AII.10 
The student will identify, create, and solve realworld problems involving inverse variation, joint variation, and a combination of direct and inverse variations. 

Essential Knowledge and Skills 
 Translate “y varies jointly as x and z” as y = kxz.
 Translate “y is directly proportional to x” as y = kx.
 Translate “y is inversely proportional to x” as y = k/x.
 Given a situation, determine the value of the constant of proportionality.
 Set up and solve problems, including realworld problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

Essential Understandings 
 Realworld problems can be modeled and solved by using inverse variation, joint variation, and a combination of direct and inverse variations.
 Joint variation is a combination of direct variations.


Vertical Articulation 
 SOL A.8  given realworld context, analyze relation to determine direct/inverse variation; represent direct variation algebraically/graphically) and inverse variation (algebraically)

Instructional Materials 
 VDOE ESS Lesson: Types of Variations  Statistics (PDF)  Exploring variations (Word)

Real World Lessons 

Practice 
 VDOE ESS: Variation Examples Chart (pdf)
 VDOE ESS: Direct, Inverse, and Joint Variations (pdf)

SelfAssessments 
 SOL MiniQuiz: AII.10  Variation

Skills 

Videos 
 Video: PH Using Joint and Other Variations

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.
 Determining a Spring Constant  Place a pan on the end of a hanging spring. Measure how much the spring stretches when various masses are added to the pan. Create a graph of displacement vs. mass to determine the spring constant of the spring.

Websites 
 Notes: Variation Equations notes from Purplemath.com

Common Core
Standards 
None 