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

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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.

Lesson Author

Rhonda Leichliter

Rogers, AR

Grade Level

Ninth grade

Subjects

Math

Standards

HSN-Q.A.1

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.*

HSA-CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HSF-IF.B.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*

HSF-IF.C.7a

Graph linear and quadratic functions and show intercepts, maxima, and minima.

HSF-BF.A.1

Write a function that describes a relationship between two quantities.*

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Warm Up

10 minutes

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.

Power Point / Frayer Model

35 minutes

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.

Exit Slip

5 minutes

Extension of a Direct Variation Application

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.

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