Teach%20GCSE%20Maths

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Teach GCSE Maths
Shape, Space and Measures
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The pages that follow are sample slides from the
113 presentations that cover the work for Shape,
Space and Measures.
A Microsoft WORD file, giving more information,
is included in the folder.
The animations pause after each piece of text.
To continue, either click the left mouse button,
press the space bar or press the forward arrow
key on the keyboard.
Animations will not work correctly unless
Powerpoint 2002 or later is used.
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F4 Exterior Angle of a Triangle
This first sequence of slides comes from a
Foundation presentation. The slides remind
students of a property of triangles that they
have previously met. These first slides also show
how, from time to time, the presentations ask
students to exchange ideas so that they gain
confidence.
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We already know that the sum of the angles of any
triangle is 180?.
e.g.
57? 75? 48? 180?
57?
exterior angle
a
75?
48?
If we extend one side . . .
a is called an exterior angle of the triangle
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We already know that the sum of the angles of any
triangle is 180?.
e.g.
57? 75? 48? 180?
57?
exterior angle
a
132?
75?
48?
Tell your partner what size a is.
Ans a 180? 48? 132?
( angles on a straight line )
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We already know that the sum of the angles of any
triangle is 180?.
e.g.
57? 75? 48? 180?
57?
exterior angle
132?
75?
48?
What is the link between 132? and the other 2
angles of the triangle?
ANS 132? 57? 75?, the sum of the other
angles.
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F12 Quadrilaterals Interior Angles
The presentations usually end with a basic
exercise which can be used to test the students
understanding of the topic. Solutions are given
to these exercises.
Formal algebra is not used at this level but
angles are labelled with letters.
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Exercise
1. In the following, find the marked angles,
giving your reasons
a
115?
(a)
60?
b
37?
(b)
40?
105?
c
30?
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Exercise
Solutions
a
115?
120?
(a)
60?
b
37?
a 180? - 60?
( angles on a straight line )
120?
b 360? - 120? - 115? - 37?
(angles of quadrilateral )
88?
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Exercise
(b)
40?
105?
150?
x
c
30?
Using an extra letter
x 180? - 30?
( angles on a straight line )
150?
c 360? - 105? - 40? - 150?
( angles of quadrilateral )
65?
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F14 Parallelograms
By the time they reach this topic, students have
already met the idea of congruence. Here it is
being used to illustrate a property of
parallelograms.
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Triangles SPQ and QRS are congruent.
So, SP QR
and PQ RS
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F19 Rotational Symmetry
Animation is used here to illustrate a new idea.
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This snowflake has 6 identical branches.
When it makes a complete turn, the shape fits
onto itself 6 times.
The shape has rotational symmetry of order 6.
( We dont count the 1st position as its the
same as the last. )
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F21 Reading Scales
An everyday example is used here to test
understanding of reading scales and the
opportunity is taken to point out a common
conversion formula.
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This is a copy of a cars speedometer.
Tell your partner what 1 division measures on
each scale.
It is common to find the per written as p in
miles per hour . . .
but as / in kilometres per hour.
Ans 5 mph on the outer scale and 4 km/h on the
inner.
Can you see what the conversion factor is between
miles and kilometres?
Ans e.g. 160 km 100 miles.
Dividing by 20 gives 8 km 5 miles
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F26 Nets of a Cuboid and Cylinder
Some students find it difficult to visualise the
net of a 3-D object, so animation is used here to
help them.
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Suppose we open a cardboard box and flatten it
out.
This is a net
Rules for nets
We must not cut across a face.
We ignore any overlaps.
We finish up with one piece.
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O2 Bearings
This is an example from an early Overlap file.
The file treats the topic at C/D level so is
useful for students working at either Foundation
or Higher level.
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e.g. The bearing of R from P is 220? and R is due
west of Q. Mark the position of R on the diagram.
Solution
P
x
Q
x
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e.g. The bearing of R from P is 220? and R is due
west of Q. Mark the position of R on the diagram.
Solution
P
x
.
Q
x
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e.g. The bearing of R from P is 220? and R is due
west of Q. Mark the position of R on the diagram.
Solution
P
x
.
Q
x
If you only have a semicircular protractor, you
need to
subtract 180 from 220 and measure from south.
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e.g. The bearing of R from P is 220? and R is due
west of Q. Mark the position of R on the diagram.
Solution
P
x
40?
.
Q
x
If you only have a semicircular protractor, you
need to
subtract 180 from 220 and measure from south.
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e.g. The bearing of R from P is 220? and R is due
west of Q. Mark the position of R on the diagram.
Solution
P
x
.
R
Q
x
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O21 Pints, Gallons and Litres
The slide contains a worked example. The
calculator clipart is used to encourage students
to do the calculation before being shown the
answer.
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e.g. The photo shows a milk bottle and some milk
poured into a glass.
There is 200 ml of milk in the glass.
(a) Change 200 ml to litres.
(b) Change your answer to (a) into pints.
Solution
(a)
200 millilitre
02 litre
1 litre 175 pints
(b)
02 litre
02 ? 175 pints
035 pints
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O34 Symmetry of Solids
Here is an example of an animated diagram which
illustrates a point in a way that saves precious
class time.
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This is a cuboid.
Tell your partner if you can spot some planes of
symmetry.
Each plane of symmetry is like a mirror. There
are 3.
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H4 Using Congruence (1)
In this higher level presentation, students use
their knowledge of the conditions for congruence
and are learning to write out a formal proof.
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e.g.1 Using the definition of a parallelogram,
prove that the opposite sides are equal.
Proof
We need to prove that AB DC and AD BC.
Draw the diagonal DB.
Tell your partner why the triangles are congruent.
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e.g.1 Using the definition of a parallelogram,
prove that the opposite sides are equal.
Proof
We need to prove that AB DC and AD BC.
Draw the diagonal DB.
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e.g.1 Using the definition of a parallelogram,
prove that the opposite sides are equal.
Proof
We need to prove that AB DC and AD BC.
D
C
x
x
A
B
Draw the diagonal DB.
BD is common (S)
So, AB DC
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e.g.1 Using the definition of a parallelogram,
prove that the opposite sides are equal.
Proof
We need to prove that AB DC and AD BC.
D
C
x
x
A
B
Draw the diagonal DB.
BD is common (S)
So, AB DC and AD BC.
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H16 Right Angled Triangles Sin x
The following page comes from the first of a set
of presentations on Trigonometry. It shows a
typical summary with an indication that
note-taking might be useful.
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SUMMARY

• In a right angled triangle, with an angle x,

where,

• opp. is the side opposite ( or facing ) x

• hyp. is the hypotenuse ( always the longest side
  and facing the right angle )

• The letters sin are always followed by an angle.

• The sine of any angle can be found from a
  calculator ( check it is set in degrees )

e.g. sin 20
03420
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The next 4 slides contain a list of the 113 files
that make up Shape, Space and Measures.
The files have been labelled as
follows F Basic work for the Foundation
level. O Topics that are likely to give rise to
questions graded D and C. These topics form the
Overlap between Foundation and Higher and could
be examined at either level. H Topics which
appear only in the Higher level content.
Overlap files appear twice in the list so that
they can easily be accessed when working at
either Foundation or Higher level.
Also for ease of access, colours have been used
to group topics. For example, dark blue is used
at all 3 levels for work on length, area and
volume.
The 3 underlined titles contain links to the
complete files that are included in this sample.
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Page 1
Teach GCSE Maths Foundation
F1 Angles
F15 Trapezia
F2 Lines Parallel and Perpendicular
O7 Allied Angles
F16 Kites
O1 Parallel Lines and Angles
O8 Identifying Quadrilaterals
O2 Bearings
F17 Tessellations
F3 Triangles and their Angles
F18 Lines of Symmetry
F4 Exterior Angle of a Triangle
F19 Rotational Symmetry
O3 Proofs of Triangle Properties
F20 Coordinates
F5 Perimeters
F21 Reading Scales
F6 Area of a Rectangle
F22 Scales and Maps
F7 Congruent Shapes
O9 Mid-Point of AB
F8 Congruent Triangles
O10 Area of a Parallelogram
F9 Constructing Triangles SSS
O11 Area of a Triangle
F10 Constructing Triangles AAS
O12 Area of a Trapezium
F11 Constructing Triangles SAS, RHS
O13 Area of a Kite
O4 More Constructions Bisectors
O14 More Complicated Areas
O5 More Constructions Perpendiculars
O15 Angles of Polygons
F12 Quadrilaterals Interior angles
O16 Regular Polygons
F13 Quadrilaterals Exterior angles
O17 More Tessellations
F14 Parallelograms
O18 Finding Angles Revision
O6 Angle Proof for Parallelograms
continued
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Page 2
Teach GCSE Maths Foundation
O33 Plan and Elevation
F23 Metric Units
O34 Symmetry of Solids
O19 Miles and Kilometres
O35 Nets of Prisms and Pyramids
O20 Feet and Metres
O21 Pints, Gallons and Litres
O36 Volumes of Prisms
O37 Dimensions
O22 Pounds and Kilograms
F27 Surface Area of a Cuboid
O23 Accuracy in Measurements
O38 Surface Area of a Prism and Cylinder
O24 Speed
O25 Density
F28 Reflections
O26 Pythagoras Theorem
O39 More Reflections
O27 More Perimeters
O40 Even More Reflections
O28 Length of AB
F29 Enlargements
F24 Circle words
O29 Circumference of a Circle
O41 More Enlargements
O30 Area of a Circle
F30 Similar Shapes
O31 Loci
O42 Effect of Enlargements
O32 3-D Coordinates
O43 Rotations
F25 Volume of a Cuboid and Isometric Drawing
O44 Translations
O45 Mixed and Combined Transformations
F26 Nets of a Cuboid and Cylinder
continued
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Page 3
Teach GCSE Maths Higher
O1 Parallel Lines and Angles
O22 Pounds and Kilograms
O2 Bearings
O23 Accuracy in Measurements
O3 Proof of Triangle Properties
O24 Speed
O4 More Constructions bisectors
O25 Density
H2 More Accuracy in Measurements
O5 More Constructions perpendiculars
H1 Even More Constructions
O26 Pythagoras Theorem
O6 Angle Proof for Parallelograms
O27 More Perimeters
O7 Allied Angles
O28 Length of AB
O8 Identifying Quadrilaterals
H3 Proving Congruent Triangles
O9 Mid-Point of AB
H4 Using Congruence (1)
O10 Area of a Parallelogram
H5 Using Congruence (2)
O11 Area of a Triangle
H6 Similar Triangles proof
O12 Area of a Trapezium
H7 Similar Triangles finding sides
O13 Area of a Kite
O29 Circumference of a Circle
O14 More Complicated Areas
O30 Area of a Circle
O15 Angles of Polygons
H8 Chords and Tangents
O16 Regular Polygons
H9 Angle in a Segment
O17 More Tessellations
H10 Angles in a Semicircle and Cyclic
Quadrilateral
O18 Finding Angles Revision
O19 Miles and Kilometres
H11 Alternate Segment Theorem
O20 Feet and Metres
O31 Loci
O21 Pints, Gallons, Litres
H12 More Loci
continued
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Page 4
Teach GCSE Maths Higher
O32 3-D Coordinates
H20 Solving problems using Trig (2)
O33 Plan and Elevation
H21 The Graph of Sin x
H13 More Plans and Elevations
H22 The Graphs of Cos x and Tan x
O34 Symmetry of Solids
H23 Solving Trig Equations
O35 Nets of Prisms and Pyramids
H24 The Sine Rule
O36 Volumes of Prisms
H25 The Sine Rule Ambiguous Case
O37 Dimensions
H26 The Cosine Rule
O38 Surface Area of a Prism and Cylinder
H27 Trig and Area of a Triangle
O39 More Reflections
H28 Arc Length and Area of Sectors
O40 Even More Reflections
H29 Harder Volumes
O41 More Enlargements
H30 Volumes and Surface Areas of Pyramids and
Cones
O42 Effect of Enlargements
H31 Volume and Surface Area of a Sphere
O43 Rotations
O44 Translations
H32 Areas of Similar Shapes and Volumes of
Similar Solids
O45 Mixed and Combined Transformations
H33 Vectors 1
H14 More Combined Transformations
H34 Vectors 2
H15 Negative Enlargements
H35 Vectors 3
H16 Right Angled Triangles Sin x
H36 Right Angled Triangles in 3D
H17 Inverse sines
H18 cos x and tan x
H37 Sine and Cosine Rules in 3D
H38 Stretching Trig Graphs
H19 Solving problems using Trig (1)
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