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Henrico County Public Schools, Virginia
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A.8
The student, given a situation in a real-world 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 real-world situation, determine whether a direct variation exists. Given a situation, including a real-world 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. Real-world problems may be modeled using direct and/or inverse variations.
Vertical Articulation
1. SOL AII.10 - ID/create/solve real‐world problems involving inverse/joint variation/ combo of direct/inverse variations
Instructional Materials
1. VDOE ESS Lesson: Inverse Variation - Functions (PDF) - Determining inverse variation (Word)
2. VDOE ESS Lesson: Direct Variation - Functions (PDF) - Determining direct variation (Word)
3. Notes: Variation (doc) | Answer Key (pdf)
4. Notes: Direct and Inverse Variation (ppt)
5. Guided Notes: Direct and Inverse Variation (doc)
Real World Lessons
Practice
Self-Assessments
Skills
Videos
Explore Learning
1. Direct Variation - Adjust the constant of variation and explore how the graph of the direct variation function changes in response.
2. 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.
3. 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
1. Interactive Notes: Direct Variation - lessons and practice problems at Regentsprep.org