Selecting and Using Mathemagic Tricks in the Classroom By: Michael E. Matthews

1. Selecting and Using Mathemagic Tricks in the ClassroomBy: Michael E. Matthews Presentation By: Courtney Baron

2. Brief Overview • This article shares four different magic tricks and how to dazzle your audience with them. • Along with the magic tricks, the article shares an algebraic or geometric explanation for how and why the trick works. • Right now, I will physically demonstrate two tricks and how they work.

3. I know everyone is dazzled by my magic skills. However, I will just explain the next two tricks using my English skills (because this presentation is supposed to be 20 minutes).

4. The Mind Control Clock Trick • Hand out paper clocks to the students, making sure that the hours 1-12 are clearly labeled on the clock. • Ask the student to pick a number on the clock and put a finger on the number (which will now be referred to as n) • Students should move 6 hours clockwise. • Then, each student should move n hours counterclockwise. • Then each student would move m hours clockwise (where m is a number picked out ahead of time) • Finally, the teacher will magically name the number that every student is “touching”.

5. Was that Magic? No, even better… It’s math! 

6. How it works… • During the second to last step, each student should be on 6, regardless of where they started. • If the student picked n:00, they are n hours away from 12:00. • The first step (6 hours clockwise) is a 180⁰ rotation, which will now have them n hours away from 6:00. • So, when the student is told to move n hours in the opposite direction, it will always lead them to 6:00. • This is why once the student moves m spaces clockwise, the teacher will know in his/her head the students will be ending up at [6+m]:00 if 1 ≤ m≤ 6, and they will be ending up at [m-6]:00 if 7 ≤ m ≤ 12

7. “The Name of the Card is” Trick • Ask a student to silently pick a 3-digit number whose digits are all unique. • Then have the student reverse the digits of this number and subtract the smaller number from the larger number. • Now have the volunteer add the digits in the answer (call the sum of the digits d), and ask the volunteer to pull out the card in the dth position from the top of the deck and show it to the class. • Then, magically name the card and amaze your students!

8. How it works… • The digits will always add to 18, so the dth position in the deck will always be the 18th card, so the teacher should just know which card is 18th from the top. • The algebra will be explained on the whiteboard…

9. NCTM Standards (Algebra) • Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions • Interpret representations of functions of two variables • Use symbolic algebra to represent and explain mathematical relationships

10. Key Points • Algebra Connections • Introduce combining like terms with the first trick • The last trick can be done after the students have started to understand how to combine like terms and you want to extend their comprehension by exploring place value through algebra. • The second tricks is an extension of systems of equations. It is a great application of systems of equations, to be used when students already have good background knowledge of the material. • Geometric Connection • The third trick is a great way to include something fun in a unit on transformations.

11. Strengths • The magic tricks discussed in the article are fun and relevant to the material. • I could use the first trick when teaching combining like terms and distribution. • The second and fourth tricks would come in handy when discussing multivariable equations • The third trick relates to transformations in geometry, but also logical thinking.

12. Strengths • I very rarely meet people who hate magic tricks, so I think these tricks would engage students and hold their interest. • People usually like to find out how the trick is done, so students attention will be held for the explanation which, of course, is algebra. • These are tricks that aren’t “five minute fillers” but provide meaningful lessons. • The article tells you at what point in the curriculum you should implement each trick.

13. Weaknesses • The tricks are rather advanced, and while students may enjoy watching the tricks, they might not be able to comprehend the logic behind the explanations. • In order to recreate the magic trick, students don’t have to understand why the trick works, they only need to memorize the steps to complete the trick. • There isn’t a clear way to assess students’ understanding of the tricks (since I wouldn’t want to ruin a fun activity with a quiz), so they might just end up being flashy “five minute fillers” to many students who don’t really understand why I chose to implement the tricks in the lesson.

14. Implementation in the Classroom • Each of the tricks would be implemented at different parts of the corresponding lessons (introduction, extension, application). • The tricks make for a very enjoyable anticipatory set for the students. Since most people enjoy magic, it should hook attention. • The teacher wants to make sure he/she has a firm grasp on the trick, so it will hook students’ attention. If the trick fails, the students might lose interest, or not continue enjoying the lesson because “my teacher doesn’t even know what she’s talking about.”

15. Citation Matthews, Michael, E. Selecting and Using Mathemagic Tricks in the Classroom. Volume 102. Number 2. September 2008.