I plan to use this activity in class on the first day. Besides being an interesting challenge, I think it can be used to the show the power and magic of mathematics. It is also a great way to introduce problem solving and different problem solving strategies including draw a picture or diagram, look for a pattern, logical reasoning, work backwards and PERSEVERANCE.
Prepare thirteen playing cards, all the same suit. Then place the cards in a specific order so that when you flip over every other card you will reveal the cards in descending order. More specifically, when you flip over the top card it will be a King, and then the next card is placed at the bottom of the pile still face down. The next card flipped over is a queen, and then the next card is placed at the bottom of the pile, etc. This process repeats until you have revealed all the cards in order from King to Ace.
When you show this trick it seems deceptively easy and students jump in and think they have it right away. Then the fun begins! When they "run through" the deck the first time, the pattern usually works up to 7, but then breaks down after that because they didn't take into account that some of the cards would come to the top of the deck multiple times. It is exciting to watch students struggle with this problem, try different strategies, get more feedback directly from the cards, and then try again.
I plan to show this trick towards the end of class on the first day and let students try to solve the problem. I am hoping some students will go home and work on it at home and then show how they solved it in class the next day.
I plan to show the students how to solve this problem by drawing a diagram.
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Using this diagram we can fill in the cards that need to be in each position. You simply write in the K, skip a line, Q, skip a line, etc. Then when you reach the end, start over and continue to skip a blank line each time.
This is a great activity for math class, but I think it could also be used effectively in other classes or advisory groups.