Mathematics Grade 8
Educational Links
Strand: FUNCTIONS (8.F)
Define, evaluate, and compare functions
(Standards 8.F.13). Use functions to model relationships between quantities
(Standards 8.F.45).
Standard 8.F.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in grade 8.)

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 Algorithms: Guess My Rule
Use a function machine to play a game where you guess three mystery algorithms, then check to see if you're correct. In the activity you test function rules and find relationships between those rules and graphs. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

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 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.

Foxes and Rabbits
This task emphasizes the importance of the "every input has exactly one output" clause in the definition of a function by using the example of fox and rabbit populations.

Function Machine
Students learn how a function machine works in this interactive from Annenberg and then use them to answer questions. Students must then apply function rules to problems, plot points on graphs, and solve rules problems. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Function Rules
The purpose of this task is to connect the a function described by a verbal rule with corresponding values in a table (one of six connections to be made between the four ways to represent a function, the other two being through its graph and through an expression). It also encourages students to think more broadly about functions as relating objects other than numbers, although this broad application is not intended to be assessed. Because of its ambiguity, this task would be more suitable for use in a classroom than for assessment.

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 nonlinear functions as well. In the second and final topic of this module, students extend what they learned in Grade 7 about how to solve realworld 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.

Graphs and Functions
This lesson plan is designed to help the student understand how to plot functions on the Cartesian plane and how the graphing of functions leads to lines and parabolas.

Interpreting DistanceTime Graphs
This lesson unit is intended to help educators assess how well students are able to interpret distance and time graphs.

Introducing Functions
The goal of this task is to motivate the definition of a function by carefully analyzing some different relationships. In some of these relationships, one quantity can be determined in terms of the other while in others this is not possible. In this way, students are led to see what is special about a function, namely that to each input there corresponds one and only one output.

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.

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.

Pennies to Heaven
The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task.

Sequencer
By using this applet students are able to create sequences by changing the values of starting numbers, multipliers, and addons.

Student Task: Linear Graphs
In this task, students are asked to match equations with linear graphs.

Student Task: Short Tasks  Functions
A set of short tasks for grade 8 dealing with functions.

Teacher Desmos: LEGO Prices
In this activity, students use sliders to explore the relationship between price and number of pieces for various Star Wars LEGO sets and to make several predictions based on that model. Students will also interpret the parameters of their equation in context.

Teacher Desmos: Linear Functions Collection
A collection of activities designed for algebra students studying linear functions as tables, graphs, and equations.

Teacher Desmos: Marbleslides Lines
In this activity, students will transform lines so that the marbles go through the stars. Students will test their ideas by launching the marbles, and have a chance to revise before trying the next challenge.

The Customers
The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant reallife context. Instructors might prepare themselves for variations on the problems that the students might wander into (e.g., whether one person could have two home phone numbers) and how such variants affect the correct responses.

US Garbage, Version 1
In this task, the rule of the function is more conceptual: We assign to a year (an input) the total amount of garbage produced in that year (the corresponding output). Even if we didn't know the exact amount for a year, it is clear that there will not be two different amounts of garbage produced in the same year. Thus, this makes sense as a "rule" even though there is no algorithmic way to determine the output for a given input except looking it up in the table.

Vertical Line Test
This interactive applet asks the student to connect points on a plane in order to build a function and then test it to see if it's valid.
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.
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