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Functionality:  Waterfall vs. Agile

Most traditional Project Mgmt uses the waterfall approach (analysis, design,, implement, test).  The first task is usually requried to be done prior to the second task, etc.  This approach explicitly calls for a Gantt chart

Most Agile approaches take things in small increments, so you do one task this week, another one next week, etc  This seems to suggest the classic tool would be a kanban board

This is how I see the differences between the two.

I know most management projects will employ hybrid of the two approaches, but if I were to use pure Agile, how do you express the order of requirements (perhaps that is a prioritization within the backlog?).

Using pure Agile, how would you normally express an order in which tasks would be done.  In pure Agile, would you use a Gantt chart?

Watch Question

The product owner adds stories/tasks to the backlog.
The product owner sets the priority for items in the backlog. To express order, put the item closer to the top to work on it sooner.
The team breaks down the stories/tasks and estimates the ones near the top of the backlog.
In sprint planning you choose items from the top of the backlog until the team reaches capacity for the sprint.

I would not use a Gantt chart with agile.