Teaching Pack – Venn diagrams
Lesson 1 – Interpreting Venn diagrams
Cambridge IGCSE™
Mathematics 0580
Version 1.0
Lesson objectives
• Understand how to use Venn diagrams to classify
objects and sort data.
• Interpret Venn diagrams.
Try this!
Where would you put each shape? Why?
a)
b)
c)
Sorting objects and data
Sort these people into those wearing a tie and those with black hair.
Wearing a tie
Black hair
Notations
n The number of elements in one set.
E Universal Set is the set that contains everything we started
with.
E
Wearing a Tie
Black Hair
n (wearing a tie) = 4
Universal set
Rather than drawing the pictures, we can just write the number of people
in each section as follows:
Wearing a Tie
Black Hair
E
Wearing a
Tie
2
Black Hair
2
3
2
We can also say n(Wearing a Tie) = 2 + 2 = 4
n(Black Hair) = 2 + 3 = 5
Try this!
In a survey, 25 people were asked their age and if they owned an iPhone.
The results were put into a Venn diagram.
E
• How many people were under 18?
• How many people owned an
iPhone?
13
10
2
Under
18
5
8
Own an iPhone
7
• How many people did not own
an iPhone?
12
• How many under 18s owned an
iPhone?
5
• How can you describe the people
represented by 10?
Over 18 and does not own an iPhone.
Try this!
The village holds an annual Fun Run. Contestants are either classified as
under the age of 13 or adults. Every contestant must enter for either the 3
kilometre run or the 10 kilometre run. This information is shown in the Venn
diagram below:
E
10
•
•
23
7
50
•
•
Under
13
Entered for
10 km
How many people entered the fun
runs?
90
How many people entered the 10 km
run?
57
How many under 13s did the 10 km run?
7
How many adults did the 3 km run?
10
Try this!
A class of students were classified using the Venn diagram below.
E
6
10
Male
12
8
Left handed
12 males are left handed.
There are 8 females.
10 people are right handed.
There are 36 people in the class.
Try this!
The same class of 36 students were asked separately:
a) If they could swim
b) If they could ride a bike
25 said they could swim 18 said they could ride a bike, 4 said they could do
neither.
E
Can ride a bike
4
Is this possible?
14
11
7
Can swim