Venn Diagrams Math 156
Venn Diagrams Paper
Math 156
Jacqueline Burrell
May 13, 2012
Evan Schwartz, instructor
How Venn Diagrams Can Help Students in Math
Venn diagrams are used in math to visually assist students when grouping real sets or implied ideas. The diagrams were invented by John Venn and are his only known accomplishments in the science of mathematical logic (Stapel, 2012).
The diagram begins with all related information and is named the universal set. In this set all the known information pertaining to the problem or ideas are grouped. Within this group we have at least two subset or classifications. Information is placed in the correlating group. This information may overlap creating an intersection of the groups. This intersection shows the similarities of the groups and provides a basis for further conclusions based on the grouping of the diagram (Billstein, Libeskind, & Lott, 2010).
Recognizing Shapes and Colors
Group A contains five (5) rectangles and three (3) triangles. All items in group A are red. Group B contains seven (7) triangles; four (4) are green. The other triangles are red. Draw a Venn diagram illustrating these conditions, and then answer the following questions by looking at the diagram (Burrell, 2012).
(Microsoft Office, 2012) 1. How many triangles are included in both groups A and B? 2. How many objects are included in group A and not in group B? 3. Write an equation to illustrate the union of A and B.
A group discussion following the exercise can include naming and identifying objects not in the diagram. An example would be hearts and circles (Burrell, 2012).
Comparing ideas
Venn diagrams are useful in graphically organizing ideas and understanding logical probabilities. Students are asked how many have eaten crawfish and how many have eaten boudin. Both are a local favorite dish within my district. Six (6) students have eaten crawfish. I find eight (8) students have eaten boudin. Three (3) of the
Math 156
Jacqueline Burrell
May 13, 2012
Evan Schwartz, instructor
How Venn Diagrams Can Help Students in Math
Venn diagrams are used in math to visually assist students when grouping real sets or implied ideas. The diagrams were invented by John Venn and are his only known accomplishments in the science of mathematical logic (Stapel, 2012).
The diagram begins with all related information and is named the universal set. In this set all the known information pertaining to the problem or ideas are grouped. Within this group we have at least two subset or classifications. Information is placed in the correlating group. This information may overlap creating an intersection of the groups. This intersection shows the similarities of the groups and provides a basis for further conclusions based on the grouping of the diagram (Billstein, Libeskind, & Lott, 2010).
Recognizing Shapes and Colors
Group A contains five (5) rectangles and three (3) triangles. All items in group A are red. Group B contains seven (7) triangles; four (4) are green. The other triangles are red. Draw a Venn diagram illustrating these conditions, and then answer the following questions by looking at the diagram (Burrell, 2012).
(Microsoft Office, 2012) 1. How many triangles are included in both groups A and B? 2. How many objects are included in group A and not in group B? 3. Write an equation to illustrate the union of A and B.
A group discussion following the exercise can include naming and identifying objects not in the diagram. An example would be hearts and circles (Burrell, 2012).
Comparing ideas
Venn diagrams are useful in graphically organizing ideas and understanding logical probabilities. Students are asked how many have eaten crawfish and how many have eaten boudin. Both are a local favorite dish within my district. Six (6) students have eaten crawfish. I find eight (8) students have eaten boudin. Three (3) of the
References: Billstein, R., Libeskind, S., & Lott, J. W. (2010). A problem solving approach to mathematics for elementary school teachers (10th ed.). Boston, MA: Addison-Wesley. Burrell, Jacqueline (2012) National Council of Teachers of Mathematics. (2012). Retrieved from http://www.ntcm.org/ Stapel, Elizabeth. “Venn Diagram Word Problems.” Purplemath. Available from http://www.purplemath.com/module/venndiag4.htm. Accessed 10 May 2012.