twelve days of christmas problem solving

Christmas Math Activities: Problem Solving With the 12 Days of Christmas

Here’s a fun way to connect your classroom holiday sing-a-long with fantastic math concepts – perfect for ages 8 and up! In fact, students who love math may get so caught up in all of the number patterns they can find in The 12 Days of Christmas song that they may not want to stop!

This activity requires no special materials, just paper and pencil and the lyrics of The 12 Days of Christmas. Y ou can find the lyrics along with some problem solving prompts and record sheets at the bottom of the post, available as a free printable download.

You’re probably already familiar with the song but in case you need a refresher, here’s how it begins:

The 12 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.

Now here’s the interesting question to pose to middle-grade students – have you ever wondered how many gifts in total were received? 

Many will immediately work on adding them up this way:

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 =

Although this is not going to produce the true answer, it can be a great opportunity to reinforce finding sums of 10 first.

By counting the ten made (1+ 9)+ (2 + 8) (3 + 7), and (4 + 6) and adding the remaining numbers ( +5, +10, +11, +12), the sum of 78 can be determined fairly quickly.

That’s quite a heap of presents! However, you might ask, “Is this really what the song says – that one gift is given each day?”

After a closer look at the lyrics, students will see that on the second day, it appears that the “true love” gives three gifts- two turtle doves and another partridge in a pear tree!

Now the math fun really begins! Ask students to list the days and the number of presents given! Have them predict the grand total before actually doing the figuring.

Day 1 – 1 gift Day 2 – 3 gifts Day 3 – 6 gifts Day 4 – 10 gifts

…. and so on.

This song is “super mathy” with patterns galore! Ask students to see if they notice any patterns as they figure the gifts. They might see this one:

Day 1 : 1 Day 2 : 3 (1 + 2) Day 3 : 6 (1 + 2 + 3) Day 4 : 10 (1 + 2 + 3 + 4)

Recognizing patterns in math is the basis of all kinds of more advanced work. Some students might notice the numbers of gifts received are all “triangular numbers,” numbers that can be formed by dots in triangles.

When students have a chance to work with the new sums, then total them, they should find that the grand total of all gifts received is 364 !

For older students, additional questions can lead to more discoveries. For example:

Which gifts will total a dozen by the end of the song? Partridges and drummers (Each day, one partridge will be given so there will be a total of 12. On just one day, Day 12, a dozen drummers will be given.)

Of the 364 gifts, which ones will be given in the greatest numbers? Geese and swans – (6 geese will be given a total of 7 days for a total of 42 geese; 7 swans will be given 6 out of the twelve days for a total of 42 swans)

We’ve included these questions in the printable 12 days of Christmas Math Activity Pack (which you can download and print below). The pack includes the song lyrics and four pages of Christmas math activities related to the song.

There you have it! A very “mathy” Christmas carol it is, and you may never be able to hear it again without thinking about all the computations and number applications!

RELATED: Looking for more holiday activity ideas for  school age kids? Check out our 12 Days of Christmas Fun for School Age Kids .

Printing your 12 days of christmas math activity sheets.

Click here to download: 12 Days of Christmas Math Activities . Save the PDF to your computer. Open the PDF and print the pages you require. When printing, select “Fit to printable area” (or similar) to ensure the page fits with your printer type and local paper size (these have been created at A4 size).

Having trouble accessing or downloading the file? Please try a different internet browser. Please note: All Childhood 101 printables are for personal use only, you may not use any part of this content for commercial purposes-that includes selling the document, giving it away to promote your business or website, or printing the file to sell. You may not share, loan or redistribute these documents. Teachers may use multiple copies for students in their own classroom.

Christie Burnett is a teacher, presenter, writer and the mother of two. She created Childhood 101 as a place for teachers and parents to access engaging, high quality learning ideas.

One Comment

Fabulous resource – thank you so much for sharing it…

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12 Days Of Christmas Puzzle

The puzzle:.

According to the traditional song, on the first day of Christmas (25th December), my true love sent to me:

• A partridge in a pear tree

On the second day of Christmas (26th December), my true love sent to me THREE presents:

• Two turtle doves • A partridge in a pear tree

On the third day of Christmas (27th December and so on) my true love sent to me SIX presents:

• Three French hens • Two turtle doves • A partridge in a pear tree

This carries on until the the twelfth day of Christmas, when my true love sends me:

• Twelve drummers drumming • Eleven pipers piping • Ten lords a-leaping • Nine ladies dancing • Eight maids a-milking • Seven swans a-swimming • Six geese a-laying • Five gold rings • Four calling birds • Three French hens • Two turtle doves • A partridge in a pear tree

After the twelve days of Christmas are over, how many presents has my true love sent me altogether?

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Free worksheet – Counting the Twelve Days of Christmas

Christmas is just around the corner… How about a little math twist on a familiar Christmas carol? I am sure we are all familiar with the “Twelve days of Christmas”, but has it occurred to you that the number of presents that “my true love sent to me” is a sequence of Triangular Numbers?

For each of the twelve days of Christmas, the number of gifts received is actually an accumulative number. On the first day, you get one gift (a partridge), on the second day you get three (a partridge and 2 turtle doves), and so on….

In this free worksheet, you’ll be asked to count the number of gifts you will receive on each day (there is a trick to it) and the total number of gifts you will receive up to the n-th day. Three sets of questions are provided, suitable for

• 1st and 2nd graders,
• 3rd to 5th graders,
• 6th to 8th graders.

Suggested solutions are provided at the end (don’t peek).

Free Twelve Days of Christmas Worksheet

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This Reading Mama

12 Days of Christmas Math Activity

By thisreadingmama 4 Comments

While my forte is literacy, ALuv’s {currently 2nd grade} is definitely math. Just last week, my mom {who helps me homeschool three days a week} challenged him with a 12 Days of Christmas math activity.

*This post contains affiliate links. **The 2016 updated printables can be found towards the end of this post. Just click on the teal download button.

He was to figure out how many gifts “my true love” gave each day altogether in the 12 days of Christmas song. My mom went home to figure out how many gifts there were in all and if he arrived at the same number, she would have a little prize waiting for him. He was very eager to try this out.

Once he had gone through the entire song, I challenged him to use mental math to add up the sum in each rectangle. This part was rather interesting. We had such rich discussion about several math concepts.

Math Concepts Covered

1- Introduction to multiplication. If you add 1 twelve times, it’s the same as saying 1 x 12, which equals 12.

2- Multiplication is commutative . When he got to the number 3 box, he was to add 3 ten times. He began to count by three’s to add them all up. Once he came to the sum of 30, I briefly showed him how knowing that 10 x 3 could help him solve 3 x 10. And just like addition, multiplication is commutative. The same thing happened when he calculated 6 x 7, then turned right around and multiplied 7 x 6.

3- Grouping numbers to add. Instead of adding 8+8+8+8+8 as individual 8’s, he grouped 16+16, then added 8 more. This strategy kept him from writing down all the numbers to add.

4- Using related sums to solve other addition problems . When he got to day nine, he used the sums of 16+16 from day eight to help him figure out- if 16+16 equals 32, then 9+9+9+9 (18+18) is just 4 more than 16+16.

5- Using a calculator to figure out sums. This was the first time he had used a calculator for schoolwork. He rather enjoyed doing it and got his total sum.

**Updated printables – added December, 2016!!**

The updated 12 Days of Christmas Math Activity Pack contains a printable page with the 12 days gifts plus a recording sheet, much like the one we originally used.

When we used it this year, we figured up how many gifts were given on each day.

Also included is a page with questions such as, “How many gifts were given on day 4?”

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Enjoy! ~Becky

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December 18, 2013 at 2:28 pm

What a great math assignment! I found this post through the After School linky, I would love if you shared this at my link-up: Anything Goes! http://www.joyfocusedlearning.com/2013/12/anything-goes-link-up-5.html

December 22, 2020 at 11:09 am

Thanks for taking the time to put this together and sharing. This is great!!!

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The New York Times

Wordplay | the twelve days of christmas puzzle.

The Twelve Days of Christmas Puzzle

On the twelfth day of Christmas, my true love gave to me: twelve Drummers Drumming, Eleven Pipers Piping, ten Lords-a-Leaping, nine Ladies Dancing, eight Maids-a-Milking, seven Swans-a-Swimming, six Geese-a-Laying, five Gold Rings, four Colly Birds, three French Hens, two Turtle Doves and a Partridge in a Pear Tree.

Yes — a complete omnishambles . And that was just Day Twelve. There were eleven days before that. A lot to keep track of (not to mention care for) — but terrific for a little math fun.

Our puzzle this week was suggested by educator Mark Saul .

Here’s something timely that I use a lot these days in schools. It’s about the “Twelve Days of Christmas” song. In that song, you don’t just get one partridge in a pear tree. You get 12 of them — one on every day of Christmas. And you don’t just get two turtle doves, either. You get a pair each day starting on the second day, to make 2×11 = 22 turtle doves. So you get lots of gifts, but the numbers don’t just keep going up and up. You get 11 pipers piping only twice, for 22 pipers, and you get 12 drummers drumming only once. So which gift do you get the most of?

Recap: Math is Cool!

Last week we were were asked to make sense of a mysterious pattern found on a tiled wall at the newly-opened Museum of Mathematics .

The solution: Ellen nailed it:

MATH IS COOL!

How about that. Obvious now, but not so obvious back then.

Our second puzzle last week was based on The Museum of Mathematics’ Coaster Rollers exhibit, which uses shapes of constant width as smooth-rolling ball bearings to support a gliding platform. Which of the following shapes have a constant width?

Shape F clearly works. We discussed this shape — known as a Reuleaux Triangle — to bits some time ago in a Numberplay post on manhole covers . This shape certainly has the same width in any direction. But what about the remaining 5 shapes?

As it turns out, each shape will work except for B and D. Shape D is clearly too squarish, and B needs to be a bit more rounded at the corners. But A, C, E and F each have a constant width, as noted by Giovanni Ciriani early in the week. From Mr. Ciriani:

B and D are definitely not possible. A is constructed starting from 3 lines that form an isosceles triangle with identical angles less than 60 degrees; C is the opposite, the the identical angles are more than 60 degrees. F comes from an equilateral triangle, and E from a regular pentagon.

Here’s a quick sketch showing how the vertical dimension for the various shapes remains constant at different rotations — except for shapes B and D.

Of the shapes that worked, Shape A was the most astonishing — it was a bit hard to believe at first that this shape, the most acorn-like of the collection, does, in fact, have a constant diameter.

Hendrik Ball of the UK-based Grand Illusions made this delightful short video demonstrating the seamless support provided by this particular constant-width shape. This property is hard to believe unless you actually see it — or feel it during that next trip to the MoMath.

Thank you to everyone who participated last week. In order of appearance: A cherian, Jeff, TK Sung, Golden Dragon, Peter Lynn, Maya, Giovanni Ciriani, deo, Pummy Kalsi, Hans, Dr W and frobozzz.

• Thank you, Mark Saul , for this week’s Twelve Days of Christmas Puzzle. Dr. Saul is the Director of the Center for Mathematical Talent at the Courant Institute of Mathematical Sciences .
• I’d also like to thank the MoMath associate director Cindy Lawrence for the photographs and diagrams that accompanied our MoMath puzzles last week.
• Thank you to mathematical sculptor/designer George Hart , who describes the origin of the MATH IS COOL! tiling pattern this way: “The idea of hiding text in a Truchet tiling came from David Reimann, a math professor at Albion College. I learned it when he presented it in a short paper at the 2009 Bridges Conference : David A. Reimann, “Text from Truchet Tiles.” In Craig S. Kaplan and Reza Sarhangi, editors, Bridges Banff: Mathematics, Art, Architecture, Culture , pages 325-326.”
• Thank you as well to Hendrik Ball of Grand Illusions for the permission to use the Grand Illusion shape of constant width demonstration video.
• To render TeX and display images, try Gary Hewitt’s Numberplay Comment Enhancer . You may also use the Enhancer to test your TeX before posting.
• Do you have a favorite puzzle? Send along with a swimming swan to [email protected]. You can also reach me directly at [email protected].

For a bit more Twelve Days fun, here’s Vi Hart with The Gauss Christmath Special.

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Teachnet.com

Creative perspectives on education and classroom management, problem solving: the twelve days of christmas.

November 6, 2010 Teachnet Staff Christmas , Math , Winter 0

Objective: Students will use different problem-solving strategies, and creative writing.

Resources: Teacher: Teacher copies of Brian Wildsmith’s “The Twelve Days of Christmas.” Student: pencil, paper, calculator.

1. Procedure: Hand out copies of “The Twelve Days of Christmas. 2. Read through the song with the class. 3. Ask students to solve the problem of how many presents were given.

Variations/Options:

* Use this lesson as an opportunity to explain sequences, in this case 1+12 six times to find the answer. * Students can research prices of each gift. * Have students substitute present-day items that they think might be more appropriate. * Discuss the historical context of each gift from the song. * Have students write their own rap version of the song. * Students can do a creative writing exercise describing the consequences of having all these gifts around twelve days or twelve weeks AFTER Christmas.

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What Are the 12 Days of Christmas, and What Do They Mean?

L ove it or hate it, “The 12 Days of Christmas” is a staple tune of, well, Christmas. Singing it over and over again, or perhaps yucking it up to a popular parody, is one of many favorite Christmas traditions . But it’s a bit bizarre! Why is it so long? Why 12 days? Why those gifts? (Can you even call flocks upon flocks of birds “gifts”?) And is there a more hidden tie-in to Christmassymbols?

If you’ve ever wondered about the meaning behind the 12 days of Christmas, don’t worrywe’ll get to the bottom of all of it. (Well, mostly.)

Get Readers Digest s Read Up newsletter for more holidays, humor, cleaning, travel, tech and fun facts all week long.

What are the 12 days of Christmas?

First of all, let’s tackle the “12 days” part. When are those days supposed to start? And where does Christmas fall in the 12 days?

All singing aside, there actually is a historical basis for the traditional Christmas carol we all know and love. Christians have historically celebrated a period of 12 days surrounding Christmas. The nearly two-week time period starts and ends with two pretty significant holidays: Christmas on Dec. 25, and the Epiphany on Jan. 6.

Christians believe that the 12 days of Christmas mark the amount of time it took after the birth of Jesus for the magi, or wise men, to travel to Bethlehem for the Epiphany when they recognized him as the son of God. The specific time period was likely part of the early church’s effort to adapt pre-Christian celebrations that helped the ancient Europeans get through the long winter nights .

With Christmas as the first day, every one of the 12 days celebrates a different saint, from St. John the Apostle on Dec. 27 to the Virgin Mary on Jan. 1. Today, howand whenthe 12 days are celebrated by Christians around the world varies. Eastern Orthodox churches use a different religious calendar, so their 12 days of Christmas start on Jan. 7 and run through the Epiphany on Jan. 19. And while Catholics celebrate the Epiphany as a single day, some Protestant churches celebrate it until Ash Wednesday, leading into the season of Lent and Easter.

Gift-giving customs also differ in some cultures. In some Latin American cultures, Christians hand out presents on Jan. 6, which they celebrate as Three Kings Day, instead of Dec. 25. And other cultures give gifts all 12 days. Like a certain “true love” we’re familiar with, thanks to an earworm of a song.

The meaning behind “The 12 Days of Christmas”

So what does the song itself mean?

Well, let’s get one thing straightit is not a secret coded song that persecuted Catholics used to teach children scripture without drawing the ire of those in power. This oft-circulated internet theory claims that each numbered “gift” represents a symbol of Christianity: “three French hens” for the Holy Trinity, “eight maids a-milking” for the eight Beatitudes, etc. But Snopes has debunked this theory; it has enough inconsistencies, and little enough evidence, to be almost assuredly just a myth.

So, what is the meaning of “The 12 Days of Christmas”? Well, it doesn’t really mean anything. Instead, the song most likely began as a memory game for kids. That’s why it’s so dang long and repetitive!

“The first known version of it was in a 1780 children’s book called Mirth Without Mischief ,” explains Ed Daly, author of The Christmas Book: The Ultimate Guide to Your Favorite Holiday . As Daly describes, “It was kind of like a more innocent ‘truth or dare.'” Basically, kids would challenge each other to recite the words from memory, adding on a new line every time (as the song does today). It was a Christmas activity where, if you messed up, you’d have to do a favor for whomever challenged you to the game, perhaps, or give them a kiss or some candy. “People would sing it at Twelfth Night [the eve of the Epiphany],” Daly says.

Have “The 12 Days of Christmas” lyrics changed over the years?

For as long as the song has been around, there have been slightly different versions of “The 12 Days of Christmas.” Even today, you’ll see some number jumbling, specifically among the bigger numbers: Is it 10 or 12 lords a-leaping, and 11 or 9 ladies dancing? And in past versions that can be found in old songbooks , it’s the narrator’s mother, not a true love, who gives all these lavish gifts.

Others still include gifts like “bears a-baiting” or “ships a-sailing” that you won’t find in the song today. And there may even be a “misheard lyrics” situation going on: Those “four calling birds” were probably originally intended to be “ colly birds” colly being an old-timey word for the color black.

And we’re likely misinterpreting one of the current lyrics as well. It’s not definitive, but it seems likely in the context of the song that the “five golden rings” are not referring to gold jewelry but instead to the markings on a ring-necked pheasant. That seems to make more sense (relatively speaking), since all the other gifts on the first seven days are birds. (So is that one pheasant or five pheasants?)

Either way, it’s a ton of birds! “Somebody was obsessed with birds when they came up with this!” jokes Daly.

The current version of the song is a little over a century old. Today, its final verse goes something like this:

On the twelfth day of Christmas, my true love sent to me Twelve drummers drumming Eleven pipers piping Ten lords a-leaping Nine ladies dancing Eight maids a-milking Seven swans a-swimming Six geese a-laying Five golden rings Four calling birds Three french hens Two turtle doves …

And, of course, “a partridge in a pear tree!”

“The song we know today, the version we know of it, was written by a guy named Frederic Austin in 1909,” Daly says. That encompasses the words we know today as well as the familiar tune. “From there, once Christmas music became a ‘thing,’ then you start having artists like Perry Como and John Denver and the Muppets [perform it]. All of a sudden, it became something that people knew.” And once you know it, you can’t un-know it. The Christmas music library is rife with versions and funny Christmas song parodies, and all year round it’s not uncommon to hear someone add “… and a partridge in a pear tree!” to the end of a comically long list.

“The 12 Days of Christmas” gifts: How much do they cost?

Now you know that the song was never intended to be a serious portrayal of holiday gifts . But it’s still fun to speculate about what it would actually be like to give and receive those unique giftsand the PNC Christmas Price Index provides a cost estimate every year. They account for everything from wages for the maids a-milking to the weirdly high cost of seven swans, the most expensive item.

In 2020, they even accounted for COVID, with price hikes for the gold ringsand, grimly for the art world (and the gift recipient!) but happily for the purchaser, a cost of $0 for all the musicians and dancers, to account for the cancellations of live performances. Man, we can’t even suspend our disbelief in a hypothetical scenario about a wacky Christmas song !

And how much would those gifts set you back? In 2022, if you wanted to stay true to the song and get your “true love” each day’s gifts the number of times they’re mentioned in the song, that was 364 gifts, for a whopping $197,071.09!

Daly’s main takeaway? “I’d rather take a trip around the world for two, for the price of [just] the swans!” he says.

Additional reporting by Jen McCaffery .

About the experts

• Ed Daly is the author of The Christmas Book: The Ultimate Guide to Your Favorite Holiday , a guide that teaches readers about the holiday’s origins, traditions and more.
• How Stuff Works : “What Are the 12 Days of Christmas?”
• Slate : “Merry (Russian Orthodox) Christmas!”
• BBC : “Epiphany”
• Vox : “The 12 Days of Christmas: The story behind the holidays most annoying carol”
• Snopes : “The Twelve Days of Christmas”
• Library of Congress Blogs : “Is it ‘Four Calling Birds’ or ‘Four Colly Birds?’ A ‘Twelve Days of Christmas’ Debate”
• PNC Christmas Price Index

Free Printable Christmas Cards

Christmas Wishes for Holiday Cards

Hilarious Christmas and Santa Puns

The post What Are the 12 Days of Christmas, and What Do They Mean? appeared first on Reader's Digest .

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Y5 Christmas Maths - 12 Activities

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

14 January 2022

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12 different activities including:

• The price of Christmas
• Santa Sacks
• Present prices
• Party planning
• Present logic puzzle
• Easier present logic puzzle
• 12 Days of Christmas problem solving
• Parcel Postage
• Christmas Co-ordinates (please note, this is an ActivInspire Flipchart file)
• 12 Days of Christmas fractions
• 12 Days of Christmas finding totals
• Christmas Maze

ks1 lks2 uks2 ks2 problem solving reasoning finishing exit tickets greater depth exceeding y1 y2 y3 y4 y5 y6

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