It’s that time of year again, and we can play the 2025 NCTM Year Game in our January lessons. Use the digits in the year 2025 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.
And so to the number of properties of 2025…
We can always check Tanya Khovanova’s Number Gossip site for properties of 2025, the common properties of 2025 are shown here. All Number Gossip properties are detailed here.
For further properties of 2025 – see Numbers APlenty for numerous properties, including the fact that 2025 is the sum of the first 9 cubes. 2025 is the square of a triangular number, so we have:
We can also check WolframAlpha for number properties of 2025.
2025 is a perfect square which reminds me of this mental Maths idea I have often used:
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From Peter Rowlett in The Aperiodical, see Numerical coincidences for 2025 for further properties.
From Alex Bellos in the Guardian, see the post and solutions to his last Monday column of the year,
Can you solve it? All you need to know about 2025.
Thank you to Andrew Jeffrey for alerting me to Inder Jeet Taneja’s site, Numbers Magic, in his January Newsletter.
Sarah Carter has several lovely New Year 2025 activities, including a challenge and several puzzles on her excellent M + A + T + H = love blog. You can find all the activities here.
Returning to WolframAlpha we can see what 2025 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 and Ancient Babylonian Numerals from MacTutor.
We could look back and use the excellent MacTutor History of Mathematics 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 which we see includes ancient Babylonian mathematics.
On the subject of dates and the new year, from trol, Teacher Resources on Line, we can make a calendar for 2025, I do like the fold-and-tuck models – no glue required.
For another source of calendars, including the option to create your own, use Matt Woodfine’s resources on Maths White Board.
We could try this Calendar Calculation from Nrich.