Year 7 |
Year 8 |
Year 9 |
Year 10 |
Year 11 |
Extension |
| Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes. |
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Distinguish between conventions, definitions and derived properties. |
Distinguish between practical demonstration and proof in a geometrical context. |
Show step-by-step deduction in solving more complex geometrical problems. |
Understand the necessary and sufficient conditions under which generalisations, inferences and solutions to geometrical problems remain valid. |
| Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle; recognise vertically opposite angles. |
Identify alternate angles and corresponding angles; understand a proof that: the angle sum of a triangle is 180°and of a quadrilateral is 360° the exterior angle of a triangle is equal to the sum of the two interior opposite angles. |
Explain how to find, calculate and use:
• the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons
• the interior and exterior angles of regular polygons.
Inscribed regular polygons
Tessellation interactivity
Tessellations with LOGO
Generalising about Polygons LOGO |
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Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle. |
Know that the tangent at any point on a circle is perpendicular to the radius at that point; explain why the perpendicular from the centre to the chord bisects the chord. |
Prove and use the facts that:
• the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference
• the angle subtended at the circumference by a semicircle is a right angle
• angles in the same segment are equal
• opposite angles in a cyclic quadrilateral sum to 180°.
Circle theorems with GSP |
Prove and use the alternate segment theorem. |
| Identify and use angle, side and symmetry properties of triangles and quadrilaterals; explore geometrical problems involving these properties, explaining reasoning orally, using step-by-step deduction supported by diagrams. |
Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometrical properties.
Quadrilaterals with 7 circles Geogebra
Transformations and tessellations DGS |
Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text. |
Solve multi-step problems using properties of angles, of parallel lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text. |
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Know that if two 2-D shapes are congruent, corresponding sides and angles are equal. |
Understand congruence and explore similarity. |
Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio; understand from this that any two circles and any two squares are mathematically similar while in general any two rectangles are not. |
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Prove the congruence of triangles and verify standard ruler and compass constructions using formal arguments. |
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Investigate Pythagoras’ theorem, using a variety of media, through its historical and cultural roots, including ‘picture’ proofs.
Proof of Pythagoras
Discovering Pythagoras theorem using GSP |
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| Use 2-D representations to visualise 3-D shapes and deduce some of their properties. |
Visualise 3-D shapes from their nets; use geometric properties of cuboids and shapes made from cuboids; use simple plans and elevations.
Building Houses
3D object viewer
Polyhedron calendars |
Visualise and use 2-D representations of 3-D objects; analyse 3-D shapes through 2-D projections, including plans and elevations. |
Understand and apply Pythagoras' theorem when solving problems in 2-D and simple problems in 3-D. |
Understand and use Pythagoras' theorem to solve 3-D problems. |
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Understand and use trigonometric relationships in right-angled triangles, and use these to solve problems, including those involving bearings. |
Use trigonometric relationships in
right-angled triangles to solve 3-D problems, including finding the angles between a line and a plane. |
Draw, sketch and describe the graphs of trigonometric functions for angles of any size, including transformations involving scalings in either or both of the x and y directions. |
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Use the sine and cosine rules to solve 2-D and 3-D problems. |
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Calculate the area of a triangle using the formula ½absinC. |
