Download Shape Space and Measure 4

Yr 9 Unit 4 - SSM – Lines, angles, shapes, transformations, mensuration
3 lessons
Support Objectives
1 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 257, 259, 262, 268
FVT Angle Facts
TVT ANGLE FACTS
TVT QUADRILATERALS
Geometers sketchpad
2 Know and use geometric properties of cuboids and shapes made from
cuboids
NT 276
Boardworks – interconnecting cubes
3 Make simple scale drawings.
NT 307
ET Scales
Design a garden
4 Know and use the formula for the volume of a cuboid; calculate volumes
and surface areas of cuboids and shapes made from cuboids
NT 340
FVT VOLUME
FVT SURFACE AREA
TVT Cuboids
Core Objectives
1 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, 290
FVT Angle Facts
TVT Angle facts
TVT QUADRILATERALS
Geometers Sketcpad
2 Visualise and use 2-D representations of 3-D objects; analyse 3-D
shapes through 2-D projections, including plans and elevations.
NT 302, 305
Boardworks – interconnecting cubes
TVT Cuboids
KS3/4 Maths - Plans and Elevations (video)
Plans and Elevations
Rotating 3d Shapes
Level
6
NNS
Ref
184189
6
198201
5
216217
6
238241
Level
NNS
Ref
6
181187
6
198201
Cuboids 3d exploration
3 Use and interpret maps and scale drawings.
NT 324
ET Scales
4 Calculate the surface area and volume of right prisms.
NT 347
FVT VOLUME
FVT SURFACE AREA
TVT Cuboids
Boardworks – interconnecting cubes
Rectangular Prism SA and Volume
Volume of prisms
5
6/7
238241
5 Present a concise, reasoned argument, using symbols, diagrams and
related explanatory text; give solutions to problems to an appropriate
degree of accuracy.
Extension Objectives
1 Understand and apply Pythagoras’ theorem.
NT 350
FVT PYTHAGORAS
TVT PYTHAGORAS
PPT Forts Problem
Spaghetti and Jelly Babies to solve problems with 3D Pythagoras
2 Calculate lengths, areas and volumes in right prisms, including cylinders.
NT 337
FVT VOLUME
FVT SURFACE AREA
TVT Cuboids
3 Begin to use sine, cosine and tangent in right-angled triangles to solve
problems in two dimensions
NT 341
PP TRIGONOMETRY INTRODUCTION
FVT TRIGONOMETRY
216217
30-31
Level
7
7
NNS
Ref
186189
238241
8
242247
KS3/4 Maths - Motivating Maths at GCSE: Outdoor Trigonometry (video)
Maths 4 Real 2: Set B - The Tangent Ratio (video)
Worksheets
Channel 4 worksheets with exam questions based on the programme
Maths 4 Real 1: Set B - The Sine Ratio (video)
Worksheets
Channel 4 worksheets with exam questions based on the programme
4 Recognise limitations on the accuracy of measurements.
NT 323
FVT Lower and Upper Bounds
EP
47
Vocabulary
Equilateral, isosceles, quadrilateral, parallel, perpendicular, cube, cuboid, face, edge, vertices,
scale, volume, surface area, parallel, intersecting, regular, irregular, polygon, net,vertex, plan,
elevation, scale, volume, cube, cuboid, prism, pythagoras, opposite, adjacent, hypotenuse, sine,
cosine, tangent, prism, volume, surface area, cross section, radius, diameter, lower bound, upper
bound, maximum, minimum
Ideas for starters
Angle acronyms e.g. 180 DIAT (180 degrees in a triangle), 5 SOAP (5 sides on a pentagon)
Practice defining terms. Read on pupil’s name out and they choose one of the key words from
the board. The second pupil must explain what that word means.
NETS 1 – Draw the net of a cube and label all the corners from A to N. Ask questions like,
which point meets with A? which edge meets with DE?
NETS 2 – Draw the net of a cube with each face coloured a different colour. Ask questions
like, which face is opposite the red face, which face is not next to the blue face etc
Key Stage 3 mental arithmetic question practice
Given a right angled triangle, calculate the length of the missing side leaving your answer in
square root (surd) form
Use Pythagorean triples for non-calculator whiteboard problems
Whiteboards – estimate the circumference and area of circles. Estimate the volume and
surface area of a cylinder
Whiteboards – calculate the circumference and area of a circle, leaving your answers in terms
of pi
Whiteboards – lower and upper bound practice
HOLS/maths investigations
Give each student a letter to draw on isometric paper so that when they are put together they
read 2D REPRESENTATIONS OF 3D OBJECTS. Decide on the height of the letter. Ask
students to work out the volume and surface area of their letter.
Design a garden. Ask pupils to draw a garden to a certain scale. Calculate the amount of
fencing, paving slabs, turf they will need and work out the cost given the cost per m or the cost
per m2
Max box investigation. Given an A4 piece of paper, calculate the volume and surface area when
different sized squares are cut out of the corner
Calculate the interior angles of regular polygons by drawing polygons inside a circle and
calculating the angles by splitting up into triangles.
Pentagon triangles investigation. By drawing two lines inside a regular pentagon, split it into one
tall isosceles triangle and two identical short isosceles triangles. Calculate the angles inside
these triangles. By putting the triangles together, calculate the total interior angles of
irregular polygons.
Painted cube investigation Draw similar triangle, investigate relationships between ratios.
Find height of a tree
Investigate errors is measuring angles of inclination by comparison with calculations based on
measure of distance.
[9ex/247] The sides of a regular pentagon are 12cm. Find the length of a diagonal.
Design a toy train using cuboids, cylinders, triangular prism. Draw it to scale. Calculate the
volume and surface area of the train. Given the costs, calculate the cost of production. Given
the need for a 15% profit margin, calculate the retail price of the toy.
A cylinder must have a volume of 1000cm3. Calculate the dimensions so that the cost of
manufacture is at a minimum. (Use excel)
Using a clinometer and measuring tape, calculate the height of a building or a tree
Calculate the area of regular pentagons that all have a perimeter of 100cm
Draw similar triangle, investigate relationships between ratios.
Find height of a tree
Investigate errors is measuring angles of inclination by comparison with calculations based on
measure of distance.
The sides of a regular pentagon are 12cm. Find the length of a diagonal.
ICT links / citizenship
Max box investigation using excel
Geometers sketchpad for investigating angles in regular polygons
Kaleidos – animation of angle properties
www.mathsnet.net interactive geometry
Boardworks – geometry
Use excel for the cylinder investigation
Ideas for plenaries
Key Stage 3 Exam Questions
Noughts and crosses – angle facts/volume of cuboids/ surface area of cuboids questions
Millionaire
Hot Seat – Ask pupils to draw a diagram with missing angles on their whiteboards. Split the
class into two teams. One pupils is chosen to sit in the hot seat. They choose a pupils from the
other team and try to answer their question. If they get it right they score a point, if they do
not the other team score a point.
Just a minute – talk for 1 minute trying to list all the important facts and methods connected
with that lesson’s learning objectives
Quiz: http://www.thatquiz.org/tq/practice.html?geometry
Quiz: http://www.thatquiz.org/tq/practice.html?angles
Ideas for homework
Need to create homework tasks for this topic
Ideas for Formative Comments
(1) Be able to find the area of a variety of 2d shapes
Unit 2 Compound area and perimeter
(2) Be able to find the perimeter of 2d shapes
Unit 2 Area and perimeter
(3) Be able to find the area of a circle
Webmaths – Area of a circle
(4) Be able to find the circumference of a circle
Webmaths – Circumference of a circle
(5) Be able to find the surface area of a cube and a cuboid
Unit 2 Surface area
(6) Be able to find the volume of 3D shapes, for example a cuboid and a triangular prism
Unit 1 Volume of a prism
Unit 2 Volume of cuboids and prisms
(7) Be able to use Pythagoras to find a missing side in a right angled triangle
Unit 1 Pythagoras hypotenuse
Unit 1 Pythagoras short side
(8) Be able to solve problems associated with average speed, distance and time
Unit 3 Speed Distance Time
(9) Be able to calculate upper and lower bounds
Unit 2 Upper and lower bounds
(10) I need to practice further questions in using trigonometry to find a missing side or
length in a right angled triangle
Mixed trigonometry