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Reasoning & Proof

The Volcano Adventure

Reasoning & Proof: The Volcano Adventure is appropriate for middle or early high school students who have a good understanding of the principle concepts in algebra and geometry. Students apply inductive and deductive reasoning processes. Special attention is given to spatial reasoning and reasoning involving proportions and graphs. Students gain an appreciation of the power of reasoning as a part of mathematics. This module follows the NCTM standards for Reasoning & Proof.

On this adventure, students will:

  • Recognize reasoning and proof as fundamental aspects of mathematics
  • Make and investigate mathematical conjectures
  • Develop and evaluate mathematical arguments and proofs
  • Select and use various types of reasoning and methods of proof

Sample Problems


Jungle lies on the west side of the Cove. In the Reasoning and Proof module, you climb to the top of a tree and learn to drive a cable car through the treetops.

Reasoning and Proof Opening
Reasoning and Proof Problem

Visit the monkeys and the abandoned tree house where artifacts are stored, and then begin your perilous journey to Funnel Mountain, the island's active volcano.

The problems in this adventure will challenge all your reasoning abilities. Open Descartes' Notebook if you have trouble, and buy a hint if you need one.

Reasoning and Proof Opening
Reasoning and Proof Spatial Problem

The cable car stops near an unusual beach hut where it seems an inventor once worked. Continue solving the problems and you will eventually make your way to the Final Quest for Reasoning and Proof.

Explore more adventures in Descartes' Cove