Education Technology

Squares and Cubes

Activity Overview

How much mathematics can be generated from a single image? This activity looks at two different number sequences that can be identified directly from the diagram. The challenge is to then prove that this relationship holds true for all positive integers.


  • Interpret a geometric pattern algebraically
  • Prove result by induction.


  • Proof by Induction,
  • Expand and factorise

About the Lesson

Students use an interactive TI-Nspire document to help interpret a geometric representation of a sequence. Appropriately scaffolded questions are provided to guide students, including a range of representations of the corresponding sequence. Students are then provided with an opportunity to generalise the result algebraically including a corresponding proof.