Have your child join with others to learn about different cultures by planning culture days. Select a different culture to focus on each month, and spend some of your time learning about the customs practiced by people in that culture. At the end of the month, arrange a culture day in which your child joins with other home-schoolers to share their findings. To ensure that each student brings something different to the table, divide up the task of studying the culture, assigning one student to study its foods and prepare a dish, another to study its traditional clothing and so forth.
Put a spin on the traditional practice of pen-pal letter writing by having your student act as a historical figure and asking another home-schooler do to the same. For example, have your student take on the role of a Northern Civil War general and ask the other student to act as President Lincoln. As the two students compose and send notes as the general and the president, they will be able to put themselves into the shoes of these two individuals, and will more fully understand the history they're learning about.
Join your child with other home-schoolers within your state in studying the land you inhabit. Place a large state map on your wall, and encourage the others who are joining in the project to do the same. Ask each member of the study group to select a landmark to visit, and to venture to that site on a field trip of sorts. After each visit, ask the student who went to the site to type up a summary of what she saw and send it to the rest of the group. As you receive these different summaries, pin them up on the map next to each site's location. At the end of this cooperative project, all the home-schoolers will know more about the state they live in.
Take your study online by partnering your student with another and having them cooperatively craft a website. Select a topic about which you are currently studying to feature as the central theme of the website. This topic could, for example, be DNA. Set up a wiki page or other easily modified website format and allow your child, along with her partner, to upload articles they write about the topic, and have themdecorate their personal educational website cooperatively, even if they live quite a distance from each other.