4.1 Angles, lines and triangles
A distinguish between acute, obtuse, reflex and right angles
B use angle properties of intersecting lines, parallel lines and angles on a straight line
C understand the exterior angle of a triangle property and the angle sum of a triangle property
D understand the terms 'isosceles', 'equilateral' and 'right-angled triangles' and the angle properties of these triangles
4.2 Polygons
A recognise and give the names of polygons
B understand and use the term 'quadrilateral' and the angle sum property of quadrilaterals
C understand and use the properties of the parallelogram, rectangle, square, rhombus, trapezium and kite
D understand the term 'regular polygon' and calculate interior and exterior angles of regular polygons
E understand and use the angle sum of polygons
F understand congruence as meaning the same shape and size
G understand that two or more polygons with the same shape and size are said to be congruent to each other
4.3 Symmetry
A identify any lines of symmetry and the order of rotational symmetry of a given two-dimensional figure
4.4 Measures
A interpret scales on a range of measuring instruments
B calculate time intervals in terms of the 24-hour and the 12-hour clock
C make sensible estimates of a range of measures
D understand angle measure including three-figure bearings
E measure an angle to the nearest degree
F understand and use the relationship between average speed, distance and time
G use compound measure such as speed, density and pressure
4.5 Construction
A measure and draw lines to the nearest millimetre
B construct triangles and other two-dimensional shapes using a combination of a ruler, a protractor and compasses
C solve problems using scale drawings
D use straight edge and compasses to:
(i) construct the perpendicular bisector of a line segment
(ii) construct the bisector of an angle
E understand and use the internal and external intersecting chord properties
F recognise the term 'cyclic quadrilateral’
G understand and use angle properties of the circle including:
(i) angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the remaining part of the circumference
(ii) angle subtended at the circumference by a diameter is a right angle
(iii) angles in the same segment are equal
(iv)the sum of the opposite angles of a cyclic quadrilateral is 180°
(v) the alternate segment theorem
4.6 Circle properties
A recognise the terms 'centre', 'radius', 'chord', 'diameter', 'circumference', 'tangent', 'arc', 'sector' and 'segment' of a circle
B understand chord and tangent properties of circles
4.7 Geometrical reasoning
A give informal reasons, where required, when arriving at numerical solutions to geometrical problems
B provide reasons, using standard geometrical statements, to support numerical values for angles obtained in any geometrical context involving lines, polygons and circles
4.8 Trigonometry and Pythagoras’ theorem
A know, understand and use Pythagoras' theorem in two dimensions
B know, understand and use sine, cosine and tangent of acute angles to determine lengths and angles of a right-angled triangle
C apply trigonometrical methods to solve problems in two dimensions
D understand and use sine, cosine and tangent of obtuse angles
E understand and use angles of elevation and depression
F understand and use the sine and cosine rules for any triangle
G use Pythagoras' theorem in three dimensions
H understand and use the formula 1 ab sin C for the area of a triangle
I apply trigonometrical methods to solve problems in three dimensions, including finding the angle between a line and a plane
4.9 Mensuration of 2D shapes
A convert measurements within the metric system to include linear and area units
B find the perimeter of shapes made from triangles and rectangles
C find the area of simple shapes using the formulae for the areas of triangles and rectangles
D find the area of parallelograms and trapezia
E find circumferences and areas of circles using relevant formulae; find perimeters and areas of semicircles
F find perimeters and areas of sectors of circles
4.10 3D shapes and volume
A recognise and give the names of solids
B understand the terms 'face', 'edge' and 'vertex' in the context of 3D solids
C find the surface area of simple shapes using the area formulae for triangles and rectangles
D find the surface area of a cylinder
E find the volume of prisms, including cuboids and cylinders, using an appropriate formula
F convert between units of volume within the metric system
G find the surface area and volume of a sphere and a right circular cone using relevant formulae
4.11 Similarity
A understand and use the geometrical properties that similar figures have corresponding lengths in the same ratio but corresponding angles remain unchanged
B use and interpret maps and scale drawings
C understand that areas of similar figures are in the ratio of the square of corresponding sides
D understand that volumes of similar figures are in the ratio of the cube of corresponding sides
E use areas and volumes of similar figures in solving problems