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Testbourne Community School Year/Strand Estimated Y11 GCSE grade based on skills at the end of Year 8 Knowledge Mathematics Department – Key stage 3 Overview of Assessment Criteria Year 8 Geometry and measures (1) strand Foundation 1-3 - Know that an angle is a measure of 'turn'. - Know that a protractor is used to measure and construct angles. - Know the names of types of angles; right angle, acute, obtuse and reflex. - Know that angles on a straight line total 180° - Know that angles around a point total 360°. - Know that vertically opposite angles are equal - Know how to use a ruler to measure lines to the nearest mm. - Know how to interpret simple scale drawings. - Know Pupils how to convert and write standards units of measurements including money and time. - Know the names of 2D and 3D shapes including special triangles. - Start to know the names of special quadrilaterals. - Know that certain shapes have lines of symmetry. - Know the simple conventions/symbols used to identify/label geometric properties in geometrical diagrams (eg. for example parallel lines, equal length line etc.) - Know the meaning of terms such as edge, face, vertex for 2D and 3D shapes and also perpendicular and parallel. - Know that angles in any triangle total 180°. - Know all of the properties of equilateral and isosceles triangles. - Know how to use the standard units of measurement for lengths/distances and time and money in a variety of contexts. - Know the formula for the area of a triangle, rectangle and how to work out the area of shapes made from rectangles. - Know what is meant by volume of a cuboid and also by surface area. - Know how to measure lengths and angles in geometric shapes/drawings. - Know how to use isometric paper to draw 2D representations of 3D shapes. Developing 4-5 Aspiring 6-7 Mastering 8-9 Additionally - Know how to solve simple problems related to angles in triangles. - Know the standard constructions for triangles (using a protractor, ruler and pair of compasses as appropriate) - Know what nets are and know how to construct simple nets for cubes, cuboids and some pyramids. - Know and recall the terms associated with parts of circles. - Know that angles in a quadrilateral add up to 360° - Know how to calculate the volume of simple cubes and cuboids. - Interpret scales on a small range of measuring instruments. Additionally - Know how to use angle facts learnt so far to solve more complex problems involving angles in geometric diagrams. - Know corresponding and alternate angles in parallel lines. - Know a proof for the total of angles in a triangle and in a quadrilateral. - Know the conversions between metric units and also approximate conversions between metric and imperial measures. - Know how to solve problems involving everyday measures such as volume, capacity, mass, time, simple bearings and angles. - Know how to solve problems involving the areas and perimeters of triangles, parallelograms, trapeziums including compound shapes. - Know how to calculate the volume and surface area of cubes, cuboids and shapes made from these. - Know how to construct scale drawings. - Know how to interpret scales on a wider range of measuring instruments. - Know the names and properties of regular polygons and identify line and order of rotational symmetry. - Know what the terms complementary angles and supplementary angles mean. - Know the term loci and construct simple loci. - Know the standard constructions for items such as perpendicular bisector of a line. - Know and use the formula for the area and circumference of a circle. Additionally Know the relationship of angles between parallel lines. Know that alternate, allied and corresponding angles are derived from the relationship between the transversal as it cuts through parallel lines. Know how to solve problems using properties of angles, of parallel and intersecting lines, and of triangles and special quadrilaterals finding missing angles and know how to justify and explain reasoning with diagrams and text. Know how to derive the formula for finding the sum of interior angles of any polygon 180 x (n-2) where n represents the number of sides. Know that the sum of exterior angles = 360° therefore 360 ÷ n (where n represents the number of sides) = the size of an exterior angle and 360 ÷ an exterior angle = n. Know how to draw the nets of cylinders, pyramids and cones. Know how to use the standard formulae for area, perimeter, volume and surface area of standard prism including cylinders. Know how to give a bearing between two points. Know how to solve more complex problems involving area and circumference of circles. Testbourne Community School Year/Strand Mathematics Department – Key stage 3 Overview of Assessment Criteria Year 8 Geometry and measures (1) strand - continued Foundation Developing Aspiring Mastering Estimated Y11 GCSE grade based on skills at the end of Year 8 1-3 4-5 6-7 8-9 Understanding - Understand that angles on a straight line total 180° and that this allows us to find missing angles on a straight line. - Understand that angles around a point total 360° and that this allows us to find a missing angle around a point. - Understand why vertically opposite angles are equal and use this knowledge to find missing angles. - Understand how to use a ruler to measure lines to the nearest mm. - Understand simple scale drawings. - Understand how to convert and write standards units of measurements, including money and time. - Recognise 2D and 3D shapes including special triangles when their names are used. - Recognise the names of special quadrilaterals. - Understand that certain shapes have lines of symmetry. - Understand the simple conventions/symbols used to identify/label geometric properties in geometrical diagrams (for example parallel lines, equal length lines.) - Understanding the meaning of terms such as edge, face, vertex for 2D and 3D shapes and also perpendicular and parallel. - Understand that angles in any triangle total 180°. - Understand the properties of equilateral and isosceles triangles. - Understand how to use the standard units of measurement for lengths/distances and time and money in a variety of contexts. - Understand formula for the area of a triangle, rectangle and how to work out the area of shapes made from rectangles. - Understand what is meant by volume of a cuboid and also by surface area. - Understand how to measure lengths and angles in geometric shapes/drawings. - Understand how to use isometric paper to draw 2D representations of 3D shapes. Additionally - Understand how to solve simple problems related to angles in triangles. - Understand the standard constructions for triangles (using a protractor, ruler and pair of compasses as appropriate) - Understand what nets are and know how to construct simple nets for cubes, cuboids and some pyramids. - Understand and recall the terms associated with parts of circles. - Understand why angles in a quadrilateral add up to 360° - Understand how to calculate the volume of simple cubes and cuboids. - Understand how to interpret scales on a small range of measuring instruments. Additionally - Understand how to use angle facts learnt so far to solve more complex problems involving angles in geometric diagrams. - Understand what a corresponding and alternate angle is in parallel lines. - Understand a proof for the total of angles in a triangle and in a quadrilateral. - Understand the conversions between metric units and also approximate conversions between metric and imperial measures. - Understand how to solve problems involving everyday measures such as volume, capacity, mass, time, simple bearings and angles. - Understand how to solve problems involving the areas and perimeters of triangles, parallelograms, trapeziums including compound shapes. - Understand how to calculate the volume and surface area of cubes, cuboids and shapes made from these. - Understand how to construct scale drawings. - Understand how to interpret scales on a wider range of measuring instruments. - Understand the names and properties of regular polygons and identify line and order of rotational symmetry. - Understand what the terms complementary angles and supplementary angles mean. - Understand the term loci and how to construct simple loci. - Understand the standard constructions for items such as perpendicular bisector of a line. - Understand and use the formula for the area and circumference of a circle. Additionally Understand the relationship of angles between parallel lines. Understand that alternate, allied and corresponding angles are derived from the relationship between the transversal as it cuts through parallel lines. Understand how to solve problems using properties of angles, of parallel and intersecting lines, and of triangles and special quadrilaterals finding missing angles and Understand how to justify and explain reasoning with diagrams and text. Understand how to derive the formula for finding the sum of interior angles of any polygon 180 x (n-2) where n represents the number of sides. Understand that the sum of exterior angles = 360° therefore 360 ÷ n (where n represents the number of sides) = the size of an exterior angle and 360 ÷ an exterior angle = n. Understand how to draw the nets of cylinders, pyramids and cones. Understand how to use the standard formulae for area, perimeter, volume and surface area of standard prism including cylinders. Understand how to give a bearing between two points. Understand how to solve more complex problems involving area and circumference of circles. Testbourne Community School Year/Strand Estimated Y11 GCSE grade based on skills at the end of Year 8 Skills Mathematics Department – Key stage 3 Overview of Assessment Criteria Year 8 Geometry and measures (1) strand continued Foundation Developing 1-3 4-5 - Using a protractor measure angles and construct angles. - Recall & recognise right angles, acute, obtuse and reflex angles - Recall and use the fact that angles on a straight line total 180° to find missing angles in problems related to a straight line. - Recall and use the fact that angles around a point total 360° to find a missing angle around a point. - Recall and use the fact that vertically opposite angles are equal to find missing angles in simple problems. - Use a ruler to measure lines to the nearest mm. - Interpret simple scale drawings - Convert metric units of length measurements and money and time. - Recognise 2D and 3D shapes including special triangles using their correct names. - Recall the names of some special quadrilaterals. - Identify and draw lines of symmetry on 2D shapes. - Label simple diagrams and shapes with the correct symbols used to identify geometric properties such as parallel lines and equal length lines. - Identify edges, faces, vertices on 2D and 3D shapes. - Identify perpendicular and parallel lines in a variety of contexts. - Solve very simple problems using the fact that angles in a triangle add up to 180° - Recall and explain the properties of equilateral and isosceles triangles. - Recall and use the standard units of measurement for lengths/distances and time and money in a variety of contexts. - Use the formula for the area of a triangle and rectangle and also work out the area of simple shapes made from rectangles. - Recall what is meant by volume of a cuboid and also by surface area. - Measure lengths and angles accurately in geometric shapes/drawings. - Use isometric paper to draw 2D representations of simple 3D shapes. Additionally - Solve simple problems related to angles in triangles. - Draw standard constructions for triangles (using a protractor, ruler and pair of compasses as appropriate) - Construct simple nets for cubes, cuboids and some pyramids. - Recall the terms associated with parts of circles. - Explain why angles in a quadrilateral add up to 360° - Calculate the volume of simple cubes and cuboids. - Interpret scales on a small range of measuring instruments. Aspiring Mastering Additionally - Use angle facts learnt so far to solve more complex problems involving angles in geometric diagrams. - Identify and solve simple problems involving corresponding and alternate angle is in parallel lines. - Explain a proof for the total of angles in a triangle and in a quadrilateral. - Perform conversions between metric units and also use approximate conversions between metric and imperial measures. - Solve problems involving everyday measures such as volume, capacity, mass, time, simple bearings and angles. - Solve problems involving the areas and perimeters of triangles, parallelograms, trapeziums including compound shapes. - Calculate the volume and surface area of cubes, cuboids and shapes made from these. - Construct scale drawings. - Interpret scales on a wider range of measuring instruments. - Recall the names and properties of regular polygons and identify line and order of rotational symmetry of these shapes. - Recall the terms complementary angles and supplementary angles mean. - Construct simple loci. - Draw standard constructions for items such as perpendicular bisector of a line. - Recall and use the formula for the area and circumference of a circle. Additionally - Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and special quadrilaterals finding missing angles and Understand how to justify and explain reasoning with diagrams and text. - Derive the formula for finding the sum of interior angles of any polygon 180 x (n-2) where n represents the number of sides. - Use the fact that the sum of exterior angles = 360° therefore 360 ÷ n (where n represents the number of sides) = the size of an exterior angle and 360 ÷ an exterior angle = n. - Draw the nets of cylinders, pyramids and cones. - Use the standard formulae for area, perimeter, volume and surface area of standard prism including cylinders. - Work out the bearing between two points. - Solve more complex problems involving area and circumference of circles. Testbourne Community School Mathematics Department – Key stage 3 Overview of Assessment Criteria Applies to all Mathematics Strands Application Grade Descriptors from the Department for Education • FOUNDATION DEVELOPING To achieve grade 2 and GCSE, candidates will be able to: • recall and use notation, terminology, facts and definitions; perform routine procedures, including some multi-step procedures • interpret and communicate basic information; make deductions and use reasoning to obtain results • solve problems by translating simple mathematical and nonmathematical problems into mathematical processes • provide basic evaluation of methods or results • interpret results in the context of the given problem To achieve grade 5 at GCSE, candidates will be able to: • perform routine single- and multi-step procedures effectively by recalling, applying and interpreting notation, terminology, facts, definitions and formulae • interpret and communicate information effectively • make deductions, inferences and draw conclusions • construct chains of reasoning, including arguments • generate strategies to solve mathematical and non-mathematical problems by translating them into mathematical processes, realising connections between different parts of mathematics • interpret results in the context of the given problem • evaluate methods and results MASTERING To achieve grade 8 at GCSE, candidates will be able to: • perform procedures accurately • interpret and communicate complex information accurately • make deductions and inferences and draw conclusions • construct substantial chains of reasoning, including convincing arguments and formal proofs • generate efficient strategies to solve complex mathematical and non-mathematical problems by translating them into a series of mathematical processes • make and use connections, which may not be immediately obvious, between different parts of mathematics • interpret results in the context of the given problem • critically evaluate methods, arguments, results and the assumptions made The national curriculum for mathematics aims to ensure that all pupils: - become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. - reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language - can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.