My youngest child is now four years old so three is still very clear in my mind. The three year old loves practical life, being involved and is often very enthusiastic. Here are a few activities we did when my son was three years old.
Cooking with heat (making pancakes).
Use a mystery bag (the child identifies what is in the bag through touch only).
Language work (working with phonics and playing sound games).
You can read all the posts for Otis when he was three years old here! Three is often the age when children begin preschool and perhaps enter their own community for the first time. It's an exciting stage of development!