The “Twelve Days of Christmas” is a well known song and poem that counts the 12 days from Christmas Day through to the day of the Epiphany (6th January). In the song, on each day, more and more gifts are received, and what do you know, there’s some important and significant maths going on there!
In case you don’t know the words, here’s a video with lyrics.

http://www.youtube.com/watch?v=oYHFYyZN8iQ

So let’s take a look at the maths and let’s see how you can explore this activity with your kids.

First, Second and Third Day of Christmas

So on the first day of Christmas you get one present from your true love; a partridge in a pear tree.

On the second day you get three presents; two turtle doves and another partridge in a pear tree.

On the third day you get six presents; 3 french hens, two more turtle doves and yet another partridge in a pear tree.

What’s going on here?

Day 1 = 1 present

Day 2 = 3 presents

Day 3 = 6 presents

Day 4 = ? presents

 

Can you see the pattern? By either seeing the pattern or by counting along to the next part of the song, you should count 10 presents. Then 15, then 21 and so on.

 

The numbers we’re discovering in the song are called Triangular Numbers.

Exploring the Song with your Kids

If you’re in a crafty mood, a great thing to do would be to cut out 1 partridge in a pear tree, two turtle doves, 3 french hens and so on. Here’s a great set of these that you could create with your kids.

Once you have created enough of each, you can begin to create a chart like this, watching the triangular numbers take shape, counting as you go.

Write the number of presents in a table and explore the pattern with your child. See if they can extend the table without counting out the presents.

Day (d)

1

2

3

4

5

6

Number  of Presents (N)

1

3

6

10

?

?

With younger children, you can easily finish at this point and you’d have achieved some excellent learning outcomes whilst having fun at the same time. If you’re enjoying yourself and your kids are interested you can take it to the next level with this next section.

Finding a Rule

For older children, especially those in Years 5 – 9, work together to find a rule for this pattern. This is an important pattern that they will see again and again, and the earlier you can work towards examining the pattern and finding a rule, the better.

Let’s explore it like this:

So on Day 10 we can calculate 10 multiplied by 11 divided by 2 which gives 55 presents!

Help your kids explore finding a rule using the days and the number of presents. Don’t show them these calculations straight away. For older more capable kids leave it with them for a few hours or a few days, asking them how they’re going. If they’re really stuck give them some hints like “it involves multiplying the days” or “there’s a divide by 2 in there somewhere” and so on.

How many presents altogether?

And my last challenge for you and your kids, how many presents do you get altogether for the 12 days? Can you find a rule for working this out too?

Photo credit: Leo Reynolds / Foter.com / CC BY-NC-SA