# What the teacher knows about Pupil N's attainment in using and applying mathematics

Pupil N poses questions and solves problems. She applies previously learnt material well and draws on mathematics from a range of contexts. For example, she suggested modifying the volume optimisation problem to find the largest closed cylinder volume that could be made from an A4 piece of card. She generated formulae and used a spreadsheet to find values for radius and length although she didn't fully appreciate all the constraints that were introduced until she tried to explain the results.

Pupil N selects appropriate mathematics to apply to a situation and communicates effectively. She gives reasons for her choices in response to probing questions. In the work on surds and indices she understood that when surds were multiplied simplification was often possible. She chooses ICT effectively to support calculations, to analyse large data sets and to explore geometric and graphical situations.

Pupil N uses short chains of deductive reasoning to solve problems. With prompting, she appreciates the difference between mathematical explanation and experimental evidence. For example, she initially used the angle measuring function to show that the triangles she created with dynamic geometry were similar. When asked if there was a different way she could show this, she used congruence properties (‘the small triangles are the same’) and the sum of angles at a point on a straight line to give a better explanation.