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

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SWBAT recognize characteristics of Direct and Inverse variation and use these key characteristics to write an equation and to find the Constant of Variation (k).

Big Idea

Frayer Models helps students sort through the information necessary to identify different representations of Direct and Inverse Variation.

Power Point/Frayer Model

20 minutes

I begin the second day of this two-day lesson again referring to this Power Point and providing each student a Frayer Model to use to complete the notes on Inverse Variation.  Students completed a Frayer Model for Direct Variation the first day of this lesson.  I begin working with students from slide eight of the Power Point through slide 14.  I taught from slides one through seven on the first day.  Here is a Sample of completing the Frayer Model from the Power Point using Inverse Variation.

The main skill that I want students to able to do after this lesson, is to understand the connection of the equation, graph, and table of inverse variation.  After this lesson, students should be able to find the constant of variation (k), and identify key features of Inverse variation from an equation, table, or graph. Students should also know that the inverse variation graph is never going through (0,0) the origin as a point or solution because it makes the equation y=k/x undefined when x is zero.

Guided Practice

10 minutes

After completing the notes from the Power Point, I provide students with this Guided practice to work with students on horizontal T-Tables.  This is to re-enforce how to recognize Direct and Inverse Variation from ordered pairs or point on the graph, and how to find the Constant of Variation (k).  I ask the students to use their completed Frayer Models on Direct and Inverse variation to guide them in today's work.  

I work on about 3 of the tables with students identifying different characteristics, and then assign the students tables 4-9.  I provide students with the answers to quickly self-assess their own progress.  I allow this time for students to ask questions if needed.  I demonstrate how to identify the constant of variation to determine direct or inverse variation and how it relates to the equation below:

After relating the ordered pairs to the constant of variation and the equations, I graph table 2 and 3 to review how to identify the graphs of direct and inverse variation.

Independent Practice

15 minutes

After the Guided Practice, I assign students this worksheet as an Independent Practice.  I like this worksheet because it provides students an opportunity to practice all of the different representations of Direct and Inverse Variation that I have presented to them over the two days of this lesson.  I allow the students to work on the worksheet for about 15 minutes, and hand each student an Exit Slip with five minutes remaining in class.

Resource Note: I found this worksheet at the following website:

(Last accessed on 3-15-15)

Most of the students will not complete the Independent Practice in 15 minutes, and will have about 10 problems left on the worksheet for homework.  I encourage students to do a couple of problems out of each section of the worksheet before leaving class so that myself or a peer may provide assistance.  I walk around the room to monitor student work, and provide some one on one tutoring while students are working on the worksheet if necessary.

The students will hand in this assignment after completing it, and I will choose 5 problems to grade. I will grade the same 5 problems for every student.  I will choose a variety of problems that will demonstrate the student's ability to identify direct and inverse variation in different representations. Throughout the lesson, I have emphasized the standard on the Algebra I PARCC exam, that each graph and equation is a a solution set of its own points.  I want students to make the connection understand the connection between the points on a graph, the image of the graph, and its own equation.

Exit Slip

5 minutes

Today I use an Exit Slip which is similar to yesterday's. To some extent, this helps me to identify whether students who struggled with the Exit Slip yesterday were more focused today. On the Exit Slip students answer questions about Inverse Variation. Like yesterday I want my students to recall this information later, so I make sure that students think about it at the end of today's lesson.

Teacher's Note:  Summarizing and Comparison are teaching strategies that I use often to improve student retention and understanding.

After I collect the Exit Slip, I will read some of the responses to the class without identifying the author. This provides an opportunity to clarify any confusion with respect to terminology.