Mathematical Models: Black Holes
A colorful graphic depicting a black hole

Featured Lesson(s)


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Essential Question

How can mathematics be used to investigate the physical properties and nature of black holes?


Black holes are very popular and mysterious subjects among students learning about astronomy. Students have endless questions about these exciting and exotic objects. Amazingly enough, many aspects of black holes can be understood by using algebra and pre-algebra mathematical skills. Black Hole Math problems can be used as classroom challenge activities, assessments or enrichment activities. Black Hole Math problems investigate black hole science and mathematics concepts, including parts of a simple black hole and calculating gravitational potential energy. Each word problem has background information providing insight into black holes. One-page answer keys accompany the one-page assignments.

Additional Resources

  Classroom Resources:


  • Videos for Students:
    • Black Hole Animation 1: Animation of a star being consumed by a black hole.
    • Black Hole Animation 2: Matter streaming into a black hole from a star; gas jets being emitted.
    • Detecting Black Holes: An explanation of how we know black holes exist -- gravitational lensing and optical effects.
    • The Environment Around a Black Hole: Accretion disks and energy emissions -- what they tell us about a black hole.
    • Black Hole Animation 3: Animation of a star being destroyed by black hole tidal forces and ultimately being consumed by the black hole.
    • Misconception 1: Black holes "suck" matter into themselves. Wrong.
    • Misconception 2: Black holes are invisible so scientists can never see them. Right, but there is more to the concept.
    • Misconception 3: Once inside a black hole, you can never get out. In theory, it depends.
    • Misconception 4: The Large Hadron Collider will create black holes that will destroy Earth. No.
    • Misconception 5: A black hole will destroy Earth in 2012. We're not clairvoyant, but we predict not.


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  Extension Activities:

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Lesson Information

Subject(s) Covered:

 • Mathematics • Physical science

Topic(s) Covered:

 • Mathematics: Algebra -- Understand patterns, relations, and functions; also problem solving, scientific notation, unit conversion • Physical science: Forces and motion

Activity Type:

 Student investigation

Grade Level:


Instructional Objective:

 Mathematics: Students will be able to calculate the radius and mass of black holes given observable quantities. Physical science: Students will be able to explain the basic concept of a black hole and dispel common black hole myths.

Time to Complete the Activity:

 Two 45 minute classes

  Materials Needed:

  • Scientific calculator

   National Content Standards:

  • 21st Century Outcome: Learning and Innovation Skills
  • 21st Century Element: Critical Thinking and Problem Solving
  • 21st Century Skill: Solve Problems
  • Math Standard: Algebra -- Understand patterns, relations and functions
  • Science Standard: Physical science -- Forces and motion