It’s that time of year again and we can play the 2019 Year Game in our January lessons. You can preview the 2019 game now. Can your students use the digits in the year 2019 and the operations +, -, x, ÷, sqrt (square root),^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100?
My students have always been curious about the double factorial function.
Excel has a function for computing double factorials, illustrated here.
This year I think I will show my students a few examples and see if they can work out what is going on!
Have a look at this definition from Wolfram Math World or have a look at this article on Ask Dr Math. Note the relationship between the double and single factorial functions.
We could also look back and use the excellent MacTutor History of Mathematics Archive from the University of St Andrews, Scotland. We could check today or any day for Mathematicians who were born or died on that day.
The site is searchable in several ways, including the comprehensive index of History Topics.
Happy Numbers is accessible for a range of abilities and offers a great lesson in the value of recording results carefully so you can use previous results and save yourself work! The Happy Numbers page includes additional resources, have you seen the Dr Who clip – Happy Primes?!
2019 is square free as its prime decomposition contains no repeated factors. I have found students are usually interested in these number properties and we could certainly usefully revise prime factor decomposition and come up with some more square free numbers.
2019 is also a lucky number, note that 13 is a mathematical lucky number!
We can also look at WolframAlpha which provides further information including what 2019 looks like in historical numeral forms. We could use the various WolframAlpha queries to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.
The Babylonian system was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.
For more on the Babylonian system including how fractions were represented see History of Fractions from Nrich.
Wishing educators and students everywhere a very Happy New Year.