# Happy New Year 2021

It’s that time of year again and we can play the 2021 NCTM Year Game in our January lessons. Full rules are here.

As I write there are still references to 2020, however note this statement “Student solutions may be submitted starting January 1, 2021, using the Web form linked on the side menu. We will begin to post student solutions after February 1, 2021.”

Can your students use the digits in the year 2021 and the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), and ! (factorial), along with grouping symbols, to write expressions for the counting numbers 1 through 100? This year, in a change to the rules, decimal points and double-digit numbers are allowed. The rules for 2021 in detail are here.

And so to number properties of 2021, 2021 is an unusual year in that it is the concatenation of two consecutive integers (20 and 21) and also the product of two consecutive primes (43 and 47). This won’t happen again for a while! Have a look at Numbers Aplenty for more on this and also many other number properties. Did you know that 2021 is a Duffinian number?

Alex Bellos also included this in his Monday Puzzles, you will find other puzzles there to keep you busy!

2021 is also an iban number – this has amused me for a long time (along with the eban numbers) – 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…

On Dave Miller’s Spire Maths, you can read his recent posts for more on consecutive prime years, 2021: the product of consecutive primes, 2021 is an Extra Special Year and 2021 is a Special Year.

A lovely geeky number fact from Chris Smith

We can always check Tanya Khovanova’s Number Gossip site for properties of 2021. The common properties of 2021 are shown. All Number Gossip properties are detailed here.

How many ways can you write 2021 as a sum of squares? We can also look at WolframAlpha for further information on the number properties of 2021 including what 2021 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.

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.

On the subject of dates and the new year, from trol, Teacher Resources on Line, we can make a calendar for 2021. I do like the fold and tuck models – no glue required Scroll down the page.

Wishing educators and students everywhere a very Happy New Year.