Yr 9 Unit 1 – Shape, Space and Measure – Higher
8 lessons
Area and Volume
Support Objectives
1 Recognise corresponding angles and alternate angles.
AQA Foundation I page 19.
2 Understand and use three-figure bearings
AQA Foundation I pages 20 – 21.
Maths 4 Real Bearings Video clip
Maths 4 Real Supporting Worksheets
1
2
3
4
Core Objectives
Find the perimeter of a semicircle.
FVT Circumference and area
Find the area of a semicircle.
Maths 4 Real Video clip Areas of Circles and Composite Shapes
Maths 4 Real Supporting Worksheets
Maths 4 Real Supporting Worksheet Answers
Calculate volumes of triangular prisms, parallelogram-based
prisms and cylinders. Convert between measures of volume.
FVT Volume
Maths 4 Real Volume of Prisms Video Clip
Maths 4 Real Supporting Worksheets
Maths 4 Real Supporting Worksheets Answers
Solve problems involving surface areas of prisms and cylinders.
Convert between measures of area.
Nets and surface area of solids
FVT Surface area
Extension Objectives
1 Find the volume and surface area of pyramids, cones and
spheres. Find the volume of the top cone of a truncated cone.
FVT Volume
2 Find the length of the major arc of a circle. Find the area of
the major sector of a circle. Find the area of a segment of a
circle.
FVT Circumference and area
3 Find the volume of the frustum of a truncated cone.
Vocabulary
Revolution
Perpendicular lines
Bearing
Polygon
Rectangle
Kite
Area
Reflex angle
Alternate angles
Corresponding angles Acute angle
Obtuse angle
Transversal
Triangle
Quadrilateral
Rhombus
Parallelogram
Pentagon
Hexagon
Perimeter
Solid
Grade
D
Ref
F3.2c
D
F3.4b
Grade
C
Ref
H3.4d
C
H3.4d
C
C
Grade
A
Ref
H3.3i
A
H3.2i
H3.4d
A*
H3.3i
Right angle
Parallel lines
Shape
Square
Trapezium
Octagon
Face
Cube
Cross section
Capacity
Pyramid
Semi circle
Diameter
Segment
Cuboid
Prism
Net
Cone
Quadrant
Circumference
Tangent
Vertex
Cylinder
Sphere
Frustum
Radius
Arc
Edge
Volume
Hemisphere
Circle
Chord
Sector
Ideas for starters
*The front of the classroom is north. Point to (or turn to face) south, then east and west.
Start from north and turn through 45, 120, 200 etc.
*Put a large clock face on the whiteboard. Put in 12, then 6, then 3 then 9. Why do these
first? What angles are involved? (Easier to sketch lines at 90 or 180 same as a straight
line.) Put in the other numbers and consider where hands point at various times from ‘o’
clocks’ via ‘half-pasts’ to harder times if appropriate. This could be done by students in pairs,
working on paper.
* Work in pairs. A draws an angle-B guesses the size. A measures it and B checks their
measurement. One point scored for a guess within 20, 2 points if within 10. Give some tips
such as comparison with 45, 90, 135, 180. Students should soon realise it is harder to
guess angles > 90 and this should lead to thinking whether an angle is obtuse before
measuring it.
*Sketch on the whiteboard the first three diagrams in learn 3, that is, one for angles round a
point, one for angles on a straight line, one for opposite angles. Label them as A, B, C, A, B, C
etc. Each student copies their assigned diagram and measures the angles. Discuss the results.
Be prepared to dispel the illusion that everyone ought to be getting exactly 180 or 360.
*Ask for a definition of parallel lines. Ask each student to think of three examples of parallel
lines in the room, or in the countryside. Repeat with perpendicular lines. Sketch a five-barred
gate with transverse strut-consider the angles on it.
*Project a map of the local area onto the whiteboard (could be a street map). Use your
hometown (or a building on the street map) as the base point. Select a town roughly due north
of the base point-how would you describe its direction from the base point? Repeat for east
or west, then roughly north- east, south- west. Now select a town on a bearing of (say) 020show the need for more precise directions: students guess at the bearing angle. Repeat for
120, then 200 then 280 (that is, for each quadrant).
HOLS/maths investigations
* AQA Foundation I page 16.
ICT links / citizenship
* Boardworks – Geometry, Dominoes, Face up / Face down Pelmanism (supplementary and
complementary angles)
* Kaleidos – Animation of angle properties, Pentangle stars (estimating and recognizing
angles), Where am I? (estimating bearings), Flight 405.
* Estimating angles – My Computer/RM Shared Documents/!We-Learn Day 2/AJP/We-Learn
Day 2 JK/TTK Effective Practices/Page 18 (Banana Hunt)
Ideas for plenaries
*Ask pairs to make up questions of the type: ‘I am facing north and have turned through 90
clockwise. Where did I start from?’
*Ask the class to think of a time when the angle between the hour and minute hands of a
clock is:
A 90 (3 o’clock or 9 o’clock are easiest)
B 120 (4 o’clock or 8 o’clock)
C 110 (20 past 12)
*Use the first three diagrams from learn 3. Ask pairs to make up questions to which the
answer is 77.
*Ask for definitions of words included In the vocabulary section.
*If the bearing from A to B is 050, what is the bearing of B from A? This is known as the
back bearing. Use corresponding or alternate angles for finding several of these.
Ideas for homework
* AQA Foundation I Homework book. Chapter 2. Numbers 1, 2, 3, 4,5.
* Make up 5 questions where another person has to work out the size of the missing angles to
bring in next lesson for your partner to solve. Make sure you work out the answers so you can
mark them.
* Learn the definitions for the different types of angles and lines.
Webmaths Y9 Angles Parallel lines
Webmaths Circumference and area of circles
Webmaths Y9 Area of a circle
Webmaths Y9 Circumference of a circle
Webmaths Y10I Circles
Webmaths Y10H Arc Length and sector area
Webmaths Y10I Volume of a prism
Ideas for Formative Comments
* Learn the difference between acute, obtuse and reflex angles.
* Make sure you use a protractor accurately to measure angles.
* Remember that the angles on a straight line add up to 1800 and the angles around a point
add up to 3600.
* Learnt the difference between perpendicular and parallel lines.
* Learn the difference between and be able to recognize corresponding and alternate angles.