Transcript 12 Days of Christmas

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My True Love
Sent to Me?
The Twelve Days of Christmas
On the first day of Christmas
my true love sent to me,
A partridge in a pear tree.
On the second day of Christmas
my true love sent to me,
Two turtle doves,
And a partridge in a pear tree.
On the third day of Christmas
my true love sent to me,
Three French hens,
Two Turtle doves,
And a partridge in a pear tree.
How many presents
Daysent:Presents
were
1 the 1215
2
3
4
5
10
1
3
th6
(a) On
Click to day?
(b) In
total?
start
music
....Four calling birds…
…Five golden rings…
…. Six geese a-laying…
….Seven swans a-swimming…
….Eight maids a-milking…
….Nine ladies dancing…
….Ten lords a-leaping….
….Eleven pipers piping…
….Twelve drummers drumming…
Make a table to help you calculate the number of presents given
on the 12th day and the number of presents given in total.
Day
Presents
Total
1
1
1
2
3
4
3
6
10
4
10
20
5
15
35
6
21
56
28
84
36
120
45
165
55
220
11
66
286
12
78
364
7
Stacking the triangular
8 one on top of
numbers
9 gives:
the other
10
Triangular
Numbers
Tetrahedral
?
Numbers
1
Pascal’s Triangle
1
1
1
1
Blaisé Pascal
(1623-1662)
1
1
7 x8
t7 
 28
2
1
1
1
t 12
9
6
7
8
5
1
2
3
4
You may be familiar with
Pascal’s triangle from
Algebra. The triangle shows
Natural/Counting Numbers
triangular and tetrahedral
numbers. You may also be
familiar with the formula for
the nth triangular number.
1
1
3
6
10 10
4
1
5
15 20 15
1
6
21 35 35 21
Triangular Numbers
1
1
7
28 56 70 56 28
36 84 126 126 84 36
tn 
n (n  1)
2
1
8
9
1
Tetrahedral Numbers
10 45 120 210 252 210 120 45 10 1
There is also a very nice
n (n  1)(n  2)
1 11 55 165 330formula
165 55 the
462 462for
330
11 1
Tet n 
calculating
6
th tetrahedral number.
n
1 12 66 220 495 792 924 792 495 220 66 12 1
12x13x14
Tet 12 
 364
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
6
12x13

 78
2
1
Pascal’s
Triangle
1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14
1
n (n  1)
2
3
4
n (n  1)(n  2)
6
6
12 x 13
2
3
6
8
12 x 13 x14
6
7
4
Day
Presents
Total
Day
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
Presents
Worksheet
Total