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

Pupil R applies the mathematics she has learned to solve new problems. Working with arithmetic sequences she formulated an algebraic expression for the nth term. She understood that her algebraic expression could be used to calculate the 50th term, for example, but she reasoned that given a term she could also find its position in the sequence, using what she knew about solving linear equations. Pupil R and her partner calculated later terms for the other to work out their positions by setting up and solving equations. When challenged to say if other numbers were terms of the sequence, Pupil R used a similar approach. For example, she solved $8\text{n}-3=89$ and interpreted the result 11.5 as showing that 89 is greater than the 11th term and less than the 12th term. She justified this by adding that ‘89 isn't three less than a multiple of 8… and the numbers on either side would be 85 and 93‧.

Pupil R interprets information presented in a variety of forms. For example, she interprets and compares linear functions and explains which graph will be steeper or cross the y-axis at a particular point. She interprets bar charts, pie charts, frequency tables and diagrams.

She interprets geometrical diagrams and symbols that identify equal angles, equal lengths and parallel lines, for example. She reasons about lines, angles and polygons. She finds angles in diagrams of parallel and intersecting lines and understands a proof of the angle sum of a triangle. She learned to enlarge 2-D shapes using a centre of enlargement and a positive scale factor. She then reasoned how to find the centre of enlargement and the scale factor when given a shape and its enlargement.