Pupils must have learnt about fractions before beginning work on this criterion. In particular they should recognise one-, two- and three-quarters of a circle. Pupils must be able to describe and represent quarter, half and three-quarter turns (clockwise and anti-clockwise). Pupils should begin by making quarter turns with their bodies, following instructions such as “Stand, and make a quarter turn clockwise. Walk in a straight line. Stop. Make a quarter turn anticlockwise.” They should be able to relate these movements to the quarter turn of a clock hand. Pupils should learn that the angle relative to the starting orientation, created by a quarter turn (in either direction), is called a right angle – programmable robots and geo-strips are useful tools for illustrating this.
Pupils should then learn to follow instructions involving 1/2 turn and 3/4 turns, clockwise and anticlockwise. They should recognise that the result of making a 1/2 turn clockwise is the same as the result of making a 1/2 turn anticlockwise. Pupils should also understand 1/2 and 3/4 turns as repeated 1/4 turns, and therefore as repeated turns through a right angle. Pupils should recognise that a right angle is the ‘amount of turn’ between 2 lines, and is independent of the length of those lines. They should be presented with a right angle created by 2 long lines (such as two metre sticks) and a right angle created by 2 short lines (such as 2 geo-strips), and understand that both are right angles. It is important that pupils know that it is incorrect to describe the right-angle made from longer lines as a ‘bigger right angle’, or that made from the shorter lines as a ‘smaller right angle’. Pupils should practise identifying right angles in their environment, for example, the corner of their desk, the panes of a window, or the hands on a clock at 3pm or 9pm. They should learn to use various tools to confirm that angles are right angles, for example a card circle with a quarter circle cut out, or a piece of paper of any size that has been folded in half and half again to create a right angle. Pupils must then learn to identify right angles in polygons. This should involve both handling shapes (for example, cut from cardboard) and working with images of shapes. When pupils are handling shapes, they should practise rotating the shapes to check each angle against a right-angle checker. Images of shapes should be presented in a variety of orientations, so that pupils’ ability to identify right angles is not dependent on the lines being horizontal and vertical. Pupils must also learn to interpret and use the standard convention for marking right angles.
Whether working with cut-out shapes or images, pupils should be able to state whether a given angle is greater than or smaller than a right angle, using the angle-checker. Pupils should recognise that:
- the only polygon in which every vertex can be a right angle is a quadrilateral.
- quadrilaterals that have 4 right angles are rectangles irrespective of the length of their sides.
- a quadrilateral that has all side-lengths equal and every vertex a right angle is a regular rectangle that can also be called a square.