The Peg Puzzle and the Towers of Hanoi: Two Great Virtual Manipulatives

The Peg Puzzle Virtual Manipulative

The Towers of Hanoi Virtual Manipulative

I asked a math teacher to allow me to challenge her eighth grade students to try to solve the Peg Puzzle Virtual Manipulative and the Towers of Hanoi Virtual Manipulative over the course of two class periods. She agreed because she saw that these activities had a lot of academic value. In addition, she thought that the skills the students would develop by working on these activities would help them on the NJASK.

First, I started by putting the Peg Puzzle Virtual Manipulative that had eight pegs on the Smart Board. Then, I explained the rules. When I asked for volunteers at least seventy-five percent of the class volunteered. Not surprising, after several people tried to complete the activity, they realized that it was much harder than it looked. I let the students continue to work with the problem. When I saw that students were getting very frustrated I gave them the two peg problem. I called on a volunteer, and he was able to get it on the first try. Then, I put the four peg problem on the Smart Board. I asked the students if they thought this one was going to be easy, and they said that they thought it would be. However, the first three students that tried it got it wrong. Finally, someone got it correct. Then, I put the six peg problem on the Smart Board. It took about ten tries before one of the students got it correct. Then, I put the eight peg problem back up. I called on volunteers once again. Finally, after about fifteen tries a student got it correct; however, it took three more tries for him to repeat it.

Once students solved the problem, we began discussing the patterns. However, the period was almost over. Thus, I gave students the website, and told them to try the eight peg problem at home until they could complete it over and over again. I also told them to write an explanation of the pattern that they saw once they became “experts” with regards to the Peg Puzzle. We discussed the patterns in class the next day, and interestingly, they were very similar patterns to what we came up with in class.

Then, I put the six ring Towers of Hanoi virtual manipulative problem on the Smart Board. Then, I explained the rules. As expected, the students struggled with it. Then, I gave them the same problem with only two rings. The students had no trouble with this. However, I had to call on three different students to solve the three ring problem and seven students to solve the four ring problem. Unfortunately, no students were able to solve the five or six ring problems in the allotted time. However, they made many attempts. At the conclusion of the activity, we discussed the patterns that they saw.

Both the Peg Puzzle virtual manipulative and the Towers of Hanoi virtual manipulative are great activities for students. In addition, since they are online, students can work on these activities individually or as a class using a Smart Board. Considering that students love to play games and love to work on a Smart Board, every teacher should consider putting these two activities in their “bag of tricks”.

In addition, I prefer both of these virtual manipulatives to the “real” manipulatives. Obviously, one reason for this is because students love to work with technology, and the virtual manipulatives accommodate this. Also, I really like that the Peg Puzzle and the Towers of Hanoi virtual manipulatives count the number of moves for you. Believe it or not, I found it difficult to count the number of moves and complete the problem with a “real-life” apparatus. In addition, the virtual Peg Puzzle problem and the virtual Towers of Hanoi problem do not let you make “illegal” moves, which is nice because there is no way of knowing that you followed the rules when the problem is solved using a “real” manipulative. In addition, the virtual Peg Puzzle problem tells the students when there are no more moves left. This is nice because it avoids the confusion of whether there are moves still available. Also, the Towers of Hanoi puzzle informs students if they have solved the problem and if they have done so using the fewest number of moves. Lastly, I felt that the “undo” button was very valuable when completing the virtual Towers of Hanoi problem. It saved several students from having to start over. Thus, as a future middle school math teacher, I would recommend using either of these activities when teaching about patterns.