Christmas Math Challenge Problem

In our homeschool, I love to give problems for my kids to try to solve that they have never seen before. That’s what mathematicians do. We solve new problems, or old problems in new ways, using tons of creative thinking, working through our frustrations, and sometimes coming up with elegant solutions. That process is valuable to me and to my kids.

For this problem, kids will need a basic knowledge of addition (multiplication would help too, but isn’t required). To set up a discovery math challenge, we present a problem to the kids and give them free reigns to try it in many ways. You can choose to let them use a calculator or not.

CHALLENGE PROBLEM: How many gifts did “My true love give to me” in the Twelve Days of Christmas? Note: On the first day, he gave 1 gift. On the second day he gave 2 + 1 gifts, etc.

If kids need a place to start, have them write down the numbers for each day. There are some fancy shortcuts they might discover.

If kids solve it with straight adding, ask them “How could you do this another way?” and “Is there a shortcut?” If they get different answers, ask them how they did it. Praise creative thinking and problem-solving efforts (not necessarily the answer). “Did you see how Susie did this? That was so creative!”


After students have tried it and found an answer, here is a story that may help them think of a different way of doing things:

Carl Freidrich Gauss went to school in Germany in the 1700’s. He was very smart in school. When was seven years old, his teacher wanted a task to keep him busy longer, so he challenged Gauss to add up all the numbers from 1-100. The teacher thought it would take a long time. However, a couple minutes later, Gauss came back with the answer, 5,050. The teacher was surprised and asked him how he got the answer so quickly.

It was quite easy for Gauss because he came up with a brilliant strategy to add the numbers by pairing them in groups of 100.

100, then 99 + 1, 98 + 2, 97 + 3, etc. until 49 + 51. There were 50 groups of 100 total. The 50 in the middle is not part of a group of 100, so he added that in too.

50 groups of 100 is 5,000, plus 50 more is 5,050.

Learn more about Gauss on Wikipedia HERE.

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