Proof: The foundation of mathematics
Primary students are capable of arguing deductively, as shown in the video Addition of Odd and Even Numbers.
You can download the Addition of Odd and Even Numbers video transcript.
A similar scenario is described in the articleon Why Reasoning? on the AAMT website. Primary students may enjoy some of the activities from Primary Proof? found on the Nrich website.
For secondary students, geometry is a common area for proof exercises. However, many Number and Algebra activities also lend themselves to formal proof. For example, the activity Magic Vs is a proof activity from the Nrich website that is suitable for years 4–10.