9 |
- Solve problems involving frustums of cones
- Find the area of a segment of a circle given the radius and length of the chord
- Solve problems for areas and volumes of similar shapes and solids
- Use trigonometry to solve 3-D problems
- Find the angle between a line and a plane
- Know the exact values of sin Ѳ and cos Ѳ for Ѳ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan Ѳ for Ѳ = 0°, 30°, 45° and 60°
- Use the sine and cosine rules to solve 2-D and 3-D problems
- Apply vector methods for simple geometrical proofs
- Calculate the new volume of a shape after enlargement
|
8 |
- Use the formulae for length of arcs and area of sectors of circles to solve problems
- Understand and use the fact that tangents from an external point are equal in length
- Prove lines are parallel or collinear
- Find points that divide a line in a given ratio, using the properties of similar triangles
|
7 |
- Prove and use the alternate segment theorem
- Use Pythagoras’ theorem in 3-D problems
- Calculate the length of a diagonal of a cuboid
- Enlarge 2D shapes, given a negative, fractional scale factor
- Use the sine rule to find unknown lengths and angles
- Use the cosine rule to find unknown lengths
- Calculate the area of a triangle using 1/2 ab sinC
- Work out the magnitude of a vector
- Calculate, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector
- Calculate the resultant of two vectors
- Solve geometrical problems in 2-D using vector methods
- Calculate the new area of a shape after enlargement
|
6 |
- Use trigonometry to find the lengths of unknown sides, using more complex algebraic manipulation
- Find angles of elevation and angles of depression
- Prove and use the fact that the angle in a semicircle is a right angle
- Prove and use the fact that angles in the same segment are equal
- Prove and use the fact that opposite angles of a cyclic quadrilateral sum to 180°
- Prove and use facts about the angle subtended at the centre and at the circumference
- Know that the tangent at any point on a circle is perpendicular to the radius at that point
- Know that the perpendicular from the centre to the chord bisects the chord
- Complete a formal geometric proof of similarity of two given triangles
|
5 |
- Find the surface area of prisms
- Find the surface area and volumes of compound solids
- Recognise the formulae for length of arcs in a circle and area of sectors in a circle.
- Use similarity to solve problems in 2D shapes
- Extend understanding of loci to include 3D problems
- Know the formula for Pythagoras’ theorem and use to find a shorter side
- Use Trigonometry to find lengths of unknown sides in a right-angled triangle
- Transform 2D shapes by a more complex combinations of rotations, reflections and translations
- Add and Subtract vectors
- Convert between compound measures (e.g. convert 2 m/s to km/h)
- Convert imperial units to imperial units
- Convert between metric and imperial measures
- Identify the scale factor of an enlargement
|
4 |
- Use accurate drawing to solve bearings problems
- Calculate missing interior angles in polygons
- Calculate volumes of shapes made from cuboids
- Calculate the volume and surface area of right prisms
- Calculate the lengths, areas and volumes in cylinders
- Calculate the radius or diameter of a circle given the circumference or area
- Find the perimeters and areas of semicircles and quarter circles
- Use information to determine whether triangles are congruent or similar
- Construct the perpendicular from or to a point on a line segment
- Construct a triangle, given right angle, hypotenuse and side
- Construct loci
- Construct angles of 60°, 90°, 30°, 45°
- Know the formula for Pythagoras’ theorem and use to find the hypotenuse
- Use vector notation for translations
- Enlarge 2D shapes, given a fractional scale factor
- Find the centre of rotation
- Describe a transformation
- Describe reflections on a coordinate grid
- Express points as position vectors and understand and use vector notation
- Know that enlargements of 2D shapes produce similar shapes
|
3 |
- Given the bearing of point A from point B, work out the bearing of B from A
- Identify co-interior angles and their values.
- Know that the sum of the exterior angles of any polygon is 360°
- Calculate the interior angles of regular polygons
- Deduce and use the formula for the area of a trapezium
- Calculate surface areas of shapes made from cuboids
- Know and use the formulae for the circumference and area of a circle
- Identify shapes which are similar
- Identify more complex nets of 3D shapes
- Draw plans and elevations of 3-D shapes
- Use straight edge and compasses to construct the bisector of an angle
- Use straight edge and compasses to construct a triangle given three sides (SSS)
- Construct an equilateral triangle and a regular hexagon inside a circle
- Use trigonometry to find the size of an angle in a right-angled triangle
- Know the names of parts of a circle
- Enlarge shapes, given a centre of enlargement and a positive integer scale factor
- Find the centre of enlargement
- Know rough metric equivalents of imperial measures in daily use
- Convert between area measures
- Convert between metric measures of volume and capacity
|
2 |
- Identify alternate and corresponding angles on parallel lines and their values.
- Find the area of triangles by counting
- Know the formulae for the volume of cube and a cuboid
- Use a formula to calculate the area of parallelograms
- Use a formula to calculate the area of triangles
- Know that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not.
- Know that translations, rotations and reflections map objects on to congruent images
- Identify simple nets of 3D shapes
- Use straight edge and compasses to construct the midpoint and perpendicular bisector of a line
- Draw a circle given the radius or diameter
- Know that translations, rotations and reflections preserve length and angle
- Recognise that enlargements preserve angle but not length
|
1 |
- Use a protractor to draw obtuse and reflex angles to the nearest degree
- Give a bearing between the points on a map or scaled plan
- Identify interior and exterior angles in a shape
- Find missing angles around a point
- Recognise and use vertically opposite angles
- Find missing angles in a quadrilateral
- Know that the sum of the interior angle and the exterior angle is 180°
- Calculate the perimeter and area of shapes made from rectangles
- Calculate the surface area of cubes and cuboids, without a net
- Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
- Use ruler and protractor to construct simple nets of 3D shapes
- Begin to use plans and elevations
- Identify regular and irregular polygons
- Draw or complete diagrams given information about rotational or line symmetry
- Plot coordinates to complete a shape
- Use properties of equilateral and isosceles triangles to solve problems
- Solve simple geometrical problems using properties of quadrilaterals
- Convert between simple metric units
|
W3 |
- Begin to estimate the size of angles
- Use a protractor to measure obtuse and reflex angles to the nearest degree
- Use a protractor to draw acute angles to the nearest degree
- Measure shapes to find perimeters and areas
- Use correct notation for labelling angles and triangles
- Distinguish between acute, obtuse and reflex angles
- Identify perpendicular lines
- Use the formula for the area of a rectangle/square
- Use nets to calculate the surface area of cubes and cuboids
- Calculate perimeter and area of compound shapes made from triangles, rectangles and other shapes
- Calculate missing angles in a triangle
- Identify simple angle, side and symmetry properties of triangles and quadrilaterals
- Recognise and visualise – rotation about a given point
- Draw lines and shapes to scale
- Use and interpret maps and scale drawings, using a variety of scales and units
- Estimate length using a scale diagram
|
W2 |
- Measure lines to the nearest millimetre
- Use a protractor to measure acute angles to the nearest degree
- Identify parallel lines
- Know the sum of angles around a point
- Understand that area is measured in square centimetres
- Choose suitable metric units to estimate length and area.
- Draw parallel lines and mark parallel lines on a diagram
- Recognise reflection symmetry
- Use correct notation for labelling lines
- Know the sum of angles in a triangle is 180°
- Recognise and visualise the reflection in a mirror line of a 2-D shape
- Translate a shape on a square/coordinate grid
- Understand and use the language associated with rotations
- Read and construct scale drawings
|
W1 |
- Know the sum of angles on a straight line
- Know how to tessellate polygons
- Find the perimeter of a square/rectangle by counting
- Identify the net of a cube
- Identify and name common solids
- Know the terms face, edge and vertex
- Suggest suitable units to measure length, mass and capacity
- Read and interpret scales on a range of measuring instruments
- Work out time intervals
- Draw sketches of shapes
- Recognise properties of squares and rectangles
- Understand and use the language associated with translations
- Understand and use the language associated with reflections
- Enlarge a shape on a grid (without a centre specified)
|