Gifting a Mathmagic Trick

Hello friends!  Every teacher should have one or 2 really good jokes, 1 really good card trick (mine is pretty amazing) and 1 or 2 math magic tricks for their students.  This trick is one of my favorite and I thought I would share it with you.

This year I gifted my students a copy of a Math Magic Trick I taught them.  Well, I did not so much as teach it to them…they had to figure out HOW I was doing the trick and tell me WHY it worked before I would give them a copy of the trick.

Before reading further – check out the trick in action (thanks to my friend Abir – a great math teacher – for her help).

Do you know how this trick works?  

Here is how I presented it to students:

1. On day 1, after completing our unit on Exponential and Logarithmic
   Functions, I told my students that I had a Math Magic Trick that they could figure out using one of the number patterns we used in our most recent units.
2. I showed the students 7 cards and said I could ‘read their minds’.  I then asked one student to write down a number from 1 to 127 large enough for the class to read it.  I turned my back so the student could show the number to the rest of the class without my knowledge.  I then told the student all they needed to do was tell the truth.  I told the class to watch carefully and try and figure out what I was doing.

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   I then proceeded to show them each of the 7 cards one at a time asking, “Is your number on this card?” and noting if they said “Yes” or “No“.  After showing all 7 cards I announced the number to the class – to their amazement I was always correct.  It is not easy to impress my Advanced Algebra students, but this amazed them.  I told them that I would do the trick every day this week and if they could figure it out I would give them their personal copy of the trick to take home and amaze their friends and family.

3. On day 2, I did the trick again.  This time I reminded them it had to do with one of our number patterns from the exponential unit and it had something to do with how computers were programmed way back in the day (I used the visual below.)
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4. Day 3 I did the trick again and sorted the ‘yes’ and ‘no’ cards into 2 piles as I announced the number they had secretly chosen. (Note:  In this picture the secret number was 109.  Can you figure out what I am doing?)  The arrangement of cards was done to help you a bit.
5. Day 4 I made a simpler problem/trick with fewer numbers and cards.  After doing this smaller trick a few times, students started to catch on.  Can you see what I am doing in the 2 sets of cards below?  The answer to the first is 10.  The answer to the 2nd set is 7.
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6. On day 5 many students had started to figure out what I was doing.  I had students do the trick for their peers.  Finally I had them explain HOW do do the trick (Are you ready?  I am about to give away the secret to my Math Magic Trick……..The secret number is the sum of all the numbers located on the upper left of all the ‘yes’ cards).
7. My next goal was to help them figure out WHY the trick works.  I showed them the cards arranged in order and asked them to look at the number patterns we know and look for a pattern……
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8. We then talked quite a bit about the Binary Counting system and that all natural numbers can be written as the sum of powers of 2.  This would be a great place if I had time to do some ‘Exploding Dots’ work (such cool stuff) from James Tanton.  Check his stuff out HERE and HERE and his video on dividing polynomials HERE blew my mind.
9. I then handed out a copy of the trick (on card-stock 1/4 of a sheet of paper size) to every student.  This was their end of 2016 gift from me (with a free homework pass attached).

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Here are some resources if you want to print out the trick and do it yourself.  Enjoy.

• A pdf of my slides: power-of-2-puzzle-slides
• My gift (recommend printing on cardstock) math-magic-trick-cards-for-gift
• A word doc with the 7 cards (1 per page) powers-of-2-card-trick
• A word doc with 4 cards (2 per page) small-power-of-2-puzzle
• counting-in-binary