alice in summerland

learning and teaching math in alice

In my own world

Why do I always end up saving blog writing for after my 8 hours of work are already over?

There are 4!, or 24, possible orderings of the four students.

Anyway I made a new world today. This world is designed to teach middle schoolers permutations and factorials by counting the number of ways that 2 , 3, and 4 students can be arranged in a line and then showing that that is the same as 2!, 3!, and 4!, respectively. I think this tutorial turned out really well! I had to describe factorials in the beginning because I wasn’t sure if the students who know what it was yet, so I’m not sure if my description was too quick for a concept that could possibly be completely new and foreign to them.

The program asks the user to represent the number of arrangements of two students using factorials.

I think that the animated reorderings is a helpful way to understand the classic problem of finding the number of ways that a certain number of people can be arranged in a line. I did do some hardcoding and often inefficient coding, which I realized needed to be fixed when I got to the 4! factorial examples, where I had to animate 24 orderings of the 4 people. I create a method called world.switchPlaces that really helped out with that. The lesson is also interactive, asking the user to represent the number of arrangements using factorials and also computing the said factorial.

The world is almost finished. I think I’ll finish it tomorrow, but I do tend to get bored with projects and more excited about moving onto the next. Just like my habit of staying an hour late to finish my blog post.

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