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Teach GCSE Maths

Shape, Space and Measures

The pages that follow are samples 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.

F4 Exterior Angle of a Triangle

This first sequence ofs comes from a

Foundation presentation. Thes remind

students of a property of triangles that they

have previously met. These firsts also show

how, from time to time, the presentations ask

students to exchange ideas so that they gain

confidence.

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

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 )

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.

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.

Exercise

1. In the following, find the marked angles,

giving your reasons

a

115?

(a)

60?

b

37?

(b)

40?

105?

c

30?

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?

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?

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.

Triangles SPQ and QRS are congruent.

So, SP QR

and PQ RS

F19 Rotational Symmetry

Animation is used here to illustrate a new idea.

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. )

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.

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

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.

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.

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.

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

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

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.

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.

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

O21 Pints, Gallons and Litres

Thecontains a worked example. The

calculator clipart is used to encourage students

to do the calculation before being shown the

answer.

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

O34 Symmetry of Solids

Here is an example of an animated diagram which

illustrates a point in a way that saves precious

class time.

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.

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.

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.

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.

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

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.

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.

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

The next 4s 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.

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

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

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

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)

Further details of Teach GCSE Maths are

available from

Chartwell-Yorke Ltd 114 High Street Belmont

Village Bolton Lancashire BL7 8AL

Tel 01204811001 Fax 01204 811008

www.chartwellyorke.co.uk/

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