Use Venn diagrams to solve problems

Key Notes :

🔵 What is a Venn Diagram?

  • A Venn Diagram is a picture with circles that show how groups (sets) are related.
  • The circles may overlap to show things that belong to more than one group.
    🟣🔵⚪

🟠 Parts of a Venn Diagram

  • Circle A ➝ First group
  • Circle B ➝ Second group
  • Overlap area ➝ Items that belong to both groups
  • Outside area ➝ Items that belong to none of the groups

✨ Example:

  • 👟 Sports players
  • 🎨 Artists
  • People who do both 👟🎨 go in the overlap!

🟢 Why Do We Use Venn Diagrams?

To compare and contrast two or more groups

To organize information

To spot similarities and differences easily

To answer questions like:

  • “How many like BOTH?”
  • “How many like ONLY one?”
  • “How many like NONE?”

📊🧠

🔴 How to Fill a Venn Diagram

Follow these steps:
1️⃣ Start with the overlap (both sets)
2️⃣ Add items that belong to only Set A
3️⃣ Add items that belong to only Set B
4️⃣ Add items that belong to neither set
5️⃣ Finally, answer the problem using your diagram

📝➡️⭕⭕➡️✔️

🟣 Example Question

20 students were asked:

  • 12 like 🍎 apples
  • 10 like 🍌 bananas
  • 5 like both

✨ Fill the Venn Diagram:

  • Put 5 in the overlap
  • Only apples: 12 − 5 = 7
  • Only bananas: 10 − 5 = 5
  • Total who like at least one fruit: 7 + 5 + 5 = 17
  • None: 20 − 17 = 3

🎉 Students learn how to compare and solve!

💡 Tips for Success

  • Always fill the middle overlap first!
  • Double-check totals by adding all parts
  • Use Venn diagrams to solve word problems easily 💪📘

🌈 Real-Life Uses

  • Sorting animals 🐶🐱
  • Comparing shapes 🔺🟦
  • Survey results in class 🧃🍪
  • Finding common hobbies 🎵⚽

Learn with an example

1) 4 of the students in Charlotte’s class have a jacket with a hood and 6 have a jacket with buttons. 3 students have a jacket with both a hood and buttons.

How many students have a jacket with buttons but not a hood?

____ students

Make a Venn diagram to solve the problem.

3 students have a jacket with both a hood and buttons. Put 3 dots in the area that is in both circles.

Now add dots to the other two areas until there are 4 dots in the “I have a jacket with a hood” circle and 6 dots in the “I have a jacket with buttons” circle.

Count the dots that are in the “I have a jacket with buttons” circle but are not in the “I have a jacket with a hood” circle. There are 3 dots.

3 students have a jacket with buttons but not a hood.

2) 4 of the children in Carrie’s class have an orange marble. 3 children have a red marble, and 2 children have both an orange marble and a red marble.

How many children have a red marble but not an orange marble?

____ children

Make a Venn diagram to solve the problem.

2 children have both an orange marble and a red marble. Put 2 dots in the area that is in both circles.

Now add dots to the other two areas until there are 4 dots in the “I have an orange marble” circle and 3 dots in the “I have a red marble” circle.

Count the dots that are in the “I have a red marble” circle but are not in the “I have an orange marble” circle. There is 1 dot.

1 child has a red marble but not an orange marble.

3) 7 of the people in Levi’s flat building like leopards and 7 like jaguars. 5 people like both leopards and jaguars.

How many people like leopards or jaguars or both?

_____ people

Make a Venn diagram to solve the problem.

5 people like both leopards and jaguars. Put 5 dots in the area that is in both circles.

Now add dots to the other two areas until there are 7 dots in the “I like leopards” circle and 7 dots in the “I like jaguars” circle.

Count the total number of dots in the diagram. There are 9 dots.

9 people like leopards or jaguars or both.

Let’s practice!🖊️