As the end of the school year approaches, report writing is in full swing and Christmas is on the horizon. It’s easy to lose focus, get distracted, and keep students occupied with ‘busy work’. However, it’s critical that we don’t waste a minute of students’ learning time, particularly when we know that over the long Christmas break some students may regress in relation to mathematical fluency and understanding.

So how can you keep mathematics engaging until the last day of school? Consider the elements required for sustained engagement to occur. Three factors are critical: cognitive, operative, and affective engagement. In terms of mathematics, true, sustained engagement occurs when students are procedurally engaged and interacting with the mathematics and with each other; when there is an element of cognitive challenge within the task; and when they understand that learning mathematics is worthwhile, valuable, and useful both within and beyond the classroom. It is easy to mistakenly think that students are engaged when they appear to be busy working, or ‘on task’. True engagement is much deeper than ‘on task’ behavior, rather, it can be viewed as ‘in task’ behavior, where all three elements; cognitive, operative and affective, come together. This leads to students valuing and enjoying school mathematics and seeing connections between the maths they do at school and the maths they use in their lives outside school (for more information see my FRAMEWORK FOR ENGAGEMENT WITH MATHEMATICS).

As this time of year it is easy to design mathematics tasks that promote high engagement and have the potential to stimulate learning. The following is a set of problem solving activities based on the famous Christmas Carol, * The Twelve Days of Christmas. *The activities are suitable for children in the middle years (grades 5 to 8), however can be easily adapted to suit younger or older learners.

*Resources Required:*

A copy of the lyrics of “The Twelve Days of Christmas”

The book “The Twelve Days of Christmas” (There are several versions available)

Price Lists

Other resources as required, eg. shopping catalogues

Possible Investigations starters/Task cards

*Teaching/Learning Activities:*

- Read the book/lyrics or listen to the song “The Twelve Days of Christmas”
- Discuss how the gift giver has to increase the number of gifts to his true love each day.
- Provide students with a price list (this can be adapted according to the ability of the group)
- At this point students can be asked to investigate the cost of the gifts, turning the activity into an open-ended investigation, or, specific questions can be posed to the students.

Examples of possible problems to explore are:

- What is the total number of gifts given?
- Is there an easy way to work this out?
- What is the total cost of the gifts?
- If the department store was holding a pre-Christmas sale and offered a 15% discount for all purchases, what would the new cost be? (This does not include performers, maids, lords etc)
- What if the discount offered only applied to live animals?
- The maids give a 10% when booked for more than two consecutive days. What would their new fee be?
- The musicians charge a 10% Goods and Service tax and this must be added to the total cost.
- How many people arrive at the true love’s house on the twelfth day?
- What would it cost to feed all the people and the animals? (Internet would come in handy here!)
- Use some Christmas shopping catalogues to replace the gifts with something more appropriate for a modern true love and calculate the cost.
- Re-write the lyrics to fit your new list of gifts.

**The full list of activities and hypothetical price list are available on PDF here:** The Twelve Days of Christmas

Other engaging end-of-year mathematics tasks are:

- Create a range of 3-dimensional calendar models. Use this task to investigate 3D objects and patterns within the calendar. Students can also make the models as Christmas gifts. http://cleavebooks.co.uk/trol/trolqc.htm
- Making snowflakes: https://nrich.maths.org/5352
- Find a range Christmas Advent calendars at Nrich where each day in December has new mathematical problems and investigations to explore http://nrich.maths.org/7778

All of the above activities have the potential to promote high levels of engagement at a time of year when it is difficult for students and teachers to remain focussed. However, it is important to remember that any activity is only as good as the teacher implementing it. To enhance students’ engagement and learning, ensure there is regular student reflection, and rich discussion about the mathematics embedded with the tasks.