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). 

Arrange their tools and materials so they are accessible (using low shelving).  

Learn to write their name. 

Flower arranging.

More complex cutting (cutting out shapes). 

Sweeping purposefully and successfully. 

Folding cloths accurately and neatly. 

Colour mixing (and using a pipette). 

Threading and hand sewing.  

Using a knitting fork. 

Kneading and making bread together.

Independently brushing teeth and taking more responsibility for care of self activities.  

Peeling and doing more complex food preparation tasks. 

Spreading and preparing own snack. 

Language work (working with phonics and playing sound games). 

More complex puzzles such as Montessori anatomy puzzles. 
 

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!