I choose these "warm-up" questions for any one or more of the following reasons: to clarify the topic I know students have probably most struggled with on the previous night's homework, to further reinforce what may be unclear to students, to introduce students to the topic we are about to cover, or to relate what is being done to what they already know.
Each day, we go over the answer to any warm-up questions given. Students may volunteer or be called on to show their work on the board at the front of the room. I sometimes call on students for answers from their seats and sometimes I give the answers. Occasionally, there are bonus points given for students who do well at this.
The greatest value of the warm-ups is the daily opportunity to practice what has been learned. If a student does a warm-up completely incorrectly, most of the time no one will be aware of the mistakes other than the student him/her-self. It is most likely that every student will get at least some of the warm-up correct. If a student does not even make an attempt at doing the warm-up, there is a 100% chance that he or she will not get any of the warm-up correct.
As we are going over the warm-up answers, students may--and should--ask questions about what is being shown. They should make any necessary corrections to the answers they have. This is also an opportunity to ask about the prior homework given.
The answers to the warm-ups must be complete. One reason for doing a good job on the warm-ups is that they serve as a template for the types of questions that are likely to be seen on quizzes and tests. The more complete a student's warm-ups are, the better the scope of information to refer to when studying.
Occasionally, I will count a warm-up as a quiz; students will pass them in for correction. These generally count for ten to twenty points and may be given at any time.
If I notice that students are not even trying to do their warm-ups--they are just waiting to copy the information off of the board when we go over the warm-up--I will be likely to give a warm-up quiz. Every student should--at a minimum--write down the information given in the problem (P=___, V=___, etcetera) and the equation that is most likely to be used.
At the end of each semester, we correct these daily warm-ups and students earn points for them. Each daily warm-up must include the date, the question, the work (if applicable) and the correct answer. No points will be given to a daily warm-up that is missing any of the above. By the end of the semester, there are more than sixty of these, which means they are worth more than a single test.
This set of warm-ups also serves as a review of what we have covered each semester. The final exam is always cumulative, which means that every topic we cover will be on the final exam. Students often forget in January and June what we have covered through the semester. Warm-ups should be a very complete and clear roadmap of each concept covered, at what time of the year it was covered, and what should have been learned about that particular concept.