 Mathematics Grade 8

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.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

• Battery Charging
This task has students engaging in a simple modeling exercise, taking verbal and numerical descriptions of battery life as a function of time and writing down linear models for these quantities. To draw conclusions about the quantities, students have to find a common way of describing them.
• 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.
• Coordinates and the Cartesian Plane
This lesson helps students understand functions and the domain and range of a set of data points.
• Exploring Linear Functions: Representational Relationships
This lesson plan helps students better understand linear functions by allowing them to manipulate values and get a visual representation of the result.
• Exploring Reasoning and Proof
Questions requiring geometric reasoning are applied to the icing of a cake in this Annenberg interactive. Students must estimate the amount of frosting needed to cover a whole cake. The classroom activity focuses on pattern recognition and geometric reasoning. 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 4: Functions (Georgia Standards)
In this unit students will recognize a relationship as a function when each input is assigned to exactly one unique output; reason from a context, a graph, or a table, after first being clear which quantity is considered the input and which is the output; produce a counterexample: an input value with at least two output values when a relationship is not a function; explain how to verify that for each input there is exactly one output; and translate functions numerically, graphically, verbally, and algebraically.
• 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.
• Linear Function Machine
By putting different values into the linear function machine students will explore simple linear functions.
• 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. http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.