12 Days of Christmas
Lesson 11 of 16
Objective: SWBAT investigate cumulative numbers with a holiday song and solve a multi-step problem.
I start by playing this song and telling students that today they will investigate how many total gifts the true love from the 12 Days of Christmas song really did get!
You can see in this video, some students are eagerly writing and making a list as the song is played while some are simply enjoying the song.
"Although algebra is a word that has not commonly been heard in grades 3-5 classrooms, the mathematical investigations and conversations of students in these grades frequently include elements of algebraic reasoning. These experiences and conversations provide rich contexts for advancing mathematical understanding and are also an important precursor to the more formalized study of algebra in the middle and secondary grades. In grades 3-5, algebraic ideas should emerge and be investigated as students --"
- identify or build numerical and geometric patterns;
- describe patterns verbally and represent them with tables or symbols;
- look for and apply relationships between varying quantities to make predictions;
- make and explain generalizations that seem to always work in particular situations;
- use graphs to describe patterns and make predictions;
- explore number properties;
- use invented notation, standard symbols, and variables to express a pattern, generalization, or situation."
The above information was summarized and quoted from this website. (Mathforum.org)
In this lesson, students investigate the number of gifts in total that you receive from your true love. This could be done by simply adding the numbers 1 to 12 together and coming up with 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78 gifts or by adding the cumulative amount of gifts in which the answer comes to 364 gifts. I ask my students to find the cumulative amount of gifts. For this problem, cumulative gifts refers to how many total gifts the true love gets over the 12 days of Christmas. On the first day, the true love gets a Partridge in a Pear Tree. On the second day she gets two Turtle Doves AND another Partridge in a Pear Tree. After the 12 day of Christmas, the true love will have 12 Partridges because she gets one each day. Students must figure out the cumulative total for all gifts received.
I then challenge them to see if they can come up with a rule that would allow them to find the number of gifts for the nth day of Christmas. This is very challenging for many of my fourth graders, however, some of the students will be able to come up with a rule.
Below you can see the relationship between this problem and Pascals triangle. This resource was adapted from this website about Pascal's triangle and the 12 Days of Christmas:
I then direct students make a pamphlet or brochure showing their work and the total number of gifts ones true love receives for the 12 days of Christmas. To incorporate Math Practice Standard 3 and 6, students explain their reasoning and thinking on their brochure while being precise when describing their thinking. I encourage them to avoid vague words like "things."
You can see in this photo, a students has come up with 364 gifts the true love receives. (This is the correct answer.)
In this photo, you can see a student's brochure stating that the true love receives 364 gifts. You can also see in the middle of the pamphlet that the students determined how many of each item the true love would get in total.
To end this lesson, students spend time sharing their pamphlets and findings with each other.