Today for a change of pace, I gave students 4 dice and asked them to find a certain number. Some classes I placed restrictions and others I did not. When there was no restriction, the students found the number fairly quickly and often used repeated numbers. For instance they might use the number 4 many times. When I placed a restriction on the number of times they could use a certain number, it made it harder for students to reach the number. In one class, where I incorporated the restrictions, about half the students were unable to get the answer because they kept trying to use certain numbers 4 or 5 times. In the rest of the classes with no restrictions, students found the number within two minutes.
I learned that adding restrictions make the activity harder to do. I think next week, I am going to give them three dice and have them find a specific number using any operation to obtain a certain number. They can do it intellectually but I want to see if they can do it with the dice. It would make it more visual.