One of the widgets I very much enjoy when teaching introductory course in data mining is Paint Data widget. In the data I would paint in this widget I would intentionally include some clusters, or intentionally obscure them. Or draw them in any strange shape. Then I would discuss with students if these clusters are identified by k-means clustering. Or by hierarchical clustering. We would also discuss automatic scoring of the quality of clusters, come up with the idea of a silhouette (ok, already invented, but helps if you get this idea on your own as well). And then we would play with various data sets and clustering techniques and their parameters in Orange.
Like in the following workflow where I drew three clusters that were indeed recognized by k-means clustering. Notice that silhouette scoring correctly identified even the number of clusters was guessed correctly. And I also drawn the clustered data in the Scatterplot to check if the clusters are indeed where they should be.
Or like in the workflow below where k-means fails miserably (but some other clustering technique would not).
Paint Data can also be used in supervised setting, for classification tasks. We can set the intended number of classes, and then chose any of these to paint its data. Below I have used it to create the data sets to check the behavior of several classifiers.
There are tons of other workflows where Paint Data can be useful. Give it a try!