About this time of year, I offer this problem to my students and think it is worthy of the attention of middle school teachers throughout New York:
On the first day of Christmas, my true love knocked upon my door. She offered me a single gift, a partridge in a pear tree. A strange gift, tis true, but I accepted it, kissed my true love goodbye, and put the gift out in the closed-in porch.
The next day my true love appeared again, this time bearing two gifts. First was a pair of turtle doves and another partridge in a pear tree. After saying goodbye, I placed both gifts on the screened-in porch.
This continued for twelve days (you can supply the lyrics for your cherubs) until my porch was overrun with well-meant gifts.
Question: How many gifts did I receive on Day 7? on Day 10? Day 12?
Question: How many gifts accumulated on my porch by Day 7? by Day 10? Day 12?
Investigation: What is a good way to observe the incremental growth of these changes from day to day?
Reflection: Investigate this problem with your class and feel free to share the discoveries, uncoveries and recoveries you and your students have shared.
Enjoy this problem with your students, and to all, a good night!