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.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.

• Baseball Cards
This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts.
• Chapter 2 - Mathematical Foundation (UMSMP)
This is Chapter 2 of the Utah Middle School Math: Grade 8 textbook. It provides a Mathematical Foundation for Proportional and Linear Relationships.
• Chapter 2 - Student Workbook (UMSMP)
This is Chapter 2 of the Utah Middle School Math: Grade 8 student workbook. It covers Proportional and Linear Relationships.
• 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.
• Chicken and Steak, variation 1
This task presents a real world situation that can be modeled with a linear function best suited for an instructional context.
• Chicken and Steak, variation 2
This task is intended strictly for instructional purposes with the goal of building understandings of linear relationships within a meaningful and, hopefully, somewhat familiar context.
• 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.
This Teaching Channel video demonstrates a lesson where students analyze patterns and represent functions. (9 minutes)
• Delivering the Mail, Assessment Variation
This task involves constructing a linear function and interpreting its parameters in a context. Thus, this task has a medium level of complexity
• Downhill
This task provides an opportunity to compare and contrast the graph of a function and what it represents with a drawing of the hill and the vertical and horizontal distances traversed with each mile down the slope.
• Finding Patterns to Make Predictions
This activity asks students to identify and contemplate mathematical patterns that we see around us. They are asked to represent them in a table and predict the pattern to the 7th, 9th, and nth terms. 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.
• Grade 8 Math Module 6: Linear Functions (EngageNY)
In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as a rule that assigns exactly one value to each input. In this module, students use their understanding of functions to model the possible relationships of bivariate data. This module is important in setting a foundation for students work in algebra in Grade 9.
• Grade 8 Unit 6: Linear Models and Tables (Georgia Standards)
In this unit students will identify the rate of change and the initial value from tables, graphs, equations, or verbal descriptions; write a model for a linear function; sketch a graph when given a verbal description of a situation; analyze scatter plots; informally develop a line of best fit; use bivariate data to create graphs and linear models; and recognize patterns and interpret bivariate data.
• Graphing Equations in Slope Intercept Form
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Graphing Equations in Slope Intercept Form Video
This is a video introduction to the topic.
• 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.
• Heart Rate Monitoring
In this task, students are asked to draw a graph that represents heart rate as a function of time from a verbal description of that function. Then they use the graph to draw conclusions about the context, for instance they have to understand that a heart rate greater than 100 beats per minute occurs when the graph is above the line y=100.
While not a full-blown modeling problem, this task does address some aspects of modeling as described in Standard for Mathematical Practice 4.
• Intercepts of Linear Equations
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Intercepts of Linear Equations video
This video introduces the topic.
• 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.
• Linear Function Machine
By putting different values into the linear function machine students will explore simple linear functions.
• Linear Functions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Linear Functions video
This video compares proportional and non-proportional linear functions.
• Modeling Situations With Linear Equations
This lesson unit is intended to help educators assess how well students use algebra in context, and in particular, how well students explore relationships between variables in everyday situations, find unknown values from known values, find relationships between pairs of unknowns, and express these as tables and graphs, as well as find general relationships between several variables, and express these in different ways by rearranging formulae.
• Modeling with a Linear Function
The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.
• 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.
• Non-Linear Functions
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Non-linear Functions video
This video introduces non-linear functions.
• Parallel Lines
This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
• Parallel Lines video
This video explains the concept.
In this task, students will help Bill to find the best price for buying printed jerseys for the baseball team.