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Geometric Modeling


9th, 10th, 11th, 12th




90 minutes

Regional Focus

Polar Regions


Google Docs, Google Slides


This lesson plan is licensed under Creative Commons.

Creative Commons License

The Math Behind Sea Level Rise

Created By Teacher:
Last Updated:
Sep 29, 2023
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In this lesson, students use geometry to investigate how the melting of all the ice in Antarctica would impact sea level rise.

Step 1 - Inquire: Students speculate how one could use geometry to calculate the water level produced by a melting block of ice placed on a classroom table.

Step 2 - Investigate: Students follow mathematical steps to answer the question "How much would sea levels rise if Antarctica melted?"

Step 3 - Inspire: Students explore the effects of sea level rise on coastal communities and the measures being taken to build resilience.

Accompanying Teaching Materials
Teaching Tips


  • Students see a real-world application of geometry tied to an important consequence of climate change.

  • Students practice volume and surface area formulas.

  • Teacher answer key is included.

Additional Prerequisites

  • Teacher needs to acquire some ice for the Inquire section.

  • Students should have a general knowledge of climate change and sea level rise.
  • Students should be familiar with the concepts of volume and surface area.
  • Students should be familiar with imperial and metric units.


  • Higher-level classes can work out the steps of the problems independently, while lower-level classes can follow the steps on the Student Document and Teacher Slideshow from the beginning.

  • The teacher can select one unit of measurement by editing the Student Document to use only meters and kilometers or to use only feet and miles.

  • The teacher can use occasional check-ins. For example, the teacher could stop the class after Step 1 in the Investigate section. This would help make sure all groups have similar answers and are off to a good start with the problem.

  • The teacher can select one resource in the Inspire section and explore the resource as a class instead of having the students explore the resources independently.

Scientist Notes

This lesson explores calculating the amount of sea level rise from melting the Antarctic Ice Sheet. Students see a real-world application of geometry tied to an important consequence of climate change. All materials have been fact-checked, and the lesson is credible for teaching. Considerations not mentioned in this lesson plan include the impact that the Greenland Ice Sheet would be simultaneously contributing to sea level rise, and that half of the current sea level rise is due to the thermal expansion of water.


Primary Standards

  • Common Core Math Standards (CCSS.MATH)
    • Geometry: Geometric Measurement & Dimension (9-12)
      • CCSS.MATH.CONTENT.HSG.GMD.A.2 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
      • CCSS.MATH.CONTENT.HSG.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
    • Geometry: Modeling with Geometry (9-12)
      • CCSS.MATH.CONTENT.HSG.MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

Supporting Standards

  • Common Core Math Standards (CCSS.MATH)
    • Geometry: Geometric Measurement & Dimension (9-12)
      • CCSS.MATH.CONTENT.HSG.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.
    • Geometry: Modeling with Geometry (9-12)
      • CCSS.MATH.CONTENT.HSG.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
      • CCSS.MATH.CONTENT.HSG.MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
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