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Handson Activity: Club Function
PreReq Knowledge (Return to Contents) Familiarity with the coordinate plane, coordinates and equations are helpful but not required.
Learning Objectives (Return to Contents) After this lesson students should be able to:
Materials List (Return to Contents) Introduction/Motivation (Return to Contents) (Prepare to show students the attached Linear Functions Presentation PowerPoint file, which is composed of three sections, delineated by three different slide background colors [blue, gray, gold]. Slides 18 are covered in the associated lesson. For this activity, show students slides 411 as you present the Introduction/Motivation section.)
(In order to relate this activity to the grand challenge in this unit, explain that the equations provided by the undergraduate student may represent a function that can tell us about the data gathered in the lab. If these equations are functions, important conclusions may be made regarding the relationships between the variables measured. Engineers employ mathematics to help model and predict what will happen in realworld phenomena. This activity provides practice with the concept of functions so students can use that concept to examine the data.)
(As necessary, review with students the content on slides 48.)
(The most important concept is the idea that one xcoordinate can only have one corresponding ycoordinate. Yet, ycoordinates can have many xcoordinates that correspond to it. In this game, zebras are "xcoordinates" and rhinos are "ycoordinates." This will be demonstrated when the teacher "maps" each group to check to see if they are allowed in the club function.)
(Show students slides 911 to explain the game and rules:)
A function is a term used to describe a group of coordinates that follow a certain set of rules. The rules are that the first element in the set (like the zebras) are paired with exactly one element of the second set (rhinos). It does not say that elements of the second set have to pair with exactly one element of the first set, so it is okay if there is some overlap in the second set. This can be described as onetoone: there is one ycoordinate for every one xcoordinate.
In our example, zebras are like x's and rhinos are like y's. There must be exactly one y for every x and at least one x for every y. So if we wanted to, we could write our mapping diagram as a set of points that is a function. (Use the classroom board to show the following example.) This would look like {(Abby, Greyson), (Benton, Irene), (Charles, Hiroshi), (Danielle, Felicia), (Eric, Hiroshi)}. See how the first element, the zebras/x's, only appears once? And Hiroshi appears twice for the rhinos/y's, but that's okay because every y must be paired with AT LEAST one x. It's okay if there is more than one, like Charles and Eric.
(Go through some examples of functions and nonfunctions in several formats [mapping diagrams, sets of points, graphs] and have students tell you whether they are functions or not.)
There is a special name for the xelements of a group of coordinates. It is called the domain. The yelements also have a special name, the range. So in our mapping diagram example, the domain is {Abby, Benton, Charles, Danielle, Eric} and the range is {Felicia, Greyson, Hiroshi, Irene}. (Go over some more examples of domain and range and have students define the domain and range of certain sets of points [in algebraic and graphic forms].)
Procedure (Return to Contents) After introducing the game and rules (see the Introduction/Motivation section), follow these steps.
Attachments (Return to Contents) Assessment (Return to Contents)
Journal Questions: After the game is over, assign students to answer the following questions in their journals to turn in at class end:
Contributors Aubrey McKelveyCopyright © 2007 by Vanderbilt UniversityIncluding copyrighted works from other educational institutions and/or U.S. government agencies; all rights reserved. Supporting Program (Return to Contents) VU Bioengineering RET Program, School of Engineering, Vanderbilt UniversityAcknowledgements (Return to Contents) The contents of this digital library curriculum were developed under National Science Foundation RET grants no. 0338092 and 0742871. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.
 
 