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Year 7 · Maths · Primes, factors and probability · Lesson 3

Venn diagrams

Sort numbers and data into Venn diagrams, read regions such as both, only and neither, and solve counting problems.

Whiteboard video lesson: Venn diagrams

23-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand sets and the universal set
  • Complete a Venn diagram
  • Read a Venn diagram
  • Use the overlap correctly
  • Solve Venn diagram problems

The method

  1. List each set.
  2. Put the overlap (in both) first.
  3. Then the 'only' parts.
  4. Anything else goes outside the circles.

Key words: Venn diagram, set, universal set, overlap, intersection.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Numbers 1 to 10. O = odd numbers. P = prime numbers. Complete the Venn diagram.

  1. Step 1: O: 1, 3, 5, 7, 9
  2. Step 2: P: 2, 3, 5, 7
  3. Step 3: In both: 3, 5, 7
  4. Step 4: Fill in each region.

Answer: See the Venn diagram

Question 2

Use the Venn diagram. How many numbers are in both O and P?

  1. Step 1: Look at the diagram
  2. Step 2: In both O and P: 3, 5, 7
  3. Step 3: Count: 3

Answer: 3

Question 3

Use the Venn diagram. How many numbers are in neither O nor P?

  1. Step 1: Look at the diagram
  2. Step 2: In neither O nor P: 4, 6, 8, 10
  3. Step 3: Count: 4

Answer: 4