A brief summary of some of the most important maths concepts to be taught in Year 3. 1. 3-D and 2-D shape Children should understand and begin to write, the following words: shape, pattern, flat, solid, hollow, side, edge, face, straight, curved, round, circular, triangular, rectangular, pentagonal, hexagonal, octagonal, right-angled, vertex, vertices, layer, diagram, surface, point, pointed, corner, sort, make, build, draw, cube, cuboid, sphere, cone, cylinder, prism, hemi-sphere, circle, triangle, rectangle, square, pyramid, hexagon, octagon, quadrilateral, semi-circle. In 3-D shape work, the main new concept is that of a prism. A prism is a shape that has the same cross-section and same size throughout its length. Some shapes such as cones and square based pyramids have the same shape throughout their length (ie circle and square respectively), but they are not prisms because the size of the circle or square changes as you move from one end to the other. There are many near prisms in real life (e.g. rulers, pencils, cans, chocolate boxes, rolls of sticky tape and exercise books), although they often have a small part such as the point of a pencil which prevents it being a pure prism. Children can generally be taught to ignore these annoying parts that manufacturers will insist on adding to spoil our maths lessons! Children should also continue to describe solid shapes with increasing definition and precision and be more able to recognise similarities and therefore be more able to classify shapes according to their properties. In 2-D shape work, the main new concept is that of a quadrilateral. A quadrilateral is a flat shape with four straight sides. Examples that are already familiar to children are squares, rectangles, rhombuses and parallelograms (although they may not yet know the names of the more difficult ones). They should be able to recognise more difficult properties, in particular the right angle, and be able to classify shapes according to more difficult properties. They should also realise that some shapes belong to larger families, e.g. squares are really just a special type of rectangle and rectangles are just a special type of quadrilateral. In year 3 children will continue to make shapes and patterns, these becoming more complex and more accurate. 3D shapes should be related to 2D representations of them, as children match familiar solids to their pictures. Drawing round shapes such as triangles, rectangles and hexagons and then cutting them out to make repeated patterns should be encouraged. When describing the patterns created, children should be encouraged to name the shapes. Often children will need to copy a pattern before they feel confident enough to create their own. When drawing round shapes the emphasis should be on accuracy and care, both in placing the shape in the right position and drawing round it. 2. Symmetry Symmetry is continued in year 3. Children should use and read terms such as: line of symmetry mirror line reflection Mirrors are essential for this work so that children can see the reflection of the shape in the mirror - they often find great difficulty predicting the mirror image without this help. Whether shapes are symmetrical can be tested using a mirror, and a line of symmetry can be drawn where the mirror has been placed. Further practical work should be continued, developing from that covered in years 1 and 2, such as making symmetrical patterns using ink blots or paint across a folded edge. Other symmetrical patterns can be made with cubes, sticky gummed paper, plastic shapes etc. Children should be encouraged to find examples of pictures, signs, letters of the alphabet etc which have a line of symmetry and to make a scrapbook up of these. Sketching the other half of a shape is very difficult, but a few examples have been included in this module. They can also create their own 'half' pictures and try to draw the mirror image. 3. Describe position and direction Children should understand and be able to use in practical contexts the following words. Where possible, they should be taught to read the words. position, over, under, underneath, above, below, on, in, outside, inside, in front, behind, beside, before, after, higher, lower, next to, opposite, between, close, far, apart, middle, centre, edge, corner, top, bottom, side, direction, left, right, up, down, forward, backwards, sideways, across, along, around, through, to, from, towards, away from, clockwise, anticlockwise, journey, route, grid, row, column, map, plan, compass point, north, south, east, west, horizontal, vertical, diagonal, descend, ascend. In addition to describing position in terms of 'behind', in front of' etc, they should now be becoming confident with describing position in an absolute sense, ie on a grid or map. They should be able to say how many squares from a zero point horizontally and vertically an object is and give these labels when appropriate (square B3, F5 etc). They should know the difference between a column and a row. Columns are vertical (as in the old Greek buildings), rows are horizontal (imagine standing at the front of a cinema and looking out at the rows of seats). They should understand that a diagonal goes from one corner of a grid to the opposite corner eg bottom left to top right. They should know the directions North, South, East and West and that on a map or plan, the North direction is almost always towards the top. The North direction should, in any case, always be indicated. North and South are generally easy to remember, but most children will mix up East and West for a long time. They should know the meaning of the words 'ascend' and 'descend'. 4. Understand angle Children should understand and use in practical contexts the following vocabulary: slide, roll, turn, whole turn, half turn, quarter turn, angle, right angle, straight line, is a greater/smaller angle than. Children should recognise quarter and half turns and know that a quarter turn is a right angle and that  a half turn (or straight line) is two right angles. They should understand the directions N, S, E and W and be able to face one direction, turn a quarter or half turn and say which way they are then facing. They should know that turning a half turn or two quarter turns results in you facing in the opposite direction. Children should be able to sort shapes according to the number of right angles they have and be able to fold a piece of paper to give a right angle with which they may test for right angles in other shapes. They should be able to use a template to draw right angles and test angles to see if they are smaller, equal to or larger than right angles. Go to year 3 shape