the trend in a data set.
- Students will understand that real world situations can be represented symbolically and graphically.
- Students will understand that the properties of integers apply to simplifying polynomial expressions.
- Students will understand that for any quadratic function in standard form, the values of a, b, and c provide key information about its graph.
- Students will understand that transformations are connected to our spatial reasoning.
Course-Level Scope & Sequence (Units &/or Skills)
Unit 1 - Representing Relationships
- Students will be able to use tables, equations, and graphs to describe relationships and make predictions.
- Students will be able to distinguish between linear and exponential relationships shown in tables, graphs, equations, and situations.
- Students will be able to write and interpret equations of linear and exponential relationships.
Unit 2 - Linear Equations and Inequalities
- Students will be able to solve linear equations with one variable, including equations with no solution or many solutions.
- Students will be able to solve multi-variable equations for a given variable.
- Students will be able to write and solve equations to represent linear situations.
- Students will be able to determine solutions to an inequality algebraically and graphically.
- Students will be able to write inequalities in one and two variables to represent constraints.
Unit 3 - Describing Data
- Students will be able to represent data with a dot plot, histogram, or box plot.
- Students will be able to calculate the mean and standard deviation or median and IQR for a data set.
- Students will be able to use shape, center, spread, and outliers to compare data sets.
- Students will be able to describe data using correlation coefficients and lines of best fit.
- Students will be able to use technology to generate lines of best fit and make predictions.
Unit 4 - Describing Functions
- Students will be able to model real-world situations with the use of a function.
- Students will be able to use multiple function types to further explore the relationship between independent and dependent variables.
- Students will be able to write functions in various ways, including the use of function notation.
- Students will be able to use domain and range to interpret constraints on a function.
Unit 5 - Systems of Linear Equations and Inequalities
- Students will be able to solve a system by graphing.
- Students will be able to solve a system using substitution.
- Students will be able to solve a system using elimination.
- Students will be able to solve problems of applications of systems.
- Students will be able to determine the most efficient method when solving a system of linear equations.
- Students will be able to explain what is meant by the solution to a system of linear equations.
- Explain what is meant by the solutions to a system of inequalities.
Unit 6 - Exponential Functions
- Students will be able to use equations and graphs to compare exponential functions.
- Students will be able to interpret situations that change exponentially.
- Students will be able to construct exponential equations and use them to model situations and solve problems.
- Students will be able to learn that the output of an increasing exponential function is eventually greater than the output of an increasing linear function for the same input.
- Students will be able to study graphs of exponential functions in terms of real-world contexts.
Unit 7 - Quadratic Functions
- Students will be able to justify whether a function is linear, quadratic, exponential, or none.
- Students will be able to identify and interpret key features of quadratics in graphs and tables.
- Students will be able to graph quadratics in standard form and factored form.
- Students will be able to write quadratic equations in factored form from a graph or description.
- Students will be able to use key features to graph quadratics in vertex form.
- Students will be able to write quadratic functions in factored form or vertex form.
Unit 8 - Quadratic Equations
- Students will be able to explain the meaning of a solution to an equation in terms of a situation.
- Students will be able to write a quadratic equation that represents a situation.
- Students will be able to interpret, write, and solve quadratic equations.
- Students will be able to solve quadratic equations by reasoning, by rewriting expressions in factored form and using the zero product property, by completing the square, and by applying the quadratic formula.
- Students will be able to rewrite expressions in vertex form to solve problems about the maximum or minimum value of a function.
- Students will be able to understand that quadratic equations may have 2,1, or 0 solutions, and that the solutions may be rational or irrational.
Course Resources & Materials: To be determined
Date Last Revised/Approved: 2023