Karen served fried chicken and hot dogs at her birthday party.
This table shows what her friends ate.
The table is nice. But is there a better way to show which friends ate both fried chicken and hot dogs?
Yes. We can make a Venn diagram.
A Venn diagram is a tool that uses circles to show how groups or sets of numbers are alike and different. The circles overlap with each other.
Take a look at this.
Let's fill in this Venn diagram with what we know about Karen's party guests.
Venn diagrams makes it easy to see how two sets, or lists, overlap.
What did Emma eat?
Yes! Emma ate fried chicken only.
What did Kevin eat?
Very good! Kevin ate hot dog only.
What did Max eat?
You got it! He ate both fried chicken and hot dogs.
Who else ate both fried chicken and hot dog?
Correct. Lia, Kyle, and Clara all ate both fried chicken and hot dog.
Great job reading a Venn diagram.
Let's create a Venn diagram together.
There are 4 triangles. There are 4 orange objects. 1 object is both a triangle and orange.
First, we create a circle for triangles.
Then, we create a circle for orange objects.
Let some parts of the circles overlap with each other.
Now let's fill them in with shapes.
We draw an orange triangle in the area where the circles overlap.
Let's add triangles to the "Triangle" area until there are 4 triangles in it.
Add orange shapes in the "Orange" area until there are 4 shapes in it.
Our Venn diagram is complete.
How many shapes are triangles but not orange?
Yes. There are 3. Count the shapes in the triangle circle that are not in the orange circle.
How many shapes are orange but not triangles?
Correct! There are 3.
How many are triangles and orange?
Very good! There's only 1.
Tip: The word "and" means that we look at the area where the two circles overlap.
Of the students in Amy's class, 9 students can play soccer and 5 can play basketball. 2 can play both soccer and basketball. How many can play soccer or basketball or both?
Let's start by drawing two circles.
Then we draw dots in the area where the two circles overlap.
How many dots do we draw?
There are 2 people who can play soccer and basketball, so we draw 2 dots.
Let's add the 7 more dots in the "Can Play Soccer" area, until there are 9 dots, since we know that 9 people in total can play soccer.
Then add 3 dots to the "Can Play Basketball" area, until there are 5 dots.
The Venn diagram is complete.
So, how many can play soccer or basketball or both?
When reading Venn diagrams, the word "or" tells us to find the number in either circle, not just the overlap.
This means that we count all the dots in the diagram.
So we see there are 12 students that can play either sport. ✅
Great job. 👏 Now, complete the practice to get even better at reading Venn diagrams.