Start with a set of 13 playing cards. Shuffle them and then lay them out like this:


Now sort them in ascending order from left to right. Pay attention to your process as you do. Then, repeat the exercise, but this time (1) touch just one card at a time, (2) think out loud to describe what you are doing.

Write instructions for your method below.

Exchange papers with a partner, shuffle the cards, and then sort them following, as literally as possible, the instructions they wrote down. After you've done, write below any feedback you have on the instructions you were given.

Now rewrite your own instructions from step 2 (or for a different method if you've come up with one) using only two actions:

  1. compare two cards
  2. swap the position of two cards

Carry out your new instructions, counting how many swaps and how many compares you had to do.
How many compares? How many swaps?

Imagine other shufflings. What do you think the most unsorted shuffle looks like? The one that would take the most compares and swaps.

Arrange the cards in that shuffle and then count the steps needed to sort them.
How many compares? How many swaps?

What if there were only 5 cards in this "bad" order? Or 3? Or 9? Fill in the table and plot the numbers below