The Scrum Team
A Scrum team does not include any of the traditional software engineering roles such as programmer, designer, tester, or architect. Everyone on the project works together to complete the set of work they have collectively committed to complete within a sprint. Scrum teams develop a deep form of camaraderie and a feeling that "we're all in this together."
A typical Scrum team is 5-9 people. Rather than scaling by having a large team, Scrum projects scale through having teams of teams. In this way I have worked on projects with over 500 people and have consulted to projects with over 1,000.
Although not the only thing necessary to scale Scrum, one well-known technique is the use of a "Scrum of Scrums" meeting. With this approach each Scrum team proceeds as normal but each team identifies one person who attends Scrum of Scrum meetings to coordinate the work of multiple Scrum teams. These meetings are analogous to the Daily Scrum Meeting, but do not necessarily happen every day. In many organizations, having a Scrum of Scrums meeting two or three times a week is sufficient.
The illustration below shows how a Scrum of Scrums approach allows Scrum to scale up (in this case to 243 people). Each cell represents one person on a Scrum team. The bottom of this illustration shows teams with nine developers on them. One person from each team (the differently colored cell) also participates in a Scrum of Scrum to coordinate work above that team. Then from those nine-person teams another person is selected (this time shown with diagonal lines) to participate in what is called a Scrum of Scrums of Scrums.
You can also read further for advice on conducting the Scrum of Scrums meeting.