The Twelve Days of Christmas

Luke Swan & Dylan Gow-Lapham
Moonah Primary School

The maths was the best. We found out about patterns. The game of Thirty-One was the best. I learnt a lot. I am really looking forward to doing more next year. Luke

It was great! I enjoyed the work we did on The Twelve Days of Christmas. I understand number patterns much more now. Dylan

 

We read The Twelve Days of Christmas and discovered there were many more gifts sent than we had thought. Each day, all the gifts that were given on earlier days were given again. For example, on the fourth day the gifts given were:
Four colly birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.
On the fifth day the verse says:
Five gold rings,
Four colly birds,
Three French hens,
Two turtle doves,
And a partridge in a pear tree.

We then found that there was a pattern when we worked out just how many gifts there were. The pattern formed a large triangle. We then explored ways of making triangle shapes using the pattern of numbers. After we had written down the pattern, we each made an estimation of how many gifts there were, before we worked it out. We got a surprise when we added them all up, using calculators.

After doing this we explored whether we could make any more patterns using the number of gifts for each day. When we added the consecutive triangular numbers, we discovered that the totals were square numbers. We found a way of displaying squares using the square numbers.

Triangular Numbers
from
The Twelve Days of Christmas
Day
1
2
3
4
5
6
7
8
9
10
11
12 		Gifts
1 = 1
1 + 2 = 3
1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15
1 + 2 + 3 + 4 + 5 + 6 = 21
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78

How many gifts? 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364

Adding Consecutive Triangular Numbers
0 + 1 = 1
1 + 3 = 4
3 + 6 = 9
6 + 10 = 16
10 + 15 = 25
15 + 21 = 36
21 + 28 = 49
28 + 36 = 64
36 + 45 = 81
45 + 55 = 100
55 + 66 = 121
66 + 78 = 144 		1 squared = 1
2 squared = 4
3 squared = 9
4 squared = 16
5 squared = 25
6 squared = 36
7 squared = 49
8 squared = 64
9 squared = 81
10 squared = 100
11 squared = 121
12 squared = 144 		1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
10 x 10 = 100
11 x 11 = 121
12 x 12 = 144

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