Lesson 9B
Y9 Objective: 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;
Pre-requisite learning:
Y7 objectives:
Identify parallel and perpendicular lines; know the sum of angles at
a point, on a straight line and in a triangle, and recognise vertically opposite angles. Begin to
identify and use angle, side and symmetry properties of triangles and quadrilaterals; solve
geometrical problems involving these properties, using step-by-step deduction and explaining
reasoning with diagrams and text.
Y8 objectives:
Identify alternate angles and corresponding angles; understand a
proof that: the sum of the angles of a triangle is 180o and of a quadrilateral is 360o; Solve
geometrical problems using side and angle properties of equilateral, isosceles and right-angled
triangles and special quadrilaterals, explaining reasoning with diagrams and text.
Resources:
OHT 9B.1, whiteboards, worksheets, (cube structure if possible)
Vocabulary: alternate and corresponding angles, parallel lines, transversal, justify, generalise.
Starter:
Frame of cube as per OHT 9B.1; whiteboards
Why have I used different colours to make this cube?
Select from the following questions:
Give me a side equal to AB?
Give me a side equal to DB?
Name a side parallel to AB? (colour)
Name a side perpendicular to AB? (push for colour generalisations)
Give me an angle equal to DBC? Get several pupils to justify answers; involve other planes.
Give me two points that are furthest apart
Give me a plane parallel to ABCD
Give me a plane perpendicular to ABCD
Main activity
Angle fact cards
(Pick first five questions from ‘drawing diagrams’ worksheet; give each group a question and get
them to draw the diagram). Agree on correct diagram and stick board to class board.
Model solution to one of them.
Give out other sheet of the problems. Pupils work in groups to produce solutions to their own
question first, convince another group.
Plenary:
Get two groups of pupils to present proofs to the rest of the class. Ask if others if they did it
another way.
Buckinghamshire KS3 Developing Geometrical Reasoning