Exploring some card tricks
Introduction
This article deomstrates card tricks, achieved with a process of elimination or identification.
Magic or Mathematical?
View the video and decide if it is magic or it's performance can be explained by slight of hand, or with mathematical knowledge!
Introductory card trick
What do you think?
- Magic?
- Slight of hand?
- Mathematical knowledge?
The performance of the trick can be explained in two general ways; conceptually and procedurally.
As you continue your quest to understand the trick, reflect:
- How does the trick work?
- Are you thinking of conceptual and procedural knowledge foryour explanation.
The table below includes two sets of directions, to learn how to do the card trick.
Both are important to understand a trick - conceptually and then develop procedures to perform it.
To illustrate differences between a conceptual and procedural instructional orientation, lets suppose a teacher wants to teach this card trick.
Their instruction might be more closely related to one of the following two paths of instruction. The path on the left procedural or the path on the right conceptual.
| Procedural orientation | Conceptual orientation |
|---|---|
The primary goal of this orientation is to learn a procedure to perform the trick efficiently and accurately. |
The primary goal of this orientation is to learn how the card tricks are designed and performed. How mathematical concepts can be used to design, explain, and perform this kind of card tricks. |
Outcome or objective: |
Outcome or objective: |
Watch the video: Wouldyou like to learn how do do the trick? Or you are going to learn how to do the trick today. Watch the 3 X 7 card trick demonstration. Then answer the following.
Practice. A Demonstrate the trick to another person or group. Done! Do you know how it works? If not, go to the conceptual orientation. |
Would you like to know how to design and perform card tricks? Watch this card trick and see if you can tell how she knows the card select. Discuss your their ideas on how the magician is able to identify the card selected. Ifyoiu thought that was too easy, then hang on, and we can see ways magicians use distraction to hide the obvious to get that wonder or amazement from their audience. The challenge. So how to extend might we extend what we learned and make what is happening less obvious? What if we explore different dimensions of the matrix or array of cards. For example: if we used a 5 x 5 array card trick, or 6 x 6, or any size square array of cards. More cards might make it less obvious. However, it is the same process and if the audience were able to understand a 4x4 or 5x5 or a 6x6 a square array would know that it would be possible this kind of card trick could be done so that one card, surreptitiously selected, in a million by million array, that's a total of 1,000,000,000,000 cards, could be identified by asking only two questions? Yes, but, who would want to deal that array? So making the array or matrix a larger square might not be the best way to distract. What about rectangular arrays? Will the same procedure work for an array of cards that is four columns with three rows? What about 7 columns and three rows? Before we jump to that think about a 4 x 3 array (short rectangle) card trick. Then view the 7X3 card trick. If you can explain how it works, Great!! If not, review these ideas.
Therefore, to identify or eliminate all cards in a tall rectangle array, we could deal and ask additional questions, for rectangles with more rows than columns (tall rectangle). SO if you understand how the trick works with a seven tall column and three wide rows, You will know that the selected cards (identified) are being moved to the top. However, we can add an additional level of distraction, by moving the known cards to the middle. Like the 3X7 card trick video When viewing the trick notice the identified cards are not put at the top of the rows, but put in the middle. This hides what the magician is doing to distract the audience. When you are confident of how the 3X7 card trick works, You can create a procedure to think about what steps you will do to perform the trick quickly and efficiently. Like in the 3X7 card trick video. |
| Assessment | Assessment |
Review:
Performance the trick. Go home and perform the trick for their families. Notice I did not ask anything about how or why the trick works, because that doesn't have to be an outcome for knowing a procedure to do the trick. |
Assessment here is doing the trick and creating different arrays and explaining how they either make the trick harder for an audience to figure out or easier.. Assessment information more than right or wrong answers. |
Video 3 X 7 trick with explanation
Video 4 X 4 trick in slow motion
Video 7 X 3 trick for expansion & assessment