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Mathematics Grade 8
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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.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

• Bike Race
The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.
• 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.
• Distance
In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.
• Distance Across the Channel
This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation
• 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.
• 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.
• 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.
• Lines and Linear Equations
This lesson unit is intended to help educators assess how well students are able to interpret speed as the slope of a linear graph and translate between the equation of a line and its graphical representation.
• 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.
• 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.
• Riding by the Library
In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.
• Student Task: Baseball Jerseys
In this task, students will help Bill to find the best price for buying printed jerseys for the baseball team.
• Student Task: Linear Graphs
In this task, students are asked to match equations with linear graphs.
• Student Task: Meal Out
In this task, students use equations to solve a problem with a restaurant check.
• Student Task: Short Tasks - Functions
A set of short tasks for grade 8 dealing with functions.
• Tides
This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

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.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.