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

Pupil W uses group discussion to engage fully with problems and investigations. He draws on strategies that have been introduced in previous work. For example, in group discussion he suggested a way to find all possible pentominoes, recalling a strategy he had been shown for checking he had all possible arrangements of four squares in an earlier lesson. When engaging with the handshakes problem, Pupil W followed the teacher's example of using diagrams to model the handshakes. After completing the diagrams for 1, 2 and 3 people, he adapted the strategy and just worked out the extra handshakes needed when one more person joined the group. He used this to develop his table of results and predict how many would be needed for 7 people even though he did not persevere to find the number of handshakes needed for the whole class.

Pupil W is beginning to express the rule for a sequence of numbers in words; for example, he identified a pattern in the sequence 6, 11, 16, 21, 26, 31 … He explained, ‘The pattern goes up in fives, but they're not multiples of five. They are all one more than a multiple of 5.’ He predicted that 101 would be in the sequence. When working on a problem of tiles for a path, he described the rule for a path that is n tiles long as ‘n lots of a blue and two whites'. With the support of group discussion, he decided this could be recorded as *n(B* + 2*W).*

He reasons about shapes, position and movement. For example, he used the clues, ‘this shape is a quadrilateral, it has just one pair of parallel sides and it also has sides that are perpendicular to each other', to identify the correct shape from a set. He also worked out which pentominoes could be folded to create an open cube, before cutting out the shapes to check.