It’s that time of year again and we can play the 2023 NCTM Year Game in our January lessons. Use the digits in the year 2023 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; full rules are here.
Playing this with younger students has been an opportunity to introduce the factorial function, and we tend to stray into double factorials as students are curious. A good exercise in algebra for your older students – can they find a relationship between the single and double factorial functions?
Excel has a function for computing double factorials, illustrated here. I like to show my students a few examples and see if they can work out what is going on.
Have a look at this article from Wolfram Math World and check this journal article – Henry Gould, and Jocelyn Quaintance. “Double Fun with Double Factorials.” Mathematics Magazine 85, no. 3 (2012): 177–92. https://doi.org/10.4169/math.mag.85.3.177.
For a digital version of The Year Game, try this Desmos Classroom activity from Craig Winske.
And so to number properties of 2023…
2023 is also an iban number – this has amused me for a long time – get your students thinking outside the box with the iban sequence: 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, 41, 42, 43, 44, 47, 70, 71, 72, 73, 74, 77, 100, 101…
The number 2023 is a Harshad number in base 10, because the sum of the digits is 7, and 2023 is divisible by 7.
How many ways can you write 2023 as a sum of squares? There are, as you can see many ways to write 2023 as a sum of squares but it cannot be written as a sum of two squares or as a sum of three squares.
2023 be expressed as a difference of two squares; see this (2009) maths item of the month from MEI, and here’s a resource for this problem on Nrich, What’s Possible? Possible questions and approached in class are included in the article with a printable worksheet for students.
We can also look at WolframAlpha for further information on the number properties of 2023 including what 2023 looks like in historical numeral forms. We could use the various historical numerals examples 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.
We could 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.
I have often mentioned Wayne Chadburn’s monthly calendars. He writes these calendars to provide regular, varied practice – a little bit of maths each day. Three versions of each monthly calendar are available, Higher, Foundation Plus, and Foundation; answers are provided. Calendars for January through to May are now available. Wishing educators and students everywhere a very Happy New Year.
For another source of calendars, including the option to create your own, use Matt Woodfine’s resources on Maths White Board.