I find that it is incredibly difficult (although not impossible) to incorporate student discovery if it’s on the first day where a new unit has started. In a class like precalculus, when a new unit is introduced, there is a lot of information that needs to be given to students in order for them to proceed with each subsequent section of the unit. For example, before a student can do transformation to trig expressions they mush know trig identities and these identities or properties are given. I can see how we can let students explore the discovery of the Pythagorean expression by drawing a right triangle on a coordinate grid but this is mostly, these properties are given. Within a time constraint, it would be difficult to have students discover all the properties themselves. Whether or not students memorize the properties or discover their applications, it seems that just as long as they are able to recall this information is what counts (merely a statement based on observation and not an opinion).