# Week 3 Assignment 2 Venn Diagram Paper

Venn Diagram Paper

Tariek McLeish

MTH/156

University of Phoenix

Jennifer Durost

December 21, 2014

The Venn Diagrams was invented by Jon Venn as a way of visualizing the relationship between different groups (Purplemath, 2014). Venn Diagrams are an important learning tactic that helps students to learn how to graphically establish and compare concepts. They are often used in English lessons, and its effect is often undermined in the mathematics classroom. They are extremely valuable for problem-solving and finding probability of events. Hence, once students are able to properly locate correct information, they will become more able to answer mathematical questions. Therefore, making it useful to students as they are given a way to link ideas and numerical data into rational visual picture (Cain, n.d.). Empirically, once students develop the ability to properly organize information in a Venn diagram; they are better able to recall information as well as locate important data. Venn Diagrams can also be useful in the math classroom by helping students to organize mathematical information in word problems; as well as help them to understand how to find probabilities. The most popular use of the Venn Diagrams in mathematics often presented by drawing two or three circles that overlap. Students are then able to fill out appropriate information from a word problem and calculate the numbers that go in each open spot (Cain, n.d.). In the world of mathematic the term "a group of things" is "a set"; Venn diagrams can be used in this instance to demonstrate both set and logical relationships. Hence, when drawing a Venn diagram, we first draw a rectangle called a "universe". The rectangle or “universe” represents the present or everything that is been dealt with presently. For instance we had a list of things: turkeys, swans, geese, ducks, penguins, seal, walruses, dolphins, rabbits, lizards and manatees. First let’s call our universe "Animals", secondly let's say we want to classify the things that are birds or that are sea mammals. Therefore, we would draw circles to display our classifications and then fill in, or "populate", the diagram. Hence turkeys, swans, geese, ducks penguins in our bird circle. Next circle we would list all our sea animals penguins, seals, walruses, dolphins and manatees. Rabbits and lizards are both animals but neither of them are birds nor sea mammals. However, they are animals hence they fit inside the universe, but outside the circles (Purplemath, 2014). Empirically, we have now populate the Venn diagram; noticing that "penguins" are listed in both circles. The purpose of Venn diagrams is to show the relationship of set members by overlapping these circles. Hence, overlap the circle and only write the word "penguins" in the overlap. This overlap show the connects between the two sets, as students discover the similarities between birds and sea mammals; as well as learn various types of birds, various types of sea mammal, that a penguin is both a bird and sea mammal and all are animals (Purplemath, 2014). Venn diagrams typically has two general applications; explaining set notation and doing a class of word problems. Worded problems and Venn diagrams are very popular with elementary students. Venn diagram word problems generally gives the student two or three classifications and a bunch of numbers. Therefore, they are required to use the provided information to populate the diagram and figure out the remaining information. For instance; Out of forty students, 13 are taking English Composition and 28 are taking Chemistry. If four students are in both classes, how many students are in neither class? How many are in either class? (Purplemath, 2014) In this problem students are given two classifications in this universe: English students and Chemistry students. First they'll draw their universe for the forty students, with two overlapping circles labelled with the...

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