Being in the Southern Hemisphere, Christmas is also the end of the school year for us. Until this year, students have always been on exam leave at the end of the year, but this year we moved the exams forward so we had 3 weeks of teaching at the end of the year, to review exams and get started on the following year's timetable! So, for the first time in 5 years I have been able to a) wear Christmas ties and b) do Christmas maths lessons. Here are a couple of the things I did.
I have previously talked about the excellent Fractal Christmas Tree, though I did not have time for that this year.
DESMOS Christmas Tree
I have previously done a DESMOS pumpkin challenge, and I changed this into a Christmas Tree challenge this year. I started by showing students this DESMOS page as inspiration, and quickly talked through the way to set domains, ranges and shade using inequalities.
I then directed students to DESMOS, and off they went. Some started by copying what I had done. One found an image online and pasted it in and then added lines to reproduce it. I then added a couple of baubles to my tree, like below.
At this point, many of the students started adding loads of baubles in different places (they quickly learned how to move them). Some started adding stars to the tops of their trees. One student asked me how to create an ellipse to create a shadow. Below are a few images of ones students created.
In the end I finally added an extra layer to my tree on the board, as below.
And my favourite finished one:
On the Twelfth Day of Christmas
I challenged a couple of classes to find the total number of presents given to me by my true love in the famous carol. All students started by finding how many presents I received on the twelfth day, not in total, but with some further prompting, they all answered the actual question. I then challenged them to do the same for 20 days, or 100 days, generalising their ideas.
In my S3 class (15 year olds), most groups were able to find the nth term for the triangle numbers, which gives the formula for working out how many presents you will get on the nth day. One student was able to work out the total number of presents you would get in the 20 days, and did identify that it was a cubic sequence, but we ran out of time to really explore this.
With my IB HL class, we have been doing taster lessons on proof by induction, and so I decided to start with them proving the following two identities.
Then I gave them the same challenge, but also asked them to prove their results using induction, and with the expectation they would use sigma notation to make a conjecture. I have been giving my HL students lesson sheets, and the one for this activity can be found here.
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.