Problem Solving with Sets and Venn Diagrams

"A pack of wolves, a bunch of grapes, or a flock of pigeons are all examples of sets of things. The mathematical concept of a set can be used as the foundation for all known mathematics.... Sets, as they are usually conceived, have elements or members. An element of a set may be a wolf, a grape, or a pigeon. It is important to know that a set itself may also be an element of some other set. Mathematics is full of examples of sets of sets." from Naive Set theory by Paul Halmos, p. 1 (see bibliography) This week is about problem solving with sets - what kinds of problems can be solved with sets, what problem solving methods are used, and what are the limitations.

Assignment Exercises Sets and Set Operations Venn Diagram Examples

Readings Bello & Britton, Sections 1.2-1.5 Limitations

Web Resources These web resources have links to different kinds of applications with Venn diagrams.

Assignment

1) Experience interactive online learning with the Venn diagram applet at: Venn Diagrams (http://www.shodor.org/interactivate/activities/vdiagram/index.html) and at the Venn Diagram Self Test web site (http://math.uww.edu/faculty/mcfarlat/143venn.htm). 2) Complete the exercises listed below. If it helps, please feel free to copy and use the Venn diagram worksheet gif on the Venn diagram worksheet page. 3) Give an example from your classroom where you would use Venn diagrams. For example, Venn diagrams are used as early as K-2 in discussing attributes; they just are not called Venn diagrams, but attribute circles.

  

Exercises

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1) in Section 1.2 Sets: A Problem Solving Tools, pp. 20 - 21, Ex. 21, 25, 26, 28, 38, 67, 68, 74

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2) in Section 1.3: Set Operations, pp. 28 - 30, Ex. 2, 3, 18, 19, 24, 25, 39, 46, 47, 48, 50, 63, 64, 65, 66, 67

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3) in Section 1.4: Venn diagrams, pp. 36-37, Ex. 3, 4, 5, 9, 10, 36, 47, 48, 49, 50

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4) in Section 1.5: Number of Elements, pp. 45-47, Ex. 3, 8, 11, 17, 27, 28

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5) Using the Figure 4 on the Limitations page, what would be: a) A B C' D b) ( A B C)'

Web Resources

The Shodor Foundation (http://www.shodor.org/) is a nonprofit research and education organization dedicated to the advancement of science and math education, specifically through the use of modeling and simulation technologies. Included on this site are instructional resources and software ready to be used in the classroom. The site has Project Interactivate with a section on Venn Diagrams with Teacher and Student Resources such as: Sets and the Venn Diagram (http://www.shodor.org/interactivate/lessons/vd1.html) Venn Diagrams Discussion (http://www.shodor.org/interactivate/discussions/vdiags.html) a worksheet (http://www.shodor.org/interactivate/activities/vdiagram/worksheet.html) Exploration Questions (http://www.shodor.org/interactivate/activities/vdiagram/worksheet.html) Application of Venn diagrams and searching from the Colorado State University Librairies http://manta.colostate.edu/howto/others/venn.html A pc software for Venn diagram software from the University of Arizona http://archives.math.utk.edu/software/msdos/discrete.math/venn/.html A Venn Diagram - self-test (http://math.uww.edu/faculty/mcfarlat/143venn.htm) Bello book site on Venn Diagrams http://college.hmco.com/mathematics/bello/top_con_mat/student/web01.html#web01 Venn diagrams in business http://www.vendiagram.com Who was Georg Cantor? http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html Who was John Venn? http://sue.csc.uvic.ca/~cos/venn/VennJohnEJC.html

 

  

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