1. SORTING DATA
VENN DIAGRAMS

2. A VENN DIAGRAM IS USED TO SORT THINGS
Even numbers
Multiples of 3
These numbers needed to be sorted into multiples of 3 and even numbers 3 5 7 10 13 15 18 24 25 27 30 36 40 50

3. A VENN DIAGRAM IS USED TO SORT THINGS
Even numbers
Multiples of 3
Multiples of 3 go inside this circle 3 5 7 10 13 15 18 24 25 27 30 36 40 50

4. A VENN DIAGRAM IS USED TO SORT THINGS
Even numbers
Multiples of 3
Even numbers go inside this circle 3 5 7 10 13 15 18 24 25 27 30 36 40 50

5. Numbers that are multiples of 3 and even numbers go here...
A VENN DIAGRAM IS USED TO SORT THINGS
Even numbers
Multiples of 3
Numbers that are multiples of 3 and even numbers go here...
...because they belong to both circles. 3 5 7 10 13 15 18 24 25 27 30 36 40 50

6. Numbers that are not multiples of 3 and not even, stay on the outside.
A VENN DIAGRAM IS USED TO SORT THINGS
Even numbers
Multiples of 3
Numbers that are not multiples of 3 and not even, stay on the outside. 3 5 7 10 13 15 18 24 25 27 30 36 40 50

7. A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 5
Multiples of 3
We need to sort these numbers into either multiples of 3 or multiples of 5

8. Multiples of 3 go inside this circle
A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 5
Multiples of 3
Multiples of 3 go inside this circle

9. Multiples of 5 go inside this circle
A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 5
Multiples of 3
Multiples of 5 go inside this circle

10. A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 5
Multiples of 3
NUMBERS THAT ARE MULTIPLES OF 3 AND 5 GO HERE
SO THEY ARE IN BOTH CIRCLES

11. A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 5
Multiples of 3 27 3 25 30 17 40 33 15 5 36 45 55 60 18 2
100 23 12
NUMBERS THAT ARE NOT MULTIPLES OF 3 OR 5 STAY OUTSIDE THE CIRCLES

12. multiples of 3&10 multiples of 6&10 multiples of 3&6 multiples
A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 3
Multiples of 6
Which numbers go in each space?
multiples
of 3&10
multiples
of 6&10
multiples
of 3&6
multiples
of 3,6&10
multiples
of 10
multiples
of 6
multiples
of 3
Multiples of 10 3 5 7 10 13 15 18 24 25 27 30 36 40 50

13. No number here is a multiple of 6, without being a multiple of 3 too!
A VENN DIAGRAM IS USED TO SORT THINGS
Multiples of 3
Multiples of 6
The numbers remaining don’t belong in any circle, so stay on the outside.
Multiples of 10
No number here is a multiple of 6, without being a multiple of 3 too! 3 5 7 10 13 15 18 24 25 27 30 36 40 50

14. We will use Venn Diagrams for a more advanced purpose…
Probability
Remember, Probability of an event occurring =

15. Ms. Avery conducted a survey of her students
Ms. Avery conducted a survey of her students. She asked her students what flavor ice cream they like. 12 students like chocolate; 7 like vanilla; 2 like both; 24 students surveyed.
Students of Ms. Avery
Chocolate
Vanilla

16. Ms. Avery conducted a survey of her students
Ms. Avery conducted a survey of her students. She asked her students what flavor ice cream they like. 12 students like chocolate; 7 like vanilla; 2 like both; 24 students surveyed.
Students of Ms. Avery
Chocolate
Vanilla 2

17. Ms. Avery conducted a survey of her students
Ms. Avery conducted a survey of her students. She asked her students what flavor ice cream they like. 12 students like chocolate; 7 like vanilla; 2 like both; 24 students surveyed.
Students of Ms. Avery
Chocolate
Vanilla 10 2

18. Ms. Avery conducted a survey of her students
Ms. Avery conducted a survey of her students. She asked her students what flavor ice cream they like. 12 students like chocolate; 7 like vanilla; 2 like both; 24 students surveyed.
Students of Ms. Avery
Chocolate
Vanilla 10 2 5

19. Ms. Avery conducted a survey of her students
Ms. Avery conducted a survey of her students. She asked her students what flavor ice cream they like. 12 students like chocolate; 7 like vanilla; 2 like both; 24 students surveyed.
Students of Ms. Avery
Chocolate
Vanilla 10 2 5 7

20. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

21. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

22. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

23. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

24. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

25. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

26. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.)
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

27. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)

28. Finding Probability Students of Ms. Avery Chocolate Vanilla 10 2 5 7
P(Chocolate) 2) P(Vanilla)
P(Chocolate Only) 4) P(Vanilla Only)
P(Chocolate & Vanilla) 6) P(Neither Choc. nor Van.
7) P(Chocolate. l Vanilla) 8) P(Vanilla l Chocolate)