• ## Course 3, Module 2: Developing Function Foundations

In this module, students build on their experience with proportional relationships and the work they did in Transforming Geometric Objects. Students will analyze and represent linear relationships using tables, equations, graphs, and scenarios. They will develop an understanding of functions. Once they know how to describe functional relationships and construct linear models, they will apply these skills to analyze bivariate data. The concepts in this module will provide the basis for the majority of their high school algebra and statistics studies.

Topic 1: From Proportions to Linear Relationships

• In this topic, students build onto their knowledge of ratio and proportional relationships to develop connections between proportional relationships, lines, and linear equations.
• MATHia Workspaces (4)
• Representing Proportional Relationships Algebraically
• Modeling the Constant of Proportionality
• Understanding the Slopes of Lines
• Graphing Linear Relationships

Topic 2: Linear Relationships

• In this topic, students develop fluency with analyzing linear relationships, writing equations of lines, and graphing lines. Using prior knowledge, students learn to calculate the slope for linear relationships represented in tables and from contexts, connecting the geometric representaions used in the previous topic with the algebraic processes used to calculate slope.
• MATHia Workspaces (14)
• Multiple Representations of Linear Functions
• Modeling Linear Functions Using Multiple Representations
• Calculating Slopes
• Connecting Slope-Intercept and Point-Slope Forms
• Writing Equations Given Slope and a Point
• Writing Eequations Given Two Points
• Modeling Linear Relationships Given an Initial Point
• Modeling Linear Relationships Given Two Points
• Analyzing Models of Linear Relationships
• Graphing Given an Integer Slope and y-Intercept
• Graphing Given a Decimal Slope and y-Intercept
• Modeling Linear Equations in Standard Form
• Graphing Linear Equations using a Given Method
• Graphing Linear Equations using a Chosen Method

Topic 3: Introduction to Functions

• In this topic, students begin to formalize the concept of function, which is a concept they may intuitively understand. They explore functions in terms of sequences, mappings, sets of ordered pairs, graphs, tables, verbal descriptions, and equations.
• MATHia Workspaces (4)
• Exploring Functions
• Exploring Graphs of Functions
• Classifying Relations and Functions
• Identifying Key Characteristcs of Graphs of Functions

Topic 4: Patterns in Bivariate Data

• In this topic, students review the statistical process and investigate associations in bivariate data, both quantitative and categorical. Students use their experience plotting points to create graphical representations of data to identify and explain patterns they notice.
• MATHia Workspaces (6)
• Estimating Lines of Best Fit
• Using Lines of Best Fit
• Building Marginal Frequency Distributions
• Analyzing Marginal Frequency Distributions
• Building Marginal Relative Frequency Distributions
• Analyzing Marginal Relative Frequency Distributions