Draw a Venn Diagram

1
Draw a Venn Diagram

• Problem Solving Strategy

2
Draw a Venn Diagram

• Another way to visually organize information is
  to create a Venn diagram.
• Venn diagrams are excellent ways to sort data
  into categories that have overlapping
  characteristics. They clearly show relationships
  between categories.

3
Draw a Venn Diagram

• When creating a Venn diagram, you can use any
  shapes to house your information like circles,
  rectangles, triangles, loops, or anything else
  that clearly relates the connections between
  data.
• When a category is completely inside another it
  is a subset of the larger category like the city
  of Bloomingtons circle would be completely in a
  circle marked Illinois since all of Bloomington
  is in Illinois.

4
Draw a Venn Diagram

• If circles intersect, then the categories have
  something they share. For instance, if one
  circle is the basketball team and one is the
  football team, students who are on both would be
  placed in the intersected area and students only
  on the basketball team would be it its circle
  while students only on the football team would be
  in the football circle.

5
Draw a Venn Diagram

• When circles dont intersect, then it shows that
  categories dont share any of the characteristics
  being looked at. For instance, geographically,
  Illinois and Florida dont share any land and
  would be represented by two circles that dont
  touch each other but they both could be placed in
  a bigger circle called the United States (set of
  all the states). Illinois and Florida would be
  considered subsets of the set of all the states.

6
Draw a Venn Diagram

• You cant use Venn diagrams on many problems but
  when youre looking for relationships between
  data, they are a very effective tool and often
  can shed some new information when used in
  combination with another problem solving strategy.

7
How many students?

• In a poll of 46 students, 23 liked rap music,
  24 liked rock music, and 19 liked country music.
  Of all the students, 12 liked rap and country, 13
  liked rap and rock, and 14 liked country and
  rock. Of those students, 9 liked all three types
  of music. How many students did not like any of
  these types?

8
Draw shapes for each of the categories
Notice that the shapes should overlap in this
problem!
Problem In a poll of 46 students, 23 liked rap
music, 24 liked rock music, and 19 liked country
music. Of all the students, 12 liked rap and
country, 13 liked rap and rock, and 14 liked
country and rock. Of those students, 9 liked all
three types of music. How many students did not
like any of these types?
9
Fill loops from the inside out!
Problem In a poll of 46 students, 23 liked rap
music (9347), 24 liked rock music (9456),
and 19 liked country music (9352) . Of all
the students, 12 liked rap and country (93),
13 liked rap and rock (94), and 14 liked
country and rock (95). Of those students, 9
liked all three types of music. How many students
did not like any of these types?
4
7
6
9
3
5
2
10
Fill in the region outside the loops
Problem In a poll of 46 students, 23 liked rap
music, 24 liked rock music, and 19 liked country
music. Of all the students, 12 liked rap and
country, 13 liked rap and rock, and 14 liked
country and rock. Of those students, 9 liked
all three types of music. How many students did
not like any of these types?
4
7
6
9
3
5
2
10
46 (7463952)
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Check the calculations
7 4 6 3 9 5 2 10 ?
4
7
6
9
46 It Works!
3
5
2
10
12
Strategy Draw a Venn Diagram

• Draw overlapping loops for intersecting sets.
• Fill regions from the inside out.
• Subtract carefully.
• After regions are filled, see what number answers
  the question.
• Check the calculations.

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Now its your turn

• Open your problem solving book and go to the
  section on Draw a Venn Diagram (pages 29-30).
• Print off a problem solving sheet and do a
  complete solution to a problem from this
  sectiondo one and submit it or do more for
  extra fun. (Children Dancers, Music Survey
  and/or The Flu and You)
• Email your complete solution, with your steps
  clearly shown to NCAMath_at_district87.org or put
  them in Nancy Powells mail box!
• Have fun and Problem Solve!