![]() He then multiplied that sum 50 times to reach the sum of the entire series, 5050. Gauss noticed that in the numbers 1 through 100, there were 50 pairs of numbers that added to 101 (1 + 100, 2 + 99, 3 + 98, … 49 + 52, 50 + 51). The mathematics behind this simple story are fascinating. ![]() His teacher was shocked when, seconds later, Gauss told him 5050 without having written anything down! To keep him busy, Gauss’s teacher told him to sum the consecutive numbers 1 through 100. The story goes that when Carl Friedrich Gauss was in primary school, he constantly provoked the wrath of his teacher. Let’s learn how it was first solved with a little story about a gentleman named Carl Gauss. Isn’t there a shorter or more efficient way to calculate the cost of window washing on a large building? It turns out this kind of math problem is a pretty old one, older even than skyscrapers. It is daunting to think about manually adding up the costs of each of the windows on each of the floors individually for fifty floors of a building. How can you solve this problem?Ĭarl Gauss. Check out some of the different launch options used some of those educators in our Educator Toolbox below. How would you start - or launch - the problem-solving process?īushra Makiya and Jon Koenig worked on ways to launch and work with students on The Skyscraper Problem as a part of a Math for America (MƒA)* Professional Learning Team (PLT). There are lots of ways to figure out the annual cost of washing windows on this building. Can you figure out how much it will cost to wash the windows of this building every year? The cost for washing the windows is $2.00 for each first-floor window, $2.50 for each second-floor window, $3.00 for each third-floor window, and so on. Once a year, all the windows will need to be washed. The skyscraper is 50 stories high and is going to be covered entirely by windows on all four sides. The board asks you to estimate the cost of window cleaning for the entire building to inform their decision. The board that commissioned it wants to know whether you think self-cleaning windows are worth the added cost. You’ve been asked to plan the construction of a new skyscraper.
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