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# Ma1 Using and applying mathematics

## Musicians problem

### Teacher's notes

• Uses a systematic approach for checking all possibilities.
• Understands that a method is more logical than a random approach.
• Uses appropriate letters to represent the musicians.

### Next steps

• Develop method further, starting with the first two letters the same, etc.
• Having found all the combinations for one musician in the first position, begin to predict the number of other combinations.

## Frog problem

### Teacher's notes

• Finds a starting point and uses an appropriate diagram to represent the problem.
• Understands the frog's progress as 2 m in each 20 min.
• Realises with the last leap up the well there was no falling back down, that is, that the last leap covers 3 m and takes only 15 min.

### Next steps

• Recognise which steps could be grouped to minimise working out, especially if the task were extended
• Plot the time and distance onto a graph to show the relationship more clearly
• Compare approaches with others in the class to consider other ways to present the solution.

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

Polly solves problems and investigates in a range of contexts. Polly often uses the approach modelled by the teacher although she develops her own strategies too. She poses questions to develop her understanding of a problem. She refers back to previous work and suggests appropriate methods to use. If Polly finds a particular problem difficult she will work through her own ideas, before seeking assistance from her discussion partner. Polly is persistent and if she does not finish a task in class, she will try to work out the solution later.

Polly presents information in a clear and concise way, beginning to use symbols and diagrams. As well as seeking assistance, she tries out her own ideas to decide which way of representing a problem is the most effective and why. She uses a range of mathematical vocabulary relating to the content at level 4, for instance percentage, square number, unlikely, parallel, and is beginning to use words associated with level 5 material, for instance prime number, perpendicular.

Polly looks for patterns and relationships in results. For example, she recognises when all numbers in a set are multiples of three, and she sees that the greater the length of the touching edges of two given shapes, the smaller the perimeter of the compound shape will be. When working on a problem, Polly checks her methods to inform her next steps, thus justifying her answers: for instance, in the 'Musicians problem', her systematic approach enables her to be confident that she has found all the possibilities. In measures problems, Polly knows to convert mixed units to one type before she completes a calculation such as litre + 725 ml. If shown a different solution to a problem Polly likes to understand how it was reached.

## Summarising Polly's attainment in Ma1

In Ma1 Polly is best described as working at the top of level 4. She is developing her own strategies for solving problems in a variety of contexts. She presents results in a clear and organised way and checks her results to ensure that solutions make sense. She identifies patterns in her work and makes simple generalisations. To progress into level 5, Polly needs experience of more complex problems requiring decisions to be made about which information to use. She needs to use simple algebra to represent her mathematics, and develop her explanations to justify her reasoning.