Start Screen

1
Start Screen

• If this is your first time using this program,
  click the first place ribbon.

Otherwise, click a box below to go to a certain
part of the investigation. If you choose the
wrong one, click on the house icon to go
back to this page.
Go to part 2
Go to part 3
Go to part 4
2
Section 7.3
Counting With Pictures
Click on Sherlock Holmes to begin the
investigation!
3
Directions
If you dont know a word or symbol that is
highlighted, click on it to see a definition!
Set
To continue the investigation, click on Sherlock
Holmes.
Who is Sherlock Holmes???
Click Me!
Dont forget! Click on the house to start over!
4

• In a class of 30 students, 17 watch
  MTV and 12 play video games.
• 5 students watch MTV and play video
  games. See if you can answer the following 4
  questions

1. How many students watch MTV but do not play
video games?
24
12
30
17
7
6
5
Almost

• Later I will help you learn to use a tool that
  will help you investigate these kinds of
  questions. Try the next question

6

• In a class of 30 students, 17 watch
  MTV and 12 play video games.
• 5 students watch MTV and play video
  games.

2. How many students play video games but do not
watch MTV?
24
12
30
17
7
6
7
Almost

• Later I will help you learn to use a tool that
  will help you investigate these kinds of
  questions. Try the next question

8

• In a class of 30 students, 17 watch
  MTV and 12 play video games.
• 5 students watch MTV and play video
  games.

3. How many students watch MTV or play video
games (possibly both)?
24
12
30
17
7
6
9
Almost

• Later I will help you learn to use a tool that
  will help you investigate these kinds of
  questions. Try the next question

10

• In a class of 30 students, 17 watch
  MTV and 12 play video games.
• 5 students watch MTV and play video
  games.

4. How many students neither watch MTV nor play
video games?
24
12
30
17
7
6
11
Almost

12

• Lets learn a way to investigate these types of
  questions that people in the business world use.

13
Notation

• First some set notation symbols.
• Assume that A is the set of even natural numbers
  between 1 and 10 inclusive.
• There are 5 elements in set A
• A 2,4,6,8,10
• Another way to say this is (A) 5

14
Think of it as saying
(A) 5 the number
of elements in set A equals 5
15
Let U be the set of all students in the class.
We know that (U) 30.
Let M be the set of students who watch MTV.
We know that (M) 17.
Let G be the set of students who play video games.
We know that (G) 12.
16
Let U be the set of all students in the class.
We know that (U) 30.
Let M be the set of students who watch MTV.
We know that (M) 17.
Let G be the set of students who play video games.
We know that (G) 12.
M
G
17
We know that (U) 30, (M) 17, and (G) 12.
Think of ALL the students in the class being
represented by points inside the rectangle U.
U
M
G
18
We know that (U) 30, (M) 17, and (G) 12.
Inside circle M are the 17 students who watch
MTV.
U
M
G
19
We know that (U) 30, (M) 17, and (G) 12.
Inside the circle M are the 17 students who watch
MTV.
Inside circle G are the 12 students who play
video games.
U
M
G
20
We know that (U) 30, (M) 17, and (G) 12.
Inside the circle M are the 17 students who watch
MTV. Inside the circle G are the 12 students who
play video games.
The 5 students who watch MTV and play video games
are in the region inside both circles which is
colored green.
U
M
G
21
We know that (U) 30, (M) 17, and (G) 12.
The green region (5 students) is denoted by M
G, which is read, M intersect G or the
intersection of M and G.
U
M
G
22
We know that (U) 30, (M) 17, and (G) 12.
The green region (5 students) is denoted by M
G, which is read, M intersect G or the
intersection of M and G.
Moreover, (M G) 5
U
M
G
5
23
We know that (U) 30, (M) 17, and (G) 12.
Lets have a quick review, how do you say the
following
A) the intersection of M and G
B) M intersect G
C) M and G together
M G
D) both choices A B
U
M
G
5
24
Great Job! A mnemonic device for remembering
that the symbol means intersection, is
thinking that the symbol looks like the
letter n for intersection!
25
We know that (U) 30, (M) 17, and (G) 12.
And remember that the green region has 5 students
in it, who watch MTV and play video games, which
is (M G) 5
So if circle M has 17 in all, but 5 of them are
in the intersection area, how many are in just
the blue area?
27
12
22
17
U
M
G
5
26
We know that (U) 30, (M) 17, and (G) 12.
We also know that (M G) 5
What about the yellow area? If circle G has 12
total, how many are in just the yellow area?
17
24
12
7
U
M
G
12
5
27
So now we have all three areas filled in!
Lets try those questions from the start of the
investigation one more time...
U
M
G
12
7
5
28
How many students watch MTV only, no video games?

5
12
17
24
6
7
U
M
G
12
7
5
29
How many students play video games only, no MTV?
5
12
17
24
6
7
U
M
G
12
7
5
30
How many students play video games or watch MTV
(possibly both)?
5
12
17
24
6
7
U
M
G
12
7
5
31
Our three regions add to 24. The 24 are all the
students who play MTV or play video games (or
both!)
12

5

7

24
U
M
G
12
7
5
32
We have a symbol in math that describes this
joining of regions. It is called union and looks
like the letter U. So M G is the union of sets
M and G. Think U for Union!
U
M
G
12
7
5
33
We know that (U) 30, (M) 17, and (G) 12.
We also know that (M G) 5 and (M G)
24
What about the white area inside the box? Use the
information at the top of this page to come up
with a guessthen click on Sherlock to try the
question on the next page
U
M
G
12
7
5
34
How many students neither play video games
nor watch MTV ?
5
12
17
24
6
7
U
M
G
12
7
5
35
Right! There will be 6 students who dont play
video games or watch MTV, but are still part of
the class, which is set U, with 30 students
total. Those 6 go in the white space.
U
6
M
G
12
7
5
36
Now click on the link below to play a game online
that will test how well you understand Venn
Diagrams.
You may see some symbols you dont know, and you
may see more than 1 circle!
This will be an exciting challenge! You can play
this till its time to go!
http//nlvm.usu.edu/en/nav/frames_asid_153_g_4_t_1
.html?openinstructions
37

• Almost! Lets look at the information from
  the previous screen again.

The 5 students in this green region is denoted M
G, which is read, M intersect G or the
intersection of M and G.
Moreover, (M G) 5
GO BACK
38

• Almost! Lets take another look

U
Circle M, the blue and green area, has 17.
M
G
Now subtract out the 5 students who are already
in there, inside the intersection area.
5
Not including the 5 in the green area, how many
are in just the blue area?
GO BACK
39

• Almost! Lets take another look

U
Circle G, the yellow and green area, has 12.
M
G
Now subtract out the 5 students who are already
in there, inside the intersection area.
12
5
Not including the 5 in the green area, how many
are in just the yellow area?
GO BACK
40

• Almost! Lets take another look

U
(U) 30, (M) 17 (G) 12.
M
G
12
7
5
(M G) 5
The whole class has 30 students, so how many are
not represented in the diagram so far?
GO BACK
41

• Almost! Lets take another look

U
Remember Circle M has the students who watch
MTV Circle G has the students who play video
games The overlapping region has the students who
play video games and watch MTV.
M
G
12
7
5
GO BACK
42
Set

• A collection of objects.
• Example The set of all even natural numbers
  less than 10 is 2, 4, 6, 8

GO BACK
43
Mnemonic Device

• A tool for remembering information easily, it can
  be a rhyme, song picture, or acronym.
• Example A mnemonic device for remembering to
  spell dessert with two ss, is to think of the
  dessert Strawberry Shortcake

GO BACK
44
Remember

• U the set of all students in the class
• M the set of students who watch MTV
• G the set of students who watch MTV

GO BACK
45
Remember

• means intersection,
• or the overlapping of two sets.

GO BACK
46
Remember

• means union,
• or the joining together of two sets.

GO BACK
47
Sherlock Holmes Info Page
In a sea of fictional detectives that includes
the greats, the near-greats, and a great many
wannabes, the lighthouse that shines above them
all is, of course, Sherlock Holmes.  Created by
Sir Arthur Conan Doyle and presented through the
narration of the fictional Dr. Watson, Holmes is
the most brilliant detective  ever.   His powers
of observation seem supernatural until he utters
the famous phrase, Elementary, my dear Watson,
and proceeds to enumerate the logical steps
that have brought him to a prescient
conclusion.   The most innocuous detail can lead
Holmes to profound revelations. 
GO BACK
From the website http//www.crimelibrary.com/gangs
ters_outlaws/cops_others/sherlock_holmes/1.html
48
Sweet! You are correct!
Click on Peter!
49
Sweet! You are correct!
Click on Peter!
50
Sweet! You are correct!
Click on Peter!
51
Sweet! You are correct!
Click on Peter!
52
Sweet! You are correct!
Click on Peter!
53
Sweet! You are correct!
Click on Peter!
54
Sweet! You are correct!
Click on Peter!
55
Sweet! You are correct!
Click on Peter!
56
Sweet! You are correct!
Click on Peter!
57
Sweet! You are correct!
Click on Peter!
58
Sweet! You are correct!
Click on Peter!
59
There is another way to refer to the students who
JUST watch MTV or JUST play video games. We use
subtraction!
The blue area, MTV only students, is the same as
M-G, because all of circle G, the green and
yellow areas, gets subtracted out.
Same thing with the yellow area, video game only
students. It is the same as G-M.
U
M
G
12
7
5