Support (from Y9 teaching programme)
• Distinguish between conventions, definitions and derived properties
• Explain how to find, calculate and use (a) the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons, (b) the interior and exterior angles of regular polygons.
• 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
• Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT |
Core (from Y9 objectives for able pupils)
• Distinguish between practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, and the effect of varying them
• Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio
• Understand and apply Pythagoras' theorem
• 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
• Know from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not; Apply these conditions to establish the congruence of triangles
• Find the locus of a point that moves according to a more complex rule, involving loci and simple constructions |
1000 Playthinks
~ 260 Three intersecting circles
~ 261 Tangents to the circle
~ 266/268 Rolling coin 1 and 2
~ 271 Rolling circle: Hypocycloid
~ 286 Polygon Wheels
~ 307 Hidden triangle
~ 328 Inscribed square
ATM 40 Problems
~ p11 Toppling a square
ATM Thinkers p31
~ Put some geometrical statements in order which creates a proof
ATM Middles
~ Around the middle pl14
MAP
Pythagoras biography
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Mymaths
Parallel Lines
Interior Exterior
Angle Proofs
Drawing Loci
Similar Triangles
Pythagoras: The Theorem
Pythagoras 3D
Circle Theorems
Congruent Triangles
Active worksheets
Various activities
Keymaths
9-3 Chapter 1, 12
ATM 40 Problems
~ p14 Inscribed and circumscribed circles
ATM Middles
~ Locus problem; Propellers; Triangle Constructions pl13; More imagining middles, pl11, Moving middles pl8
KS3
~ L3-L5, 9S1.1 Lines and angles L5
~ GR minipack
MAP
~ Circles investigations
~ 9 points on a circle
~ Compare relationships between the sides in acute / obtuse / right-angled triangles. (Sigma)
~ Locus Hocus Pocus
~ Gilbert the Goat
~ Square areas
~ Pythagorean triples
~ Pythagorean birthdays
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GSP
Construct a triangle, then the squares on the sides of the triangle. Calculate areas of the squares. Demonstrate what particular triangles give one square to be the sum of the other two. What happens with acute angled and obtuse angled triangles?
LOGO~
Use Logo software to help with reasoning of interior/exterior angles
HORN, Cornwall
~ Overlapping circles
~ Pythagorean triples
KS3/ICT
~ Generalising about polygons |
Using diagrams to support problem-solving - e.g. finding area of square with diagonal 10m, identyfing the link between the longest side and the largest angle of a triangle.
KS3 GR Minipack
~ Buildups
MAP
~ Generic assessment criteria |
Is the hypotenuse always the sloping side?
How can we identify the hypotenuse?
Is the longest side always opposite the largest angle?
The hypotenuse of a right-angled triangle is 13cm. What are the other two sides? Is there more than one solution?
Are there any patterns in the Pythagorean triples? (See Pythagorean triples )
A square has a diagonal of length 5m. What is its area?
How can you make a right angle using a piece of string?
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MAP – Level Ladders
~ Geometrical reasoning
~ Construction, loci
Extended tasks: Square areas ; Pythagorean triples
Group work
Written explanations
Oral explanations
Physical resources
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