1. Position, direction and co-ordinates Children should be familiar with all the words from previous years plus the following and should be able to use, read and write them: position, direction, ascend, descend, journey, route, map, plan, grid, row, column, origin, co-ordinates, compass, point, north, south, east, west, north-east, north-west, south-east, south-west, horizontal, vertical, diagonal. Co-ordinates from now on are numbered on the lines on both axes, not in the spaces. The reason for this is that it prepares the way for the later use of fractional co-ordinates such as (3.2, 4.8) to give greater resolution and access to more points on the grid. The origin is the point (0,0). It is an unbreakable rule that when giving the position of a point as a set of co-ordinates, the first number refers to the distance from the origin horizontally and the second the distance from the origin vertically. The point (3,2) is therefore different to the point (2,3). In the context of a grid, children should understand that horizontal means across the grid from left to right and vertical means across the grid from towards you to away from you. In the context of real life, they should understand that horizontal means a line or surface that is parallel to the horizon and vertical means a line or surface going straight up (at right angles to the horizon). Remember that columns are vertical (old Greek buildings) and rows are horizontal (cinema seats). Children should now have a good grasp of N, S, E and W and should be extending this to North-east, North-west, South-east and South-west. Use maps on journeys (or to plan a journey) whenever possible. 2. Angle Children should be able to use, read and write the following vocabulary: Turn, rotate, whole turn, half turn, quarter turn, angle, right angle, straight line, degree, ruler, set square, angle measurer. The most important thing that children should understand about angles is that they are a measure of turn. When we measure with a ruler we are measuring length; when we measure with a thermometer we are measuring temperature and therefore when we measure an angle with a protractor or similar device we are measuring a turn. Many children do not appreciate this fact and it is worth emphasising many times. If this is not understood, then it is impossible to see which of two angles is greater or to use a protractor properly. For those who are only familiar with the protractor for measuring angles, there is a device in which one part remains stationary and the other moves around the angle being measured. This gives a better appreciation of an angle as a measure of turn. Children should appreciate that angles are measured in degrees and that ninety of them make a right angle, one hundred and eighty make a half turn and three hundred and sixty make a complete turn. It is therefore easy to see that forty five degrees is half a right angle and thirty degrees is one third of a right angle. These facts will be used, for example, when studying the rotation of the hands on a clock (one hour's movement of the hour hand is 30 degrees). Children are not yet expected to measure angles to the nearest degree with a protractor. They should be able to use the angles on 45 degrees and 60 degrees/30 degrees set squares to measure and draw these angles. They should also appreciate that the third angle in a set square is a right angle. Given a set of angles of 30 degrees, 45 degrees and simple multiples of these, children should be able to put them in order of size. Go to Position and Angle Concepts