##
* *Reflection: Real World Applications
Are x and y Directly or Inversely Proportional? (Day 1 of 2) - Section 3: Exit Slip

As an application of Direct Variation, there is an online article about Leonardo Da Vinci and how body parts are directly proportional. If time permits, I assign the students this article to read and 2 problems to work with their table partner.

I demonstrate setting up the proportions to the problems in this video:

Web source: (accessed November 26 2013)

http://www.regentsprep.org/regents/math/algtrig/ATE7/Variation%20in%20ARt.htm

*Extension of a Direct Variation Application*

*Real World Applications: Extension of a Direct Variation Application*

# Are x and y Directly or Inversely Proportional? (Day 1 of 2)

Lesson 12 of 20

## Objective: SWBAT recognize and describe Direct Variation using multiple representations and solve for the Constant of Variation (k).

## Big Idea: This lesson introduces students to Direct Variation by comparing the equation y=kx to the now familiar equation y=mx + b.

*50 minutes*

#### Warm Up

*10 min*

This Warm Up takes about 10 minutes for students to complete and for me to review with the class. I introduce students to Direct Variation in this Warm Up. I expect my students to recognize that the relationship in this problems is proportional. I also want students to recognize that the y-intercept is 0 on the graph of the data.

I demonstrate my review of the Warm Up with the students in the video below.

#### Resources

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#### Power Point / Frayer Model

*35 min*

After reviewing the Warm Up task, I begin to introduce my students to the difference between a situation involving a Direct Variation and a situation that can be modeled as an Inverse Variation. I provide my students with a Frayer Model to take notes as I present to them using this PowerPoint presentation.

Today, we will focus on Direct Variation. Tomorrow we will discuss Inverse Variation. I choose to use a Frayer Model because I want my students to focus on the appearance of a Direct Variation in different algebraic. The representations I will discuss are: ordered pairs in a table, an equation, and a graph. The Frayer Model helps students organize their notes for each representation. I want them to be able to refer back to this Graphic Organizer to compare Direct and Inverse Variations (as well as other bivariate relationships). Here is a Sample of a completed Frayer Model.

*expand content*

#### Exit Slip

*5 min*

Today's Exit Slip will help me to determine how well my students documented the information conveyed during the lesson. I expect this Exit Slip to take about five minutes for the students to complete. After students turn in their Exit Slips, I will share out the answers and encourage students to add information to their Frayer Models, as needed. Although the Exit Slip is not too challenging, I find that summarizing key points at the end of the lesson helps my students with retention of the content.

Tomorrow we will continue with Inverse Variation.

#### Resources

*expand content*

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Sequences
- LESSON 2: The Recursive Process with Arithmetic Sequences
- LESSON 3: Recursive vs. Explicit
- LESSON 4: Increasing, Decreasing, or Constant?
- LESSON 5: Change Us and See What Happens!
- LESSON 6: Why are lines parallel?
- LESSON 7: Get Perpendicular with Geoboards!
- LESSON 8: Dueling Methods for Writing the Equation of a Line
- LESSON 9: Comparing Linear Combinations in Ax +By= C to y=mx +b
- LESSON 10: Equations for Parallel and Perpendicular Lines.
- LESSON 11: Assessment of Graphing Lines through Art!
- LESSON 12: Are x and y Directly or Inversely Proportional? (Day 1 of 2)
- LESSON 13: Are x and y Directly or Inversely Proportional? (Day 2 of 2)
- LESSON 14: Writing, Graphing, and Describing Piecewise Linear Functions
- LESSON 15: Introduction to Scatter Plots, Line of Best Fit, and the Prediction Equation
- LESSON 16: Predicting the Height of a Criminal (Day 1 of 2)
- LESSON 17: Predicting the Height of a Criminal (Day 2 of 2)
- LESSON 18: Predicting Bridge Strength via Data Analysis (Day 1 of 2)
- LESSON 19: Predicting Bridge Strength via Data Analysis (Day 2 of 2)
- LESSON 20: Linear Assessment