Welcome to Day 4 of the Twelve Days of Mathematics for Christmas:
These activities were inspired by one of my grandsons’ favorite Christmas songs: the Twelve Days of Christmas. There are activities for K-3. Intermediate – MS (grade 4 – grade 7), and Secondary (Grade 8 –Grade 12) and correlated to the number of the day. Check below for the links to the FREE resources for both TES US and TES UK.
The Twelve 
Days of Mathematics
Day 4: Four Calling Birds
On the fourth day of Christmas my true love gave to me four calling birds, three French hens, two turtledoves and a partridge in a pear tree.
We move to the number 4. Beginning mathematicians and younger mathematicians will
be communicating about the number four through several activities that include writing, problem solving, and creating problems. There is something for everyone no matter what their challenges.
This next activity is fit for mathematicians of all ages!
Intermediate and middle school students will enjoy a coloring activity that is pure mathematics! The four color theorem will be investigated first by predicting how many colors they think it will take to color the Christmas package (top view is used to facilitate the investigation.)
One of my favorite websites: The MacTutor Archives of Mathematics has a wonderful article on the Four Color Theorem. Check it out here: http://www-history.mcs.st-andrews.ac.uk/HistTopics/The_four_colour_theorem.html
Another of my favorite websites – NRich – has an extensive piece on the theorem as well.
http://nrich.maths.org/6291 The Four Colour Theorem 
There are also a couple of fun adaptations on this famous theorem which can be found at The Math Forum with Marvin Gardner’s April Fool’s Map: 
http://mathforum.org/wagon/fall97/p840.html Problem of the Week 840
and the Treebeard’s Stumper Christmas Tree map found at:https://www.rain.org/~mkummel/stumpers/15dec0
0a.html 
For the secondary students there is an investigation focused around quartics. The investigation is open enough that just transformations on basic graphs can be examined or, as desired, symmetry, inflection points, and nature and number of zeros. See the facilitation notes for suggestions. The screenshots were taken using the TI84 CCE SmartView emulator. It is suggested that students use a graphing utility as a tool of investigation. Whether it is a calculator such as the TI-84 family of the TI-Nspire or Geometer’s Sketchpad or Desmos, all wil benefit students if used as a tool of investigation for this activity.
Enjoy the fourth day of Mathematics and check back tomorrow for Day 5!
Links for TES US:
The 12 Days of Christmas K – 3 Day 4: https://www.tes.com/us/teacher-lessons/twelve-days-of-mathematics-for-christmas-day-4-k3-11177374
The 12 Days of Christmas Intermediate – MS Day 4: https://www.tes.com/us/teacher-lessons/twelve-days-of-mathematics-for-christmas-day-4-int-ms-11177369
The 12 Days of Christmas Secondary Day 4: https://www.tes.com/us/teacher-lessons/twelve-days-of-mathematics-for-christmas-day-4-secondary-11177379
Links for TES UK:
The 12 Days of Christmas K – 3 Day 4: https://www.tes.com/teaching-resource/twelve-days-of-mathematics-for-christmas-day-4-k3-11177378
The 12 Days of Christmas Intermediate – MS Day 4: https://www.tes.com/teaching-resource/twelve-days-of-mathematics-for-christmas-day-4-int-ms-11177373
The 12 Days of Christmas Secondary Day 4: https://www.tes.com/teaching-resource/twelve-days-of-mathematics-for-christmas-day-4-secondary-11177382
