Lesson 1-4 AP Computer Science Principles Number Systems Lesson 1-4 AP Computer Science Principles

Objectives Students will be able to: Reason about permutations and symbols as arbitrary abstract concepts that can be used to represent numbers. Invent their own “number system” with symbols and rules for getting from one permutation to the next.

Vocabulary Permutation: an ordered arrangement of objects Number System: a collection of symbols and the rules for ordering them

Journal How many ways can you represent the quantity 7?

Various Number Systems

Activity Download the activity guide from the website. In groups of 2: Develop your own number system using circles, triangles, and squares. To do so, you will create rules that generate every possible permutation of length 3 that can be made with these shapes. Note: Shapes can be used multiple times within a permutation, and order matters. For example, the picture to the right shows two length-3 permutations using squares and circles. They are different length-3 permutations because the shapes appear in a different order.

Step 1 Record all the permutations you can find Use the cut-out shapes provided to explore all the possible length-3 permutations. Write down the all the unique ones you find and keep track of how many there are. Suggestion: try to find the permutations in some kind of organized or systematic way, rather than just randomly.

Step 2 Make an ordering for the permutations Now that you’ve listed out all of the combinations of circle, triangle, and square, let’s put them in a systematic order. You can use any system you like, as long as you create and follow a clear set of rules for getting from one line to the next.

Step 3 Jot down the rules of your system Suggestion: to test your rules, have someone follow them to see if they can recreate your organized list above.

Turn in… Complete the worksheet on the Hancock web site. You can draw shapes or print the worksheet and just use color dots. You must state you rules!

Stage 4 Complete Stage 4