There are so many math concepts that can be covered during calendar. I would take a look at your math standards and see which ones fit into calendar for your grade so you cover the most possible at calendar time. Some things I start at the beginning of the year, others I might add later in the year to change it up for the kids a little and add a more challenging concept.
Some of the things I covered when teaching grade 2:
- patterning - you can create simple to complex patterns with the numbers for the calendar
- odd and even - we used unifix cubes adding one each day. They were put into pairs so the kids learned how to tell if it was an odd or even number (every block had a friend).
- skip counting - we use the calendar for counting by 2's, 3's, 5's, etc.
- money - add a penny each day and trade up for nickles, dimes, quarters.
- place value - you can use sticks or straws and add one each day, bundling on the tenth day.
- equations - I had the kids orally give me equations for the date, this was a great activity because it worked for kids of many different abilities, so if it was the 10th of the month they came up with equations that equaled 10. Some would be quite simple addition and subtraction, others got more complex and used multiplication and division. They liked to challenge each other to come up with the most complicated they could, I had one kid who even loved to use square roots and exponents! This was in a multiage 1/2/3
- graphing - you could have the student of the day check the temperature and then record on a graph. Graph number of students at school or have a question of the day and graph the responses.
- tallying - we used calendar to teach how to make tally marks, we did a tally of the number of days we were in school.
A lot of teachers I know have the students do an individual calendar at their desk right before calendar time in a duotang or binder. They have a blank calendar for the month where they put the date on, record the weather, do their tally marks, etc.
Jessica Meacham has some great ideas for calendar on her website and info and downloads for doing the calendar binders or folders.
Hope that helps