This guy is using unit blocks to try and enclose himself into a space under a shelf. What a great self-motivated and fully engaging activity to discover properties of length and measurement.
Many new teachers that I mentor tend to get overwhelmed trying to find play-based math activities for preschoolers. For a more seasoned teacher like myself, finding opportunities to explore math concepts throughout the day is easy. Through years of teaching and refining my awareness, I see math in our every day world. For those who are newer and struggling in this area, I'm reposting a list that my instructor posted for our class of a few simple math activities, many of which work both for toddlers and preschoolers:
Comparing big and small objects
Exploring coins (use a magnifying glass to look at shiny new pennies)
Read books that talk about more than on character (such as 10 ants going marching)
Pose problems and seek answers
Sort items by color
Look for shapes in the room
Make patterns of items (such as red block, blue block, green block)
Matching games (lotto)
Use a measure tape to measure items in the classroom
Use scales to measure more or less
Use measuring cups
Clearly from this list, preschool math is not only about teaching numbers and numerals. It's about offering materials that provide inherent math concepts so that the child can learn with their hands and heart. It's also about being aware of when the interest level is at its peak and offering curriculum that appeals to the interest level. (For instance, our new measuring tape and dial scale is based on our recent continuous dialogue about length and measurement).
Using measuring cups
Lining up objects