Fun Christmas Math Problems

I teach at a very small private school, and each year we have a math team to compete at the state math meet. A team consists of ten students, and ten students is about the size of our entire high school (which is wonderful when you get to teach class sizes of anywhere from one to eight students, but is not so great for raising up a ten person math team). We usually end up having half a team, and half of the students are middle schoolers.

We know that we're not going to be "competitive," but I try to make sure that the students have some fun doing problem solving activities together. One of the big challenges is trying to create competition-style problem sets that have something that's feasible for my entire range of students from sixth graders to twelfth graders.

This year I put together a set of Christmas-themed problems for my students to work on as a team. The problem set is the attached printable file, and there is a solution key below.

This problem set would also work well as a Christmasy problem-solving activity for a high school math class.

Christmas Problems

1. How many gifts were given in all in the song “The Twelve days of Christmas”?
    
2. The earth has eight billion people, and the average family size is 2.5 people. 75% of all families have children, and
   3

   8
    of those families have only “nice” children. If Santa only visits families that don’t have any “naughty” children, how many families does he have to visit?
    
3. I have a certain amount of money to spend on Christmas gifts. I spent half of it on my wife, a third of the remaining money on my son, and half of the remaining money on my daughter. When I was all done, I had $12 to spend on the baby. How much money did I start with?
    
4. The Christmas eggnog was not creamy enough; it was only 30% cream. How much half-and-half (50% milk, 50% cream) must be added to five gallons of eggnog to make it 45% cream?
    
5. Santa’s workshop is filled with elves, reindeer and snowmen. Elves have two legs, reindeer have four, and snowmen have none. In all there are 72 “creatures” in the workshop, and 176 feet. Only elves and snowmen wear hats, and there were 40 hats in the workshop. How many snowmen were there?
    
6. In how many distinct ways can the letters of the name “SANTA” be arranged?
    
7. Hermie can open presents at a rate of three presents every two minutes. Rudolph can open presents at a rate of two presents every five minutes. If they work together, how many minutes will it take them to open 133 presents?
    
8. At dawn on December 1st, Frosty the Snowman is 62 inches tall. Every day Frosty melts a little, decreasing his height by 4 inches. Every night it snows a little, increasing his height by 3 inches. On what day will Frosty reach a height of zero inches?

Christmas Problems: Solution Key