Download Yr 9 Unit 1 - Web Maths!

Yr 9 - Unit 1 - SSM – Lines, angles, shapes, construction and loci
5 lessons
Support Objectives
1 Identify alternate angles and corresponding angles; understand a proof
that: the sum of the angles 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.
NT 252, 257, 259, 262
FVT Angle facts
Kaleidos – animation of angle properties
TVT ANGLE FACTS
TVT QUADRILATERALS
2 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.
NT 267, 268
PP ANGLES- MEAUSRING AND DRAWING
3 Use straight edge and compasses to construct:
- the mid-point and perpendicular bisector of a line segment;
- the bisector of an angle;
- the perpendicular from a point to a line;
- the perpendicular from a point on a line;
construct a triangle, given three sides
NT 283, 288,
www.mathsnet.net interactive geometry
Core Objectives
1 Distinguish between conventions, definitions and derived properties.
NT page 273
2  Explain how to find, calculate and use:
- the sums of the interior and exterior angles of quadrilaterals,
pentagons and hexagons,
- interior and exterior angles of regular polygons
NT 278
FVT Angle facts
Properties of quadrilaterals task
Regular polygons worksheet
Investigate using LOGO or Geometers Sketchpad
Interior angles of polygons
Level
NNS
Ref
5
180183
5
180183
7
Level
6
220223
NNS
Ref
181189
Exterior Angles
3
4
5
6
Polygon tool
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.
NT 273, 286
FVT Angle facts
TVT ANGLE FACTS
TVT QUADRILATERALS
Kaleidos - Animation of angle facts
Parallel and Perpendicular Lines
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.
NT pg 92
PPT Parts of a circle
Parts of a circle
Circles (Lgfl)
The Circle (PowerPoint)
Use straight edge and compasses to construct a triangle, given right
angle, hypotenuse and side (RHS); use ICT to explore constructions of
triangles and other 2-D shapes
NT 294
Find the locus of a point that moves according to a simple rule, both by
reasoning and by using ICT.
NT 297
6
181189
5
194197
5
182
7
224227
Maths 4 Real 2: Set B - Loci (video)
Worksheets
Channel 4 worksheets with exam questions based on the programme
PP LOCI
Extension Objectives
1 Distinguish between practical demonstration and proof; know underlying
assumptions, recognising their importance and limitations, and the
effect of varying them.
NT 247, 248
2 Understand and apply Pythagoras’ theorem
NT 254
FVT PYTHAGORAS
TVT PYTHAGORAS
PPT Forts Problem
3 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
Level
7
NNS
Ref
184189
NT 285
Investigate using Geometers sketchpad
Boardworks - Geometry
4 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.
NT 270
5 Find the locus of a point that moves according to a more complex rule,
involving loci and simple constructions
NT 287
PP LOCI
8
223
7
224227
Vocabulary
Alternate angle, Corresponding angle, Exterior angle, Interior angle, Bisect, Perpendicular
bisector, construction lines, equidistant, midpoint, Interior, exterior, polygons, parallel, radius,
diameter, circumference, chord, tangent, sector, segment, hypotenuse, locus
Ideas for starters
Whiteboards – Draw an angle on a straight line where the missing angle is …..
Whiteboards – Two angles on a straight line are….., Two angle in a triangle are…, what is the
missing angle
Whiteboards – describing a shape, pupils must write down the name of this shape
Boardworks – Geometry
Mental arithmetic practice – use questions from past KS3 Mental Tests
Whiteboards – Interior and exterior angles of regular polygons
Whiteboards – Sketch the locus given a particular rule
Whiteboards – substitution problems with squares (e.g. a=5, b=7 calculate a2+b2)
Whiteboards – square roots and squaring numbers, including decimals and fractions
Whiteboards – calculate the length of hypotenuse or short side, leaving answer as a square
root.
HOLS/maths investigations
Pupils in the hall or outside. Construct loci with pupils.
Investigate angle properties of regular polygons. Use Geometers Sketchpad.
Pythagoras Fort’s Problem – Where should the bridge be put so that the soldiers walk the
shortest distance possible? (Use Powerpoint introduction). Excellent to use with an Excel
spreadsheet.
Take students into hall or outside. Construct loci using students
Investigate SSS SAS ASA RHS SSA and AAA. Which are unique, and which can be drawn in
different ways?
ICT links / citizenship
www.mathsnet.net interactive geometry
Geometers sketchpad for investigating angle properties
Excel – use to investigate the Forts Problem
Ideas for plenaries
Noughts and crosses – use angle fact questions
Millionaire – use angle fact questions
In the hot seat – pupils to draw a difficult angles question on their whiteboard. One pupil
comes into the hot seat, chooses a pupil from the other team and must answer their question
Boardworks – geometry. Use for constructions to summarise and recap at end of lesson.
KS3 Exam Questions
Given a right angled triangle, calculate the missing side leaving your answer as a square root
KS3 Exam questions
Ideas for homework
Webmaths – Angle facts 1
Webmaths – Angles-parallel lines
Webmaths – Pythagoras hypotenuse
Webmaths – Pythagoras short side
Ideas for Formative Comments –ALL LINKS ARE FROM WEBMATHS
(1) Be able to use angle facts to solve problems
Unit 1 Angle facts 1
Unit 1 Angles in a triangle
(2) Be able to use parallel and intersecting lines to solve angle problems
Unit 1 Angles-parallel lines
Unit 1 Mixed angle facts 2
(3) I need to practice constructing triangles
(4) I need to practice more questions on finding the interior or exterior angle in any regular
sided polygon
Unit 4 Regular polygons
(5) I need to be able to use Pythagoras rule to find the missing side ina right angled triangle
Unit 1 Pythagoras hypotenuse
Unit 1 Pythagoras short side
(6) I need to be able to find the locus of a point that moves according to a simple rule, both
by reasoning and by using ICT.
(7) I need to recognise and name different parts of a circle