There are 3 NRICH Mathematical resources connected to Disproof by counterexample, you may find related items under Thinking Mathematically.Broad Topics > Thinking Mathematically > Disproof by counterexample
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
These tasks provide opportunities for learners to get better at proving, whether through proof by exhaustion, proof by logical argument, proof by counter example or generic proof.
A introduction to how patterns can be deceiving, and what is and is not a proof.