In this final Christmas themed post, I am including a range of open-ended investigations that are suitable for upper primary and lower secondary students (from the book *Engaging Maths: Everyday Investigations Years 3 to 6)*. You will notice that some of the investigations extend beyond the mathematics curriculum and integrate quite easily into other key learning areas. This is intentional. If we want to engage students in mathematics, then making it contextual often requires it to either be embedded within another subject area or at least have some connections to other areas. Another consideration is the General Capabilities of the Australian Curriculum: Mathematics. When we incorporate contextual mathematics and investigation-based tasks, we are more likely to include the General Capabilities and this is evidenced in the activities below.

Short activities:

- If you have a Christmas tree in your house or school, how tall is it? Can you reach the top of the tree by reaching up? How much taller than you is the Christmas tree? What fraction of the height of the tree is your height?
- Draw a picture of a Christmas tree. Use your drawing as a plan to show where you will place the decorations.
- Tie a piece of tinsel to the very top of the Christmas Tree. Wind the tinsel around the tree until you reach the lowest branch. What is the length of the tinsel?
- If the individual lights of a string of Christmas lights are 30 cm apart, how many lights would you need so decorate the perimeter of the classroom?
- How would you work out how much wrapping paper needed to wrap 10 presents that were each the size of a shoe box?
*Record all of your working out. What mathematics did you use?*

Investigations:

- Plan a Christmas party for some of your friends. Show all the mathematics that you need to use for your planning.
- Many families start to budget for Christmas presents several months before Christmas day. Design a budget for the Christmas presents that you would like to give to your family members, relatives and friends. Perhaps you might like to include your teachers.
- Survey the other students in your class using the question, “Do you have a Christmas tree in your home?” “Is it a real tree or an artificial tree?” “Which type of tree do you prefer and why?” Present the data that you have collected and present a report to your class.

Extension Activities:

- Investigate and research the tradition of decorating a tree for Christmas. Answer questions such as “When did the tradition start?”
- Plan menus for the meals for family for Christmas Day and Boxing Day and include a budget.
- Make a list of the things you would like for Christmas. Sort your items into needs and wants. How would your list compare to the list of a child in a different country? Investigate.

I hope you have enjoyed this series of posts that have included many rich activities to keep students engaged with mathematics until the very last day of the school year. If you do implement any of the tasks, I would love to hear from you and see your students’ work samples!