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Second/Data Graphing

Completing Venn Diagrams: 3 Sets

Use logic to find missing values in complex 3-set Venn diagrams.
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Practice Questions

  1. There are 30 students who like Pizza (Total). How many students like ONLY Pizza?
    Show answer

    (A) 15

  2. There are 20 students who like Red (Total). How many students like ALL THREE colors?
    Show answer

    (A) 3

  3. How many students like Math in TOTAL?
    Show answer

    (B) 25

  4. There are 40 students who like Cats (Total). How many like Cats AND Dogs but NOT Birds?
    Show answer

    (A) 10

  5. There are 50 students in the class. Everyone plays at least one sport. How many play ONLY Basketball?
    Show answer

    (A) 10

Quick Tip
Look at the 'Total' for the circle and subtract the known parts to find the missing piece.
Teacher Resources
Teaching Notes

Ensure students understand that the 'Total' for a circle is the sum of its 4 parts.

Vocabulary
Sum: The result of adding numbers.
Difference: The result of subtraction.
Common Mistakes
  • Forgetting the center piece when subtracting
  • Not subtracting triple intersection from double.
  • Incorrectly calculating 'only' regions.
  • Adding all numbers without considering overlaps.
  • Misinterpreting problem phrasing.
Differentiation
SupportList the 4 parts of the circle separately.
ChallengeCreate a problem where two numbers are missing.
Discussion Questions
  • How many parts does a 3-circle Venn diagram have?
  • What does the intersection of three circles represent?
  • How do you find the number that belongs only to one set?
  • Why is subtracting overlaps crucial in Venn diagrams?
  • Can Venn diagrams represent more than three sets?
Extension Activities
  • Use real class data.
Parent Tip

Give your child 15 blocks. Ask them to divide them into 3 groups. Then ask how many are in the largest group.

Learning Path
Skill Cluster

Data Analysis & Logical Reasoning

Estimated Time

20 minutes

Skills Practiced
Advanced venn logic