Announcing the release of Announcing the release of

VERSION 6VERSION 6

This Demo shows just This Demo shows just 2020 of the 10,000 available slides and of the 10,000 available slides and takes 7 minutes to run through. Please note that in the takes 7 minutes to run through. Please note that in the

proper presentations the teacher controls every proper presentations the teacher controls every movement/animation by use of the mouse/pen.movement/animation by use of the mouse/pen.Click when ready

•750 MB of Presentations750 MB of Presentations

•500+ files/10 000+ Slides500+ files/10 000+ Slides

•New Functional Maths ElementNew Functional Maths Element

•100’s of Worksheets100’s of Worksheets

•100’s of teacher Q + A Sheets100’s of teacher Q + A Sheets

•1000’s of Teaching Hours1000’s of Teaching Hours

•1200 Interactive SAT/GCSE Boosters1200 Interactive SAT/GCSE Boosters

•Huge Enrichment AreaHuge Enrichment Area

•Database of PresentationsDatabase of Presentations

Click when ready

Whiteboardmaths.comWhiteboardmaths.com

© 2004 - 2008 All rights reserved

Stand SW 100

In addition to the demos/free presentations in this area there are at least 8 complete (and FREE) presentations waiting for download under the My Account button. Simply register to download immediately.

Drawing the graph of a quadratic

function?

This is a short demo that auto-runs.

0 1 2 3 4-1-2

1

2

3

4

5

6

7

8

-1

-2

-3

-4

-5

-6

-7

-8

5

y

-3

-9

x

y = x2 - 2x - 8

x -3 -2 -1 0 1 2 3 4 5

x2

-2x

-8

y

9 4 1 0 1 4 9 16

25

6 4 2 0 -2 -4 -6 -8 -10

-8 -8 -8 -8 -8 -8 -8 -8 -8

7 0 -5 -8 -9 -8 -5 0 7

LoSEquation of Line of symmetry is x = 1

Drawing quadratic graphs of the form y = ax2 + bx + c

Example 1.

Minimum point

at (1, -9)

Look at graphs of some trig functions?

sinx + circle90o 180o

0o 270o

1

-1

The Trigonometric Ratios for any

angle

0 90 180 360270-90-180-270-360

0 90 180 270-90-180-270-360 360

450o0o 90o 180o 270o 360o-90o-180o-270o-360o-450o

360o

0o

90o

180o

270o

x

270 36090-360 180

y = f(x)

0-90-180-270

1

-1

2

-2

f(x) = cosx f(x) = cos2x f(x) = cos3x f(x) = cos ½ x

Introducing addition of fractions with

different denominators?

23

14

+

+

=1112 2015

1612

129

86

43

Multiples of 3 and 4

12 is the LCM

812

Equivalent312

Equivalent

Probability for Dependent Events

Conditional Probability: Dependent Events

When events are not independent, the outcome of earlier events affects the outcome of later events. This happens in situations when the objects selected are not replaced.

A box of chocolates contains twelve chocolates of three different types. There are 3 strawberry, 4 caramel and 5 milk chocolates in the box. Sam chooses a chocolate at random and eats it. Jenny then does the same. Calculate the probability that they both choose a strawberry chocolate.

Conditional Probability: Dependent Events

P(strawberry and strawberry) = 3/12 x

A box of chocolates contains twelve chocolates of three different types. There are 3 strawberry, 4 caramel and 5 milk chocolates in the box. Sam chooses a chocolate at random and eats it. Jenny then does the same. Calculate the probability that they both choose a strawberry chocolate.

Conditional Probability: Dependent Events

P(strawberry and strawberry) = 3/12 x 2/11 = 6/132 (1/22)

Enlarge on object?

D

To enlarge the kite by scale factor x3 from the

point shown.

Centre of Enlargement

ObjectA

B

C

Image

A/

B/

C/

D/

Enlargements from a Given Point

1. Draw the ray lines through vertices.

2. Mark off x3 distances along lines from C of E.

3. Draw and label image.

No Grid 2

Do some Loci?

Q2Loci (Dogs and Goats)

Scale:1cm = 3m

Shed

Wall

Wall

A

B

1. Draw arc of circle of radius 5 cm

2. Draw ¾ circle of radius 4 cm

3. Draw a ¼ circle of radius 1 cm 4. Shade in the required region.

Billy the goat is tethered by a 15m long chain to a tree at A. Nanny the goat is tethered to the corner of a shed at B by a 12 m rope. Draw the boundary locus for both goats and shade the region that they can both occupy.

Investigate some Properties of

Pascal’s Triangle

Pascal’s Triangle

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

3 3

4 6 4

55 10 10

6156 15 20

7 72121 35 35

88 285628 56 70

9 36 84 126 126 84 36 9

10 45 210 252 210 120 45120 10

11 55 330 462 462 330 165165 55 11

12 66 495 792 924 792 495220 220 66 12

171613 78 286 715 1287 1716 1287 715 286 78 13

Pascal’s Triangle

1. Complete the rest of the triangle.

Blaisé Pascal (1623-1662)

Counting/Natural Numbers

Triangular Numbers

Tetrahedral Numbers

Pyramid Numbers (square base)

Fibonacci Sequence

1716

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

3 3

4 6 4

55 10 10

6156 15 20

7 72121 35 35

88 285628 56 70

9 36 84 126 126 84 36 9

10 45 210 252 210 120 45120 10

11 55 330 462 462 330 165165 55 11

12 66 495 792 924 792 495220 220 66 12

13 78 286 715 1287 1716 1287 715 286 78 13

Add the numbers shown along each of the shallow diagonals to find another well known sequence of numbers.

1 2 3 8 13

21 55 89

1 5

34 144 233 377

The sequence first appears as a recreational maths problem about the growth in population of rabbits in book 3 of his famous work, Liber – abaci (the book of the calculator).

Fibonacci travelled extensively throughout the Middle East and elsewhere. He strongly recommended that Europeans adopt the Indo-Arabic system of numerals including the use of a symbol for zero “zephirum”

The Fibonacci Sequence

Leonardo of Pisa 1180 - 1250

8

7

65

49

3

2

1

27

26

2524

23

28

22

21

20

29

17

16

15

1413

18

12 11

10

1937

36

35

34

3338

32

31 30

39

4746

45

44

43

48

42

41

40

49

National Lottery Jackpot? 49 balls choose 6

Choose 6

Row 49 13 983 816

There are 13 983 816 ways of choosing 6 balls from a set of 49. So buying a single ticket

means that the probability of a win is 1/13 983 816

49C6

Row 0

The Theorem of Pythagoras?

625

576

49

72+ 242

=

252

49 + 576 = 625

7

24

25

A 3rd Pythagorean Triple

7, 24, 25

In a right-angled triangle, the square on

the hypotenuse is equal to the sum of the

squares on the other two sides.

Perigal’s Dissection

The Theorem of Pythagoras: A Visual Demonstration

In a right-angled triangle, the square on the

hypotenuse is equal to the sum of the squares on

the other two sides.

Draw 2 lines through the centre of the middle square, parallel to the sides of the large square

This divides the middle square into 4 congruent quadrilaterals

These quadrilaterals + small square fit exactly into the large square

Henry Perigal

(1801 – 1898)

Gravestone Inscription

Look at one of the 6 proofs of the Theorem from the Pythagorean

Treasury.

We first need to show that the angle between angle x and angle y is a right angle.

•This angle is 90o since x + y = 90o (angle sum of a triangle) and angles on a straight line add to 180o

Take 1 identical copy of this right-angled triangle and arrange like so.

Area of trapezium

= ½ (a + b)(a + b) = ½ (a2 +2ab + b2)

Area of trapezium is also equal to the areas of the 3 right-angled

triangles.

= ½ ab + ½ ab + ½ c2

So

½ (a2 +2ab + b2) = ½ ab + ½ ab + ½ c2

a2 +2ab + b2 = 2ab + c2

a2 + b2 = c2 QED

a

b

cxo

yo

a

bc

xo

yo

Draw line:The boundary shape is a trapezium

To prove that a2 + b2 = c2

President James Garfield’s Proof(1876)

Sample some material from the Golden section

presentation.

Constructing a Golden Rectangle.

1. Construct a square and the perpendicular bisector of a side to find its midpoint p.

3. Set compass to length PM and draw an arc as shown.

2. Extend the sides as shown.

L M

4. Construct a perpendicular QR.

O N

Q

THE GOLDEN SECTION

LQRO is a Golden Rectangle.

1

P R

THE GOLDEN SECTION

Johannes Kepler 1571- 1630

"Geometry has two great treasures: one is the Theorem of Pythagoras, and the other the division of a line into extreme and mean ratio; the first we may compare to a measure of gold, the second we may name a precious jewel."

Or just simply ride your bike!

Wheels in Motion

Wheel

The Cycloid

It’s true! The point at the bottom of a moving wheel is not moving!

Choose Order Forms/New for V5 to view latest material

and other catalogues.

Click when ready

Whiteboardmaths.comWhiteboardmaths.com

© 2004 - 2008 All rights reserved

Stand SW 100

Don’t forget to pick up your 8 free presentations.