S: Mind Reader by Kari Speer
FC: Mind Reader | By: Kari Speer
1: What you will need: | 1. A Deck of Cards 2. A Pencil 3. A Piece of Paper 4. A Partner
2: Background Information | Pencils are categorized according to their marking materials (graphite pencils, solid graphite pencils, charcoal pencils, carbon pencils, coloured pencils or pencil crayons, grease pencils, and watercolour pencils), to their use (carpenter's pencils, copying pencils, erasable colour pencils, non-reproducing, stenographer's pencil, and gold pencil), their shape (triangular or reuleaux triangle, hexagonal, round, and bendable or flexible plastic), size, manufacture, and other types. Most pencil cores are made up of graphite mixed with a clay binder (regular pencil). The other types of pencil cores are charcoal (used for sketching), waxy core (colored pencils), crayon-like waxy core (grease pencils). The most common type of pencil casing is a wooden cylinder that is bonded around the core. Some other material that is also used for the pencil casing are plastic or paper (this can be found at http://enwikipedia.org/wiki/Pencil). | Playing cards are believed to have been invented in Ancient India. A deck of cards, also known as playing cards, consists of 52 cards plus 2 jokers. It has four suits consisting of hearts, diamonds, clubs, and spades. A jack is also known as a knave, and all of the face cards have special names (this can be found at http://en.wikipedia.org/wiki/The_Deck_of_Cards and http://en.wikipedia.org/wiki/Playing_card). | Paper is made by pressing together moist fibers, typically cellulose pulp derived from wood, rags or grasses, and drying them into flexible sheets. Some manufacturers have started using a new, significantly more environmentally friendly alternative to expanded plastic packaging made out of paper, known commercially as paperfoam (this can be found at http://en.wikipedia.org/wiki/Paper).
3: What To Do: | 1. Remove the tens and the face cards (jacks, queens, and kings) from the deck, and set them aside. While you're at it, get rid of the jokers too. 2. Shuffle the cards. 3. Ask your friend to pick a card from the deck. 4. Tell your friend not to show it to you, but to memorize the number on their card. (It doesn't matter what suit it is - that term refers to whether it's a heart, club, spade, or diamond. All you care about is the number. 5. Have your friend put his card on the table, face, down. 6. Now you pick a card from the deck. Don't show it to your friend. 7. Memorize the number on your card. 8. Lay your card face down on the table next to your friend's card. Your card should be on the right side of your friend's card as your friend sees it. 9. Give your friend the paper and pencil so that they can do some math. Tell your friend to: Double the value of their memorized card. Add 2 to that number. Multiply that answer by 5. 10. Now it's your turn to do a little math. No paper and pencil for you - in your head, subtract the number of your memorized card from 10. 11. Have your friend subtract your answer from their final answer. 12. Say "Are you thinking of this number?" Flip over your friend's card and flip over your card. The two cards together should make the number that your friend has calculated.
4: How to Do the Experiment Using the Scientific Method
5: Step 1 -Exploration | Make some observations based on trying out the experiment. Make a T-Chart and write down your observations and I wonder questions. | Sample T-Chart Observations and I wonder questions: | Observations cards are white and blue cards are smooth and stiff people are different ages pencil is a #2 standard pencil paper is white with blue lines | I wonder... what would change if we used different people and ages if older people would figure out how the trick works if the cards have been used before how the cards, pencil, and paper are made
6: Step 2-Researchable Question | The next step in conducting an experiment is to take your I wonder questions that you want to find out the answer to. An example would be: What is the effect of age on their perception of the magic trick? *NOTE: A researchable question usually has a manipulated variable and a responding variable. The example from above is What is the effect of age on the perception of the magic trick ? Where in the example above the first blank is the manipulated (or changed) variable and the second blank is the responding variable (or what is responding to the change).
7: Step 3 - Hypothesis | The next step is to create a hypothesis, or an informed theory about what you will think will happen in the experiment. In doing the experiment you will be trying to prove if your hypothesis is right or wrong. An example hypothesis would be: If the person's age changes, then as the ages increase they will be able to understand how the magic trick works. *NOTE: Most hypothesis statements start with an If/then statement. If this happens, then this will be the resulting factor.
8: Step 4-Operational Definitions | In this step of the Scientific Method, we want to define what we are working with. Variable are either manipulated (things that can be used or changed), responding (things that are a result of the manipulated variable), and controlled (variables that do not change). Below is an example of the Variables and their Operational Definitions. | Variables | 1. Manipulated Variable: age environment 2. Responding Variable perception | Controlled Variables | 1. Deck of Cards 2. Number of cards 3. Number of times the magic trick was done on one person | Operational Definitions | 5, 11, 18, 23, 28, 38, 53 in their own homes did they figure out the trick? Bicycle (blue and white) 36 3
9: Step 5-Experimental Plan | In this step is where we outline or map out what we need for the experiment and have detailed steps on how you are going to do the experiment. | Outline Example | I. Materials Needed: 1. A deck of playing cards 2. A piece of paper 3. A pencil 4. A partner II. The Plan 1. Conduct the experiment on a partner and see if they can figure it out. 2. Conduct the experiment on the partner again if they did not figure it out. 3. Conduct the experiment on the partner again to see if they can figure it out. 4. If they did not figure it out explain how the magic trick works (see page 14 & 15 for an explanation). 5. Conduct the experiment on another partner and continue conducting the experiment on different partners until you feel you have enough data to prove your hypothesis wrong or right.
10: Step 6-Conduct Experiment | At this step is where you record your data in a table to see if the people you conducted the experiment on were able to understand how the trick worked and if it took them 1, 2, or 3 tries to figure out how it worked. Also while you are conducting the experiments you need to record any new observations or new I wonder questions that you may have. | Sample Data: | Mean is the average of the data. Median is the middle number or answer. Mode is the answer given most often. Range is the distance between the smallest and largest number. (We will not have a range since there is not a numerical answer).
11: Step 7-Analyze Data | At this step you want to refer back to your hypothesis (If the person's age changes, then the older the person is they will be more likely to understand how the magic trick works) and see if your data you collected supports or disproves your hypothesis.
12: Step 8-Conclusion | Did Our Data Prove Our Hypothesis? | This is the last step. Here is where you decide if your hypothesis was right or wrong. (You do not want to go back and change your hypothesis to make yourself right). | YES!! | Looking at our data the older the person got they were able to understand how the magic trick worked. When reporting about your science experiment, you might say: "My data supports the hypothesis because the older the person was the more they were able to understand the magic trick."
13: Continue for Problem Solving Tips and how the experiment actually works
14: If the two cards do not match your friend's answer, the problem is probably one of two things. Either, you put your card to the left instead of the right of your friend's card (and this is your friend's right as they are looking at the cards), or your friend needs their math checked. You now know the number of your friend's card so say something like, "I know the magic works, so let's check your math." Then work through the math together. | Having Trouble? | Can you figure out how this works? It's very tricky. To show you, we'll run through an example of this card trick. Suppose your friend chooses a card that has the number 3 on it. Following the above directions, your friend would do this math: 3 x 2 = 6 6 + 2 = 8 8 x 5 = 40 Suppose your card was an 8: 10-8=2 Your friend then does this calculation: 40 (their result) - 2 (your result) = 38 Then you flip over your friend's card. You don't know what it is until you flip it over, but when you flip it over you'll find a 3. Flip over your card and you'll find an 8 (you already knew that , of course. The two cards together spell out 38, and that's the number your friend has calculated. Amazing! To understand why this works, you need to think about what the 3 and the 8 in 38 really means. The position of the 3 and the 8 are important - after all, 38 and 83 are very different numbers! In 38, the 8 tells you how many ones there are - it's in the ones place. The 3 tells you haw many tens there are - it's in the tens place. In 38, there are 3 tens. Three tens is the same as 30. (30 _ 8 - 38!) When you had a friend do all that arithmetic, it was a round-about way of moving their card number to the tens place and putting your card number in the ones place.. After you try this trick a few times, you'll soon realize that it doesn't matter what numbers you or your friend choose. The trick works no matter what. | Whats Going On?
15: Mind Reader Explanation | We gave you a simple explanation of the Mind Reader trick on the previous page. Here's a more mathematical explanation for those of you who are more mathematically inclined. To see what's going on, let's go through the steps of the trick one at a time. Because it doesn't matter what number your friend chooses, we're going to represent that number with an Y. This Y could be any number from one to nine. First you told your friend to double their number. that means they multiplied their number by 2, like this: 2 x Y Next you told your friend to add 2, which gives you this: (2 x Y) + 2 Then you told your friend to multiply by 5, so you get this: ([2 x Y] + 2) x 5 That may look pretty complicated, but you can make it look simpler. What you are really doing is adding two numbers - (2 x Y) and 2 - and then multiplying each number by 5 and then adding them together. That means that this: ([2 x Y] +2) x 5 is the same as this: ([2 x Y] x 5) + (2 x 5) is the same as this: (10 x Y) + 10 By doing all that math, your friend multiplied their number by 10 and then added 10 to the answer. So if their number was 3, now has: (10 x 3) + 10 = 40 You don't need to know what number they get - as long as you know that it's 10 times their original number plus 10. Then you need to have them subtract enough to make the 10 that you had them add on equal the number on the card you chose. Let's say your number was 8. You want them to get to 38. How do you do that? Well, you subtract your number from 10. So if your number was 8, you subtract your number from 10 and got 2. Then you ask your friend to subtract 2 from their number. Their number was 40. 40 - 2 = 38 Your friend ends up thinking of 38. You turn the cards over and there's the answer: a 3 and an 8. Magic! (Or maybe a little bit of math)
16: Tips and Tricks for Adults | If there are students that do not know how to multiply or add you will need to help them with that. Also, check to make sure when they are doing the experiment that they put their card to the right of their partner's card at their partner's point of view. If you do not have a deck of cards you can use a piece of paper and have the partner write a number from one to nine on that piece of paper and lay it face down on the table and then have the student write a number from one to nine on a piece of paper and lay it face down on the table to the right of their partner's piece of paper. Take pictures while the student is doing the experiment with other students so they have post them on their Science Fair board. Also, ask permission to the student and/or adult to use their picture on the Science Fair board.
17: Tips and Tricks for Students | If one of your partners does not know how to add or multiply have an adult or another person who knows how to to add and multiply to help them. If you do not have or lose your deck of cards have your partner write down on a piece of paper a number from one to nine and lay it face down on the table, and then you write a number from one to nine on another piece of paper and lay it face down to the right of your partner's piece of paper. To put together a science fair board you will want to use any pictures you have taken and data you have written down should be put on the board. Place the cards pencil and paper on the table so if people want to try it out you can conduct the experiment with them. You will want to prepare a short speech about the experiment. Talk about how the math works only with the single digit numbers.