###### Secondary Mathematics I [2011]
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Interpret functions that arise in applications in terms of a context.
For F.IF.4 and 5, focus on linear and exponential functions. For F.IF.6, focus on linear functions and intervals for exponential functions whose domain is a subset of the integers. Mathematics II and III will address other function types. N.RN.1 and N.RN.2 will need to be referenced here before discussing exponential models with continuous domains.
F.IF.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

• Distance-Time Graphs
This tutorial is designed to help students understand the concept of slope and how distance-time graphs represent the relationship of collected data.
• 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.
• Function Flyer
The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
• Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
• Growth Rate
In this lesson from Illuminations, students are given growth charts for the heights of girls and boys in order to approximate rates of change in the height of boys and girls at different ages. Students will use these approximations to plot graphs of the rate of change of height vs. age for boys and girls.
• Interpreting Functions Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for the Secondary Mathematics 1 Cluster "Understand the concept of a function and use function notation." / Standards F.IF.1, F.IF.2, F.IF.3 and Cluster "Interpret functions that arise in applications in terms of a context" / Standards F.IF.4, F.IF.5 and F.IF.6 and Cluster "Analyze functions using different representations" / Standards F.IF.7 and F.IF.9.
• Multi-Function Data Flyer
The applet in this lesson allows students to plot ordered pairs and then change the values in order to observe the effects of those changes.
• Rate of Change and Slope
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.
• Rate of Change and Slope video
This video introduces the concepts.
• Slope Slider
This website's applet lets the student manipulate a linear function in order to better understand the relationship between slope and intercept in the Cartesian coordinate system.
• Walk the Line: A Module on Linear Functions
This is a set of 5 lessons in which students must graph data and analyze linear equations in both algebraic and graphic formats.

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 Office 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 Office of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.