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…

We can always check Tanya Khovanova’s **Number Gossip site for properties of 2023**, the common properties of 2023 are shown here. All Number Gossip properties are detailed **here**.

2023 is a **polite number** as it can be written as the sum of two or more consecutive **positive** integers. Have a look at **Consecutive Sums from The Shell Centre**.

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**.

On the subject of dates and the new year, from ** trol, Teacher Resources on Line**, we can make a

**calendar for 2023**, I do like the fold-and-tuck models – no glue required.

For a calendar with a difference, try this **Astronomy Calendar 2023** from **Varun Jain**.

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**.