## King Arnold problem

### Teacher's notes

- Establishes a starting point.
- Uses diagrams, as modelled in question.
- Finds four of six possible solutions and repeats one solution.

### Next steps

- Develop a more systematic approach and organised way of recording.
- Compare results, discuss which are the same or different and find all possibilities.

## What the teacher knows about Paulo's attainment in Ma1

Paulo suggests suitable ways of starting a problem and sometimes selects and uses appropriate apparatus to support his work. In problems when he is finding 'How many waysâ€¦?' he needs to be more systematic in his approach.

He discusses his methods and strategies, using mathematical vocabulary. He sometimes uses pictures, diagrams and symbols to explain, and this helps him to visualise a solution. He increasingly chooses to make recordings and jottings when working independently.

Paulo explains his thinking: for example, he identifies and explains the first steps needed to solve the 'Sail away'
^{1}
problem.

In this logic problem, he soon loses sight of the mathematics and offers other practical solutions such as 'One man could swim back to the island.'

His explanations are becoming more detailed, though he sometimes needs prompting to be more specific. Paulo looks for patterns in numbers. For example, when working with addition sequences, he identifies how much is added each time and uses the rule to find missing numbers and to extend the sequence.

## Summarising Paulo's attainment in Ma1

Paulo's attainment in Ma1 is best described as working at secure level 2. He sometimes needs support to break into a problem but he then selects the mathematics to solve it. He discusses his work using some mathematical language and he sometimes represents solutions using simple diagrams. He explains why an answer is correct with increasing independence; however, he needs to try different approaches and organise his work more systematically.

^{1}
'Sail away' resource in
Mathematical challenges for Years
3 and 4, Primary National Strategy