 We call this activity past the candy, and we find that it's an instructive and fun activity for introducing the topic of recursion or reinforcing the concept. Prior to class, you will need to prepare a bag of candy or other small items for each student. For this activity, it's better to vary the amount of candy each student receives. Later in the video, we'll discuss tips on how to distribute the candy. Let's get started. Divide the class into groups. Each group should be made up of three students. If your class size is not evenly divisible by three, place the extra students in groups so that you have no more than four students in each group. Arrange the students so that they are seated facing each other. Each student should then be given a tally sheet and a bag of candy. The tally sheet is provided on this site. On the tally sheet, have each student record the number of candies in each group member's bag. These values are our initial starting values. Iteration zero. At your instruction, each student will divide their candy in half and pass half of their candy to the person on his or her left, keeping the remaining half for themselves. Pass the candy. Pass the candy. The first student has 20 pieces, so she passes 10. The next student has six pieces, so she passes three. The third student has 16 pieces, so he passes eight. Have each student count the number of candies in his or her new pile, what they kept, plus what their neighbor gave them, and have them record the number of candies for each group member on their tally sheets. At your instruction, each student will repeat the iterative process, having their candy and passing half to the left. Notice that student two now has 13 pieces. She will keep seven and pass six. Alternatively, you could choose to have students pass the extra piece instead of keeping it for themselves. Either way, be consistent with how students handle having odd number of pieces. Continue this iterative process and observe the outcome. In this activity, there are three distinct outcomes possible. The final states are referred to as equilibriums. When distributing your candy to the class, you may want to do so in a way that ensures that each type of equilibrium occurs. This will allow rich discussion with the class. In some scenarios, each person ends up with the same number of candies. An example of this is if in a certain group, one student begins with 20, one begins with six, and the third begins with 16 pieces, as was the case in our demonstration. Here you see the completed tally sheet for such a distribution. Notice that in this example, each student ends up with 14 pieces. In another scenario, eventually the amount each person has remains the same from step to step. However, different group members have different amounts. An example of this is if in a certain group, one student begins with zero, one begins with 10, and the third begins with 16 pieces. Here you see the completed tally sheet for such a distribution. Notice that in this example, one student ends up with eight pieces while the other two end up with nine. In the final scenario, eventually one extra piece or pieces of candy moves from member to member in an infinite loop. An example of this is if in a certain group, one student begins with 20, one begins with 16, and the third begins with four pieces. Here you see the completed tally sheet for such a distribution. Notice that in this example, at any given time, one student has 14 pieces while the other two have 13. To facilitate discussion following the activity, you can have a member from each group record the following information on the board. Initial number of candies for each student in their group, final number of candies, the equilibrium values, the type of equilibrium, and the number of iterations to reach that state. The students can record the collective information on their tally sheets. As a next step, have your students write recursive equations modeling this activity. From there, you and your students can explore the various situations using technology. We have provided a link with helpful tips on this process.