12 days of Christmas math: a 40-minute pattern activity, grades 6–8

1. Hook (3 min): describe the song's pattern without singing it. On day 1 there is one gift. On day 2, two of a new gift plus one of the first. On day 3, three plus two plus one. Ask: "How many gifts arrive across all 12 days?" Everyone writes a guess.
2. Day by day (10 min): pairs make a table with three columns: day, gifts that day, running total. Fill in days 1 to 4 together. Gifts that day: 1, 3, 6, 10. Running totals: 1, 4, 10, 20.
3. Find the pattern (8 min): "What do you notice about 1, 3, 6, 10?" Each adds the next whole number. These are triangular numbers; build them as cube triangles to show why. Ask for a rule for day n and guide students toward n(n + 1) ÷ 2. Test it: day 12 is 12 × 13 ÷ 2 = 78.
4. Finish the table (10 min): pairs complete all 12 rows. The grand total is 364. Ask: "That's almost one gift for every day of the year. Why so many?"
5. Second puzzle (7 min): which gift was given the most times? The first gift arrives every day, so 12 times. The second gift comes in pairs on 11 days, so 22. Students find that gift k is given k × (13 − k) times. The 6th and 7th gifts tie at 42. Ask why the products peak in the middle.
6. Share (2 min): a pair explains its rule.

Extension: the running totals 1, 4, 10, 20, 35 are tetrahedral numbers, which you can build as cube pyramids. Advanced students can test the rule n(n + 1)(n + 2) ÷ 6: 12 × 13 × 14 ÷ 6 = 364.

Differentiation: for students who need support, give them the first six rows filled in and focus on the pattern and the rule. For advanced students, stretch the song to 20 days and predict the total without a table. For English learners, post a word bank: pattern, term, rule, total, triangular. Hands-on learners build each day's triangle with cubes.

Quick check: "How many gifts arrive on day 9? Show how you know without counting them all." (9 × 10 ÷ 2 = 45.)

If you try it, share the wildest guess your class made before working it out.