Interesting math patterns make me happy, so I really enjoyed doing a unit on math masterpieces with my 4th graders several years ago that included Fibonacci, Sierpinski, Pascal, and the 12 Days of Christmas. Unfortunately, several of the links that I included in that post back in 2016 no longer exist. But the good news is that some newer ones have surfaced. Time, then, to go back to the drawing board…
If I was doing this lesson today, I would begin by posing the question of how we could figure out exactly how many presents the extremely generous “true love” would have purchased by the end of the famous “12 Days of Christmas” song. After some discussion, suggestions, and student collaboration (and maybe listening to this funny version from Straight No Chaser), I would then introduce this great spreadsheet Eric Curts just posted. It will help students think about their math and learn a few spreadsheet skills. After students complete this and you debrief, you could then ask them what they think the price of all of those gifts would add up to today. PNC has a nice summary of the cost of each gift and the total, but don’t show it to them until you’ve gotten some estimates! Students who need a challenge could be tasked with designing a new spreadsheet for those calculations.
Next class, I would introduce them to Pascal’s triangle. I wouldn’t tell them what it is at first. I would give them this worksheet, this one, or the first page of this one to complete. You can see on the latter link that there are some additional pages that give suggestions for patterns students can look for in the triangle once they have successfully added the correct numbers. Even more patterns can be found here. Note the Fibonnacci numbers, and how you can get Sierpinski’s triangle by coloring in certain numbers! And then, you can point out the pattern, shown here, that reveals how many total presents are received each day. (The printable triangles I linked to don’t have that many rows, so it’s up to you if you want them to make that connection on their own.)
For more advanced students, you can show them this video, which demonstrates how Pascal’s Triangle can be used to find coefficients or probability. Here is an interactive from Mathigon for those students who want to go deeper, too. Shodor also has an online triangle you can manipulate and color as well as recommended lessons. This Geogebra one is fun to play with, too.
If you’re loving these math resources, don’t forget that you can go to my Wakelet page, where I have links to two different math collections full of engaging activities, “Math, Art, and Nature” and “Math Sites that Won’t Make You Fall Asleep.” You’ll also find my December collection and Fun Stuff!