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.) A key skill in moving towards generalisation and proof is being able to transfer your thinking from one example to another new example. Similarities and differences
between the two cases may become apparent. Exploring further examples means that strategies might emerge which

*always* work, which is the essence of a generalisation.

The tasks below provide opportunities for learners to get better at transferring their thinking.

##### Age 5 to 7 Challenge Level:

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

##### Age 5 to 7 Challenge Level:

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

##### Age 5 to 11 Challenge Level:

Dotty Six is a simple dice game that you can adapt in many ways.

##### Age 7 to 11 Challenge Level:

Design an arrangement of display boards in the school hall which fits the requirements of different people.

##### Age 7 to 11 Challenge Level:

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

##### Age 7 to 11 Challenge Level:

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?