Students will learn how to evaluate the floor function, given decimals or fractions. Then students will learn how to graph the floor function, with and without transformations. Here's a video covering \(y = \lfloor x \rfloor,\) \(y = \lfloor 2x \rfloor,\) and \(y = \lfloor x - 2 \rfloor.\) And here's a video covering \(y = \lfloor 2x - 1 \rfloor.\) This is how I recommend teaching graph transformations, in general. Start with zero transformations, then one, then two, and so on.
Next, give your students these challenges:
Conclude by leading this investigation: