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.