Linear Functions
Unit description: Students will learn to use functions to model relationships between quantities. The students will develop an understanding of congruence and similarity using physical models, transparencies, or geometry software. They will also learn to investigate patterns of association in bivariate data.
Download the complete Grade 8 Math Unit 6 framework to customize for your own planning.
Essential Outcomes of the Unit
Functions
Use functions to model relationships between quantities.
8.F.4 . Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Geometry
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
Statistics and Probability
Investigate patterns of association in bivariate data.
8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of
association between two quantities. Describe patterns such as clustering, outliers, positive or
negative association, linear association, and nonlinear association.
8.SP.2 Understand that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.3 . Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
Essential Questions and Big Ideas
- How can I construct a function to model a linear relationship?
- A linear relationship is represented as y = mx+b where m represents the slope and b represents the y-intercept.
- What kind of patterns and associations can you see from looking at a scatter plot?
- A scatter plot can show a linear, nonlinear, or no association.
- A scatter plot can show a positive or negative association.
- Outliers and clustering determine if a scatter plot has a weak or strong association.
- How can I write a linear function to represent a line of best fit on a scatter plot?
- A linear function is written in the form y = mx + b where m represents the rate of change and b represents the y-intercept.
- How can you use a linear equation to make predictions about bivariate data?
- The slope of a linear equation represents the rate of change in a set of data.
- The y-intercept of a linear equation represents the y value when the x-value is 0.