What are your best ways to make home to school connections?

Example

I've let the kids email their teacher a picture when we've taken a subject from school they enjoyed, and we took it a step further at home. Or brought in a special project they did at home. The teachers are always wonderful about writing back or giving them feedback at school. 

One of my daughter's teachers was really excited when we got a puppy. My daughter, Maya, emailed a picture and we wrote a description/letter about life with a puppy. My next daughter has the same teacher, who asked how our dog was, so Ava, sent an updated picture and email. 

Sometimes the kids come home with a project or little take home book they are very interested in, but done with learning at school. We've taken that as a trampoline to learn more about the subject.