# Different Exit Cards For Different Purposes

What exactly do I want to know?    That question has been rattling around in my head a lot since reading Mark’s post on exit cards.   In his post, he talks about different kinds of exit cards – those intending to engage a student’s metacognition, those examining procedural knowledge, those targeting concepts, and those intended to clarify misconceptions.   While I try to incorporate all of those things into my lessons and my assessments, I really  haven’t been as intentional in thinking about the kind of thinking my exit cards elicit as I might be.

As I have been teaching my students about the GCF and LCM, I have tried to incorporate a wider array of exit card types.

Procedural Knowledge

Following lessons on how to find the GCF and LCM, I gave my students two numbers and asked them to find both the GCF and LCM.   This was intended to assess whether they could correctly find the GCF and LCM   I think knowing where students are with regard to a skill is important.   Knowing a skill isn’t enough, though.

Conceptual Understanding

My primary curriculum is Connected Math.   They have several great investigations in which students explore problems utilizing the GCF and LCM.   They pose real questions and students solve the problems.   The questions explore how the GCF and LCM are used in real contexts but don’t specifically direct them to them as solution paths.    Students determine when two ferris wheels of different sizes will align, when two different species of cicadas will simultaneously emerge, how many equal-sized snack packs can be made from a given set of  apples and packages of trail mix, and how many students a set of juice boxes and crackers will feed.

Following this exploration  I asked students what it was about a problem that would indicate that finding the GCF would be a good solution path and what it was about a problem that would indicate that finding the LCM would be a good solution path.   (This is my version of one of the CMP reflection questions at the end of the investigation.)   I wanted to know if they had grasped the fundamental understanding that the LCM is used to solve problems of alignment and that the GCF is used to solve problems of grouping.

Clarifying Misconceptions

Having taught these concepts for several years now, it has become clear that students confuse the GCF and the LCM fairly frequently.    They don’t seem to deeply grasp the fact that the GCF is a factor and must be less than or equal to the numbers and that the LCM is a multiple that must be greater than or equal to the numbers.   They don’t always make sense of the problems they face and don’t have those alarm bells screaming that something doesn’t make sense when they try to find/use the wrong one.   Over the last few years, I have tried to make this thinking a lot more explicit as we discuss the concepts in class and on the quizzes/tests that I give.    Last week, I posed this question on a quiz:

• Choose all that apply. When finding the GCF of two numbers,
1. the GCF is always less than the two numbers
2. the GCF may be less than the two numbers
3. the GCF may be equal to the two numbers
4. the GCF is never less than the two numbers
5. the GCF is always greater than the two numbers
6. the GCF is never equal to the two numbers

Despite my efforts to draw this out in our previous discussions, the response was only fair.   I decided I needed to keep working with this with my students so I incorporated the same sort of question into an exit card following a lesson dealing with fraction subtraction.   This is the exit card.

LCD Always Sometimes Never Exit Card Select All That Apply

My TakeAways

As I have explored using different kinds of exit cards, I have learned a lot about what my students know and what they don’t know.   I think looking deeper gave me a better understanding of my students’ thinking and gave my students a better  understanding of the math.