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3. My True Love Sent to Me?

4. 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 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.....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… Day 1 Presents 1 Day 2 Presents 3 Day 3 Presents 6 Day 4 Presents 10 Day 5 Presents 15 How many presents were sent: (a) On the 12 th day? (b) In total? Click to start music

5. DayPresentsTotal 111 234 3 4 5 6 7 8 9 10 11 12 DayPresentsTotal 111 234 3610 4 20 51535 62156 72884 836120 945165 1055220 1166286 1278364 Triangular Numbers ? Numbers Tetrahedral Numbers Stacking the triangular numbers one on top of the other gives: Make a table to help you calculate the number of presents given on the 12 th day and the number of presents given in total.

6. 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 33 464 5510 6156 20 7 721 35 88 2856285670 9 3684 126 84 36 9 10 45 210 252 210 120 45 120 10 11 55 330 462 330 165 55 11 12 66 495 792924 792 495 220 66 12 1716 13 78 286 715 1287 1716 1287 715 286 78 13 Pascal’s Triangle Blaisé Pascal (1623-1662) Triangular Numbers Tetrahedral Numbers 1 14 3003 14 91 364 1001 2002 3432 30032002 1001 364 91 1 Natural/Counting Numbers You may be familiar with Pascal’s triangle from Algebra. The triangle shows triangular and tetrahedral numbers. You may also be familiar with the formula for the n th triangular number. There is also a very nice formula for calculating the n th tetrahedral number.

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9. Worksheet DayPresentsTotal 1 2 3 4 5 6 7 8 9 10 11 12 DayPresentsTotal 1 2 3 4 5 6 7 8 9 10 11 12