Strand: FUNCTIONS (8.F)

Define, evaluate, and compare functions (Standards 8.F.1-3). Use functions to model relationships between quantities (Standards 8.F.4-5).

Standard 8.F.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

• Chapter 3 - Mathematical Foundation (UMSMP)
This is Chapter 3 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Representations of a Line.
• Chapter 3 - Student Workbook (UMSMP)
This is Chapter 3 of the Utah Middle School Math: Grade 8 student workbook. It covers Representations of a Line.
• Chapter 4 - Mathematical Foundation (UMSMP)
This is Chapter 4 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Functions.
• Chapter 4 - Student Workbook (UMSMP)
This is Chapter 4 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Functions.
• Chapter 5 - Mathematical Foundation (UMSMP)
This is Chapter 5 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Simultaneous Linear Equations.
• Chapter 5 - Student Workbook (UMSMP)
This is Chapter 5 of the Utah Middle School Math: Grade 8 student workbook. It focuses on Simultaneous Linear Equations.
• Comparing Exponential, Quadratic, and Linear Functions
This interactive requires the student to examine functional relationships to determine whether they are quadratic, exponential, or linear. The classroom activity for the lesson shows the student 3 graphs and has them determine what sort of function they reflect. They also solve word problems using the interactive activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Functional Relationships Between Quantities: Calculating Fuel Consumption
This lesson consists of interactive visualizations to help students examine the relationship between a car's mpg to gallons per mile. They can use the interactive slider to see how the relationship changes as a car's efficiency is changed. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Functions (8.F) - 8th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Functions.
• Grade 8 Math Module 5: Examples of Functions from Geometry (EngageNY)
In the first topic of this 15 day 8th grade module, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. Once a formal definition of a function is provided, students then consider functions of discrete and continuous rates and understand the difference between the two. Students apply their knowledge of linear equations and their graphs from Module 4 to graphs of linear functions. Students inspect the rate of change of linear functions and conclude that the rate of change is the slope of the graph of a line. They learn to interpret the equation y=mx+b as defining a linear function whose graph is a line. Students compare linear functions and their graphs and gain experience with non-linear functions as well. In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve real-world and mathematical problems related to volume from simple solids to include problems that require the formulas for cones, cylinders, and spheres.
• Grade 8 Unit 5: Linear Functions (Georgia Standards)
In this unit students will graph proportional relationships; interpret unit rate as the slope; compare two different proportional relationships represented in different ways; use similar triangles to explain why the slope is the same between any two points on a non-vertical line; derive the equation y = mx for a line through the origin; derive the equation y = mx + b for a line intercepting the vertical axis at b; and interpret equations in y = mx + b form as linear functions.
• Graphing Linear Equations: T-Charts
This teaching module takes the student step-by-step through graphing linear equations. They are shown how to graph by making a T chart, plotting points, and drawing the line.
• Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
• Interpreting Distance-Time Graphs
This lesson unit is intended to help educators assess how well students are able to interpret distance and time graphs.
• Introduction to Functions
This lesson introduces students to functions and how they are represented as rules and data tables. They also learn about dependent and independent variables.
• Introduction to Linear Functions
This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions.
• IXL Game: Nonlinear functions
Designed for eighth graders this game will help the student understand linear functions, specifically how to identify linear and nonlinear functions. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Manipulating Graphs
This video demonstrates how to use the slope-intercept of a line to the graph of that line. The classroom activity has them demonstrate their understanding by finding equations for a set of lines through the origin. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
In this task, students are asked to match equations with linear graphs.