In the third stage of the problem-solving process, learners are aiming for generalisation and possibly proof.  (See the article Mastering Mathematics: The Challenge of Generalising and Proof.)  Being able to prove is the highest step on the reasoning journey (see our Reasoning Feature and particularly our article Reasoning: the Journey from Novice to Expert), following on from convincing and justifying.

The tasks below provide opportunities for learners to get better at proving, whether through proof by exhaustion, proof by contradiction, proof by logical argument, proof by counter example or generic proof.

Proof by Exhaustion

Age 5 to 11

These tasks involve finding all possible solutions and so lend themselves to proof by exhaustion.

Proof by Counter Example

Age 5 to 11

These tasks offer opportunities to explore proof by counter example.

Proof by Logical Argument

Age 5 to 11

These tasks are useful contexts in which to explore proof by logical argument.

Generic Proof

Age 5 to 11

Here we have gathered together tasks which focus on generic proof.

Proof by Contradiction

Age 5 to 11

Explore proof by contradiction with these tasks.