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Victor J. Donnay


6th, 7th, 8th, 9th, 10th, 11th, 12th


Science, Physics, Mathematics

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  • Videos, 4 minutes, 11 seconds, CC, Subtitles
  • Interactive Media
  • Articles and Websites
  • Assessments

Regional Focus


Is Our Climate Headed for a Mathematical Tipping Point?

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  • This animated video illustrates the concept of mathematical tipping points using billiards as an example. 
  • The video shows how the chaotic motion caused by slight changes to a billiards table is conceptually similar to how small changes in global temperatures can have massive climate impacts. 
Teaching Tips


  • The video uses animated diagrams to convey key concepts.
  • There are questions, additional resources, and discussion prompts that accompany the video.

Additional Prerequisites

  • Students over 13 years old can create a free account to save their answers and participate in discussion boards.
  • Teachers can create a free account to customize the lesson and view student work.
  • The video assumes students have a strong foundational understanding of geometry.
  • In the Dig Deeper section, the link to the Nature article summary and the link to the Bill Nye videos are broken.


  • In a math course, students could create their own mathematical models for how the billiard ball would move on a circular table from different starting points, as described in the video. The  Dig Deeper section includes multiple links to programs that can help students digitally explore these types of models.
  • In a science course, students could gather additional evidence to decide if or when they think we will reach a climate change tipping point. Students could then present their findings to the class.
  • Other resources about tipping points include this video by Grist, this video by Our Changing Climate, and this course by Climate Science.
Scientist Notes
The video spotlights the impact of human activities on the climate. CO2 levels have increased and the earth is gradually shifting to a tipping point in the coming years, more chaotic events will occur if collective actions are not taken urgently to stabilize the climate system. This resource is recommended for teaching.
  • Next Generation Science Standards (NGSS)
    • ESS3: Earth and Human Activity
      • MS-ESS3-4 Construct an argument supported by evidence for how increases in human population and per-capita consumption of natural resources impact Earth's systems.
      • HS-ESS3-6 Use a computational representation to illustrate the relationships among Earth systems and how those relationships are being modified due to human activity.
  • Common Core Math Standards (CCSS.MATH)
    • Geometry: Circles (9-12)
      • CCSS.MATH.CONTENT.HSG.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
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