5 hours Year 9 Core Autumn Term Unit 4 Geometrical reasoning: lines, angles and shapes

NNS 178–189

Autumn Term

Spring Term

Summer Term

Support (from Y8 teaching programme)
• Identify alternate angles and corresponding angles
• Understand a proof that (a) the sum of the angles of a triangle is 180 ° and of a quadrilateral is 360 ° (b) the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
• 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 geometric properties

Core (from Y9 teaching programme)
• Distinguish between conventions, definitions and derived properties
• 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.
Solve problems using properties of angles, of parallel & intersecting lines, and of triangles and other polygons , justifying inferences & explaining reasoning with diagrams and text

Extension (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.
Understand and apply Pythagoras' theorem

Starters

Main

ICT

Scaffolding

Key Questions

Notes

1000 Playthinks
~ 454/455/456 Quartering shapes
~ 464 / 468 Square in to 2 square / square into 3 squares

KS3 Interacting Y9 GR
~ Visualisations
 

MAP

~ Angle facts

~ Polygons

~ Exterior angles

 

Mymaths

Angler Game

Measuring Angles

Angle Sums

Reasoning

Parallel Lines

Interior Exterior

Pythagoras: The Theorem

Active worksheets

Various angle activities

Keymaths

9-2 Chapter 13, 1

 

ATM We can work it out
~ 16 Inscribed shape L6

KS3 Interacting Y9
~ GR Problem bank: Problems with diagrams; Problems where a diagram needs to be drawn; Pentagrams; Problems with plane mirrors

KS3 T5
~ Add-on 8: Shapes and angles

MAP
~ 3x3, 4x4, 5x5 dotty paper activities
~ Given squared dotty paper, what squares can you draw, where the vertices have to be on the dots? Are there squares of certain areas that are impossible to draw in this way?
~ Angles in polygons

HORN, Cornwall
~ Geometrical visualisations 3

KS3/ICT
~ Generalising about polygons

LOGO~

Use Logo software to help with reasoning of interior/exterior angles

MAP

~ Spokes OHTs:

~ clock (30°);

~ compass rose (45°),

~ 90° spray

~ Geostrips

~ Generic assessment criteria

~ 3x3 , 4x4 , 5x5 dotty paper


CORNWALL
Vocabulary and key questions related to the Framework

Using KS3 Interacting Y9 , resource sheet 'Flowchart of logical reasoning';

 

What reasoning links 'Angles on a straight line are 180°' to 'Vertically opposite angles are equal'?

 

Are there other links?

Why are the geometrical facts organised in this particular order, starting at the top and working down the chart?

 

What are the links and arrows intended to show?

Can you explain how to use the given facts to deduce that (a) vertically opposite angles are equal (b) alternate angles are equal?

Are the facts about triangles and polygons correctly placed in the chart?

 

MAP - Level Ladders

~ Geometric reasoning

Group work
Written explanations
Oral explanations
Physical resources

Extended tasks:
~ Squares on dotty paper
~ Angles in polygons

Whole unit can be planned from the KS3 GR unit plan