1. Investigate some
Properties of
Pascal’s Triangle

2. 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)

3. 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

4. 8
7
6
5
49
3
2
1
27
26
25
24
23
28
22
21
20
29
17
16
15
14
13
18
12 11
10
19
37
36
35
34
33
38
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