Virtual Manipulatives- Peg Puzzle (gr. 6-8) & Towers of Hanoi (gr.3-5)

Algebra gr. 6-8 Peg Puzzle
I used this virtual manipulative on my husband. I first started my giving him the directions and the goal of this assignment. The goal is to switch the pegs on the left with the pegs on the right by moving one at a time. I explained that you can not move backwards and you can not jump over more than one. He first started with 4 pegs. He completed this puzzle with no problem. He than tried the 6 peg puzzle. After the third move he got stuck. The best thing about the activity is that unlike the hands on one from class the virtual notifies you when you are stuck. It states," You're Stuck-none of the pegs are allowed to move." I feel that this is beneficial because instead of wasting time trying to figure out if you can move you can start over right away. After a few tries he was able to solve the 6 peg puzzle. So I challenged him to the 8 peg puzzle. He than realized that there was a pattern to the 4 and 6 peg puzzle he tried several more times to figure out the pattern so that when he begins the 8 peg he can move through it easily. He began to write down each move in order to see if it can be replicated if more pegs are added. When he started the 8 peg puzzle you can see that he was a little frustrated, he solved it once and than couldn't figure out how he did it. He tried over and over until he was comfortable to solve it and explain what the pattern was he used to solve it.

Algebra gr. 3-5 Towers of Hanoi
For the towers of Hanoi I decided to test it on a third grade student from my building. I chose this student because he was in my class during lunch. In the virtual manipulatives game its default is 3 disks. However, for practice I told the student to start off with 2 disks. I explained to the student the directions and the goal. The goal of the towers of Hanoi is to move a stack of disks from one peg to another in as few a moves as possible. I also explained the rules which are you can only move one disk at a time and that you can not stack the larger disk on the smaller one. The student than began to solve the 2 disks. He was able to do it on the first try. He was then notified that Congratulations! You moved the towers in as few moves as possible-3. The student was very happy to see that. He than tried 3 disks. He completed it but unfortunately he did not complete it using the least amount of moves. So he tried a few more times until he did. I was very proud of him. I than asked him if he thought there was a pattern? He said that he wanted to try a few more times so that he can see if there was one. After trying several more times he stated that the smallest peg moves the most out of all of them,and that it moved from the first spot to the last and than from the last spot to the middle and then from the middle to the first again and finally back to the last spot, also that the largest peg only moved once which was from the original spot to the last spot. Unfortunately, we did not have enough time to try 4 pegs.