We propose and illustrate a method for developing algorithms that can adaptively learn from data streams that change over time. As an example, we take Hoeffding Tree, an incremental decision tree inducer for data streams, and use as a basis it to build two new methods that can deal with distribution and concept drift: a sliding window-based algorithm, Hoeffding Window Tree, and an adaptive method, Hoeffding Adaptive Tree. Our methods are based on using change detectors and estimator modules at the right places; we choose implementations with theoretical guarantees in order to extend such guarantees to the resulting adaptive learning algorithm. A main advantage of our methods is that they require no guess about how fast or how often the stream will change; other methods typically have several user-defined parameters to this effect. In our experiments, the new methods never do worse, and in some cases do much better, than CVFDT, a well-known method for tree induction on data streams with drift.