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# What the teacher knows about Pupil R's attainment in shape, space and measures

Pupil R creates and interprets drawings of 3-D objects such as prisms and cuboids using isometric grids. She also represents more complex shapes. For example, she represented a shape made with five linking cubes and its reflection in a mirror line.

Working with quadrilaterals, Pupil R uses properties relating to pairs of parallel sides, the lengths of sides and diagonals and angles at the vertices and where diagonals intersect. She uses the angle properties of regular polygons, knows the sum of exterior angles is 360° and expresses the sum of interior angles in algebraic form. For example, Pupil R was given a diagram of a triangle with a line parallel to its base drawn though the opposite vertex:

She used the properties of parallel and intersecting lines to identify equal angles. She used the sum of angles at a point on a straight line to prove that the angle sum of a triangle is 180°.

Pupil R reflects, translates and rotates 2-D shapes on grids. She understands that when she transforms shapes in these ways, lengths and angles do not change. Pupil R also enlarges shapes using a centre of enlargement and a positive scale factor. She knows that when the centre of enlargement is the origin, (0, 0) and the image is enlarged by a scale factor of 2 then the coordinates of each vertex are doubled. She also knows that this rule does not apply to other centres of enlargement. Pupil R recognises that when enlarging shapes the side lengths are multiplied by the scale factor.

Pupil R knows and uses the formula for the area of a triangle. When she investigated parallelograms with the same base and area as a given rectangle, she found they had the same perpendicular height. She used this to derive a formula for the area of a parallelogram. She calculated the areas of other parallelograms using the base length and the perpendicular height. With the support of group discussion, Pupil R found a different way to calculate the area so that she could check her formula. She completed a rectangle around a parallelogram on her grid:

She then calculated the area of the rectangle and subtracted the areas of the triangles.