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Grade Ladder – Shape
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 sin⁡C
  • 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)
All BTEC results have been emailed to student school email accounts 02.09.2020