A.8 
The student, given a situation in a realworld context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically. 

Essential Knowledge and Skills 
 Given a situation, including a realworld situation, determine whether a direct variation exists.
 Given a situation, including a realworld situation, determine whether an inverse variation exists.
 Write an equation for a direct variation, given a set of data.
 Write an equation for an inverse variation, given a set of data.
 Graph an equation representing a direct variation, given a set of data.

Essential Understandings 
 The constant of proportionality in a direct variation is represented by the ratio of the dependent variable to the independent variable.
 The constant of proportionality in an inverse variation is represented by the product of the dependent variable and the independent variable.
 A direct variation can be represented by a line passing through the origin.
 Realworld problems may be modeled using direct and/or inverse variations.


Vertical Articulation 
 SOL AII.10  ID/create/solve real‐world problems involving inverse/joint variation/ combo of direct/inverse variations

Instructional Materials 
 VDOE ESS Lesson: Inverse Variation  Functions (PDF)  Determining inverse variation (Word)
 VDOE ESS Lesson: Direct Variation  Functions (PDF)  Determining direct variation (Word)
 Notes: Variation (doc)  Answer Key (pdf)
 Notes: Direct and Inverse Variation (ppt)
 Guided Notes: Direct and Inverse Variation (doc)

Real World Lessons 

Practice 
 Worksheet: Variations CW (doc)
 Worksheet: Variations HW (doc)
 ExamView Quiz: Direct Variation
 Prentice Hall Quiz

SelfAssessments 
 SOL Mini Quiz

Skills 
 JMU Pivotal Question: Direct and Inverse Variation (doc)

Videos 
 Video: PH Using Direct Variation to Describe a Situation
 Video: PH Using a Proportion as an Equation of Direct Variation
 Video: PH Using a Proportion to Solve a Direct Variation Problem
 Video: PH Using Inverse Variation

Explore
Learning 
 Direct Variation  Adjust the constant of variation and explore how the graph of the direct variation function changes in response.
 Direct and Inverse Variation  Adjust the constant of variation and explore how the graph of the direct or inverse variation function changes in response. Compare direct variation functions to inverse variation functions.
 Introduction to Functions  Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.

Websites 
 Interactive Notes: Direct Variation  lessons and practice problems at Regentsprep.org

Old Website Links 

Common Core
Standards 
