Before our winter break, we had a sing along, and at one point we sang the familiar favourite, “The Twelve Days of Christmas.” We got to wondering, if you were the person in the song receiving all those gifts from your true love, after the 12th day, how many gifts would you have received?
image by Leo Reynolds https://www.flickr.com/photos/lwr/with/71774909/
It’s an interesting problem. We had to spend a lot of time working on our understanding of it. We found it depended on what counted as a gift. We ended up discussing a few other questions as well. We also found that keeping track of our thinking and our solutions got tricky, and organising how we recorded our ideas made a big difference.
If you have some thoughts to contribute toward tackling this question, please feel free to add them in a comment. Happy New Year!
if each gift counts as one and the repeats in the song are gust about what was already received not new gifts. if i was the person in the song i have received twelve presents in twelve days.
Explaining how you are counting up the gifts helps us as readers to understand your solution. Based on this way of thinking about the gifts in the song, could you figure out how many gifts you’d receive if there was a 13th or a 20th day or any number of days?
One amount of gifts is 12.
Two turtle doves counts as one gift and the partridge counts as one because the tree comes with the partridge and the second dove comes with the first one.
GOODBY
I see how you are counting the gifts. Thinking of the gifts in this way, how many partridges in pear trees would you end up with?
How many gifts would you receive in total after the 12th day?
on the 12 day of Christmas I would have received 364 gifts
OK, how do you figure that? Why wouldn’t it be 360 or 7 or 83? Show how you know; help us see your thoughts.
The 12 Days Of Christmas
So what I did for the 12 days of Christmas was I counted how much times it says a partridge in a pear tree or two turtle doves or three french hens whatever it says and count how much you get in one day of a partridge in a pear tree whatever it says and then you will get the answer. So if I was the person in the song I would have received 364 gifts
P.S. I got three answers but I think this one was the one that I wanted to show everyone
Interesting. It seems like you organised your work around the types of gifts there were; that was probably helpful. Did you notice any patterns that also helped? How did you keep track of your counting? Did you keep a tally as you sang the song or write down the number of partridges, turtle doves, hens, etc.?
If i was the person in the song “The 12 Days Of Christmas” and i received all those gifts, well, there are different answers to this question.The one i’m going to say is that you would end up with 78 gifts after the 12th day. I made a table showing what day i’m on, how many gifts i received that day, and the total of gifts i have after that day. I added the total i had the day before by how many gifts i received that day. I ended up with 78 gifts.
I can get a good idea of how you came up with your solution from this short, clear description. Have you used this strategy (making a table) before? What made it useful; how did it help you as you thought about and worked on your solution?
I think that this is a awesome challenge and i really like challenges.When i was writing i was way behind because i was taking a vacation.When this suddenly came up i panicked.So when i started i messed up because i was to panicked to really think.Over the time i became more calm and continued with my answer.My answer is…371.My answer is that is that because i treated when he got the presents over and over he got a duplicate and i treat the numbers as if he got that much.
I’m glad you enjoyed the challenge. What do you think made you panic over the problem? How were you able to calm down? Do you think this experience will help you if you find yourself feeling the same way in the future?
The strategies that i used to answer the problem was organised table and solving a simpler problem.If i were the person that was receiving the gifts i would get 365 gifts in total
I’m glad you can identify some useful strategies. Can you say more about how those strategies worked (and maybe help some readers who might not be familiar with those strategies understand what they are).
i found this problem really interesting because there are more then one answer these are some answers that i got.I got 75,376 and 12
Seventy-five thousand three hundred seventy-six gifts!? Wow! That would take up a lot of space. Tell us more about what went into that figure.
I would have 78 gifts if i get one thing on the 12 days of Christmas and if i got the same thing and the new thing on the 12 days of Christmas Then I would have 358 Gifts.
I’m afraid I don’t quite follow you. Which things are you writing about? Maybe a specific example from a particular day would help your readers understand what you mean.
If I was the person singing the song “The 12 Days of Christmas” I would have received 78 gifts after the 12 days of Christmas if I only got new gifts every day and was just singing about the gifts I got everyday.
Since I was in class to hear ideas and questions many people shared, I think I know what you mean. I’m not sure that other readers will know what you are getting at. Maybe tell us what it would mean if you weren’t “just singing about the gifts [you] got [every day].”
If I was the person in The Twelve Days Of Christmas receiving the gifts I would’ve gotten 78 gifts here’s how I got it. How I got that much gifts is everyday I get 1 gift but I’m so happy about the previous gifts that I keep on singing about them so there’s how I got the gifts.
I understand how some of us have come up with 78 gifts, but I’m a little confused by your explanation. If you received one gift each day and the repetition in the song is just an expression of joy and not a description of repeat gifts received daily (i.e. on day two you get 1 new gift, the turtle doves, but do not receive another partridge), then wouldn’t you end up with only twelve gifts?
A strategy I used was a organized table. I realized that it was much, much easier then using some of my first couple ideas, such as using a calcalator, drawing, etc.
Go and check out my solution!!!
https://docs.google.com/document/d/17NAbs_7hw3gXury1_BWLZwLOWYr8CjIUJhnhbHPqR9w/edit?usp=sharing
The link to your document showing your table worked well; thank you for showing your thinking. Would this strategy help you find other solutions? Do you think you could generalize your solution to find the number of gifts for ANY number of days?
my questions are do you get the same gifts every day like one gift for the first day and two for the second day and do you have to add them or not and my answer for total gifts was 78 how i got the answer was i counted the numbers that the song sang and that’s how i came with my answer.
It seems like you must have answered the questions you started your comment with if you came up with 78 gifts as a total. Did you count one gift for day one and two gifts for day 2 and so on?
How i got this answer wasn’t easy but i found a way i had a mission. to found out have many gifts where in 12 days of Christmas. i had 12 gifts i had to plus them and add them 1 to 12 and my running total was coo coo but my answer was seventy eight.
What did you notice about your running total that was cuckoo? How were you able to decide that you were satisfied with the sum you came up with (78)? Do you think there could be other possible solutions?
After the 12 Days of Christmas you would have received 78 gifts
How I understand the problem was that I started from 12 because there are 12 days of Christmas and I subtracted one and added the number of gifts each day
How did you determine what the number of gifts each day was? (We talked in class about how there might be different ways of understanding the story as told in the song.) Were you able to find a pattern or shortcut? Might there be other possible solutions?
The way I got the number 364 is I add all the number together
What numbers did you add? Why?
i pretended on the 5th day i got 5 presents then i got 6 presents on the
6th day i added all the presents i got 78 if there was a 13th day i would have 91
presents
What strategies did you use to help keep track of your work? Did you find a way to calculate the number of gifts received after any number of days?
I have 2 interpretations to the question, one being the interpretation which you count “two turtle doves” as two gifts, and you repeatedly get “partridges in pear trees” 12 times. The answer for interpretation 1 is 364. My second interpretation is where “two turtle doves” count as two gifts but, you only get “a partridge in a pear tree” once on the first day. The answer to interpretation 2 is 78.
Your comments bring two questions to my mind. Did you find any patterns or shortcuts that helped you make the calculation for your first interpretation of the problem, the one that lead to there being 364 gifts? What difference would it make if you counted each gift as just one gift, no matter how many items it included (e.g. two turtle doves given together are counted as just one gift) but you receive gifts repeatedly (ending up with 12 partridges among other things).
You are the person In the song The 12 Days Of Christmas.
2 turtle doves count as 2 gifts and your true love gives you repeat gifts.
If you were receiving these gifts the after the 12 Th day of Christmas you would have received 364 gifts.
Also the first day of Christmas is Dec 25 and the last is Jan 6.
That would be a lot of gifts! What strategies helped you? Are there other possible solutions? Did you find any patterns that could help us find the number of gifts for any number of days?