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Calendar Magic - Trick #1
A Simple Squares Prediction
Your Task: • Explore this magic trick • Investigate why and how it works What you will need: • One checkerboard diagram • One pencil • One friend Checkerboard Diagram 1 5 9 13 2 3 4 6 10 7 8 11 15 12 14 16 1 How to Perform the Magic Trick: 1. Write a prediction number on a sheet of paper, fold it, and set it aside. (Later, you will investigate what number to write down.) 2. Give the checkerboard diagram and pen to your friend. 3. Instruct your friend: •
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Circle any one of the 16 numbers. Draw lines through the rest of the column and row that contain this number. Circle any one of the numbers you have not crossed out. Draw lines through the rest of the column and row that contain this number. Circle any one of the numbers you have not crossed out. Draw lines through the rest of the column and row that contain this number. Circle any one of the numbers you have not crossed out. Draw lines through the rest of the column and row that contain this number. 4. Now, all of the numbers on the diagram have been either crossed out or circled. 5. Instruct your friend: • Add up the four numbers that you circled. For example, your friend might write: 1+ 6 +11 + 16 = 34 1. 6. Unfold your piece of paper to reveal the same number that your friend wrote down. 2 Investigating the Magic Trick 1. Practice the trick multiple times. Record the numbers your friend picks in the table below. Number 1 is the number from the first row, Number 2 is the number from the second row, Number 3 is the number from the third row, and Number 4 is the number from the fourth row. The Final Sum is the sum of Numbers 1 through 4. Number 1 Number 2 Number 3 Number 4 Final Sum 2. Do you notice any patterns in the Final Sum? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 3 3. How will the pattern you observed in #2 help you perform the magic trick? What number should you write on the sheet of paper in Step 1 of the magic trick? Now that you know the secret, practice the trick. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 4. Why does the pattern you observed in #2 work? Use scratch paper to explore your ideas with your group. On this page, write your explanation. __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 4 Calendar Magic–Trick #2
An Amazing Prediction
Your Task: • Explore this Calendar magic trick • Investigate why and how it works What you will need: •
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A calendar One sheet of blank paper One pen One friend or spectator How to Perform the Magic Trick: 1. Give your friend the pen and calendar. Tell your friend • Draw any square on the calendar enclosing 16 dates. 2. Write a prediction number on a sheet of paper, fold it, and set it aside. (Later, you will investigate what number to write down.) 3. Instruct your friend: •
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Circle any one of the 16 dates. Draw lines through the rest of the column and row that contain this number. Circle any one of the dates you have not crossed out. Draw lines through the rest of the column and row that contain this number. Circle any one of the dates you have not crossed out. Draw lines through the rest of the column and row that contain this number. Circle any one of the dates you have not crossed out. Draw lines through the rest of the column and row that contain this number. 5 4. Now, all of the dates in the square have been either crossed out or circled. 5. Instruct your friend: • Add up the four dates that you circled. For example, your friend might write: 1+ 6 +11 + 16 = 34 6. Now, unfold your piece of paper to reveal the same number that your friend wrote down. 6 Investigating the Magic Trick 1.
Practice the trick multiple times. Record the First Date, Last Date, and Final Sum in the table below. First Date is the first date in the square selected by your friend. Last Date is the last date in the square selected by your friend. The Final Sum is the sum of the 4 dates chosen by your friend. First Date Last Date Final Sum 7 2. Do you notice any patterns between the First Date, Last Date, and Final Sum? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 3. How will the pattern you observed in #2 help you perform the magic trick? Given a square, what prediction should you write on the piece of paper? Now that you know the secret, practice the trick. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 8 4)* Why does the pattern you observed in #2 work? Use scratch paper to explore your ideas with your group. On this page, write your explanation in full sentences. __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 9 Card Trick # 1
Columns and Rows
Your Task: • Practice performing this card trick. • Discover how it works. What You Need: • A deck of cards • One friend or audience member How to Perform the Magic Trick: 1. Deal out 16 cards face up in a square with 4 rows and 4 columns. 2. Tell your friend • Pick a card and write it on this sheet of paper. • Don’t let me see the paper. • Just tell me which of the 4 columns the card is in. 3. Now, collect the 16 cards back into a deck following these rules: • Collect them one column at a time. • For each column, pick up cards from the top of the column to the bottom, keeping them in the same order. 4. Deal the cards out following these directions: • Deal out 4 cards horizontally in a row, then 4 more cards just below the first 4, then 4 more, and then 4 more to give a square. 1 5. Ask your friend: • Which of the four columns is your card in? 6. Now, you have enough information to say: “The card you picked is ________________________________.” 2 Investigating the Trick
Answer the following questions to discover: • The card that your friend picked • and how the trick worked. 1) Practice the trick twice and record both the square of cards dealt in Step 1 and the square of cards dealt in Step 4. Practice 1 Step 1 Square: Practice 2 Step 1 Square: Step 4 Square 3 Step 4 Square How does the square change between the two deals? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 2) If you know which column a card is in in the Step 1 square and which column a card is in the Step 4 square, can you figure out the card? Why or why not? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 3) How does your answer to the previous question help you perform the magic trick? Now that you know the secret, practice the magic trick. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 4 Card Trick # 4
A Baffling Prediction
Your Task: • Practice performing this card trick. • Discover why it works. What You Need: • A deck of cards • One friend or audience member • Pen and paper How to Perform the Magic Trick: Step 1: Hand your friend the deck of cards and ask her to shuffle them a couple times. Step 2: As she shuffles or when she hands the cards back, be sure to note the card on the bottom of the stack. Step 3: Now, tell your friend: “Before we begin, I am going to write a prediction on the this piece of paper.” Step 4: Write the card from the bottom of the deck on this piece of paper. Fold the paper and set it aside. Step 5: Deal out 3 rows of 4 cards so that all of the cards are facedown. 1 Step 6: Tell your friend: “Flip over any 4 cards.” Step 7: Collect the remaining 8 cards and put them on the bottom of your deck. Step 8: Say to your friend: “Let’s deal additional cards under each of your cards, to bring the value of the card up to ten.” Specifically: • If the card is an ace, deal 9 cards facedown in a pile under the card. • If the card is a two, deal 8 cards facedown in a pile under the card • If the card is a three, deal 7 cards facedown in a pile under the card. • If the card is a four, deal 6 cards facedown in a pile under the card. … • And, if the card is a ten, jack, queen, king, do not deal any cards. Step 8: Now, say to your friend: • Add up the values of the cards that you chose. (Aces are 1, and jacks, kings, and queens are 10) • Tell me the number. Step 9: Take your deck. Deal out the cards facedown counting until you reach the number that your friend calculated. On that number, flip the card over. Step 10: Say, “I knew we were going to end at this card all along.” Unfold your piece of paper to reveal the name of the card that you just flipped over. 2 Investigating the Trick
Answer the following questions to discover how the trick worked. 1) Practice the trick three times and make sure that you can perform it correctly. 2) Perform the trick several more times. Now, keep track of the number of cards that you deal at each step. # Dealt in Step 5 # Dealt in # Dealt in Total # Step 8 Step 9 Dealt Do you notice any patterns? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 3 3) Work through the trick and explain why the pattern you observed in the last question holds. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 4) How does your answer to the previous question explain why the magic trick always ends on the card that was originally on the bottom of the deck? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 4 Coin Trick # 1
The Mystery of Nines
Your Task: • Practice performing this coin trick. • Discover how it works. • Explore ways to change the magic trick. What You Need: • A collection of about 18 pennies, arranged in the Nine Diagram below • One small piece of paper • One friend or audience member Nine Diagram 1 How to Perform the Magic Trick: 1. Show your friend the Nine Diagram and give her the small piece of paper. Then turn your around so you can no longer see the diagram. Give your friend these instructions: • Pick any number larger than 7, but don’t tell me what it is. • Start at the first penny in the nine’s tail. • Count up and around the nine counterclockwise until you reach your number. For example, if your friend picked 13, he would begin in the diagram where it says “Start here” and then count to 13, ending where the diagram says “End here.” 2 2. Now tell your friend: • Beginning at the coin you last touched, count from one until you reach your number, going clockwise around the circle in the Nine Diagram. • Conceal the small piece of paper under the coin that you stopped on. For example, if your friend had picked 13 as before, he would begin in the diagram where it says “Start Here” and then count to 13, ending on the penny where it says “End Here.” He would put the small piece of paper under that penny. 3. Turn around and flip over a penny to reveal the small piece of paper. (You will investigate how to know where the paper is on the next page). Then say: See, I knew you were going to end there all along! 3 Investigating the Trick
Answer the following questions to discover: • the penny where your friend will put the paper, • and how the trick works. 1) Label the pennies in the circle portion of the 9 Diagram using capital letters as shown below: 2) Practice the trick with different numbers. Keep track of the chosen number and the final position using the table. Beginning Number Final Position 4 3) Is there a relationship between the chosen number and the final position? What can you say about the final position? Under which penny will your friend put the small piece of paper? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 4) Why does this pattern you observed in #3 happen? Use scratch paper to explore your ideas with your group. On this page, write your explanation in full sentences. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 5 Investigate Why the Trick Works Divide the Nine Diagram into the circle part and the tail part. 5) Practice the trick with different numbers. Keep track of the number of pennies you count in the circle during the first two steps of the magic trick. Number of Pennies Number of Pennies Difference between Counted Counter-­‐ Counted Clockwise the Numbers of Clockwise in the in the Circle in Pennies Circle in Step 1 Step 2 6 6) Do you notice a pattern in the difference between the number of pennies? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 7) How does your answer to the previous question explain why the magic trick always lands on the same penny? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 7 Coin Trick # 2
Which Hand?
In this activity, you will: • Practice performing a magic trick using coins. • Investigate why the trick works. Needed Materials: • A nickel and a dime Goal of the Magic Trick: predict which hands the two coins are in. 1 Understanding the Problem Read the following instructions out-­‐loud with your partner. One important piece of the magic trick instructions will be missing. Magic Trick Instructions STEP 1: Give your partner the nickel and dime and tell him: • Put one coin in each hand. • Do not let me see which coin is in which hand. For example, your partner might put the nickel in his left hand and the dime in his right hand. STEP 2: Now, instruct your partner: • Multiply the value of the coin in your left hand by any even number and the value of the coin in your right hand by any odd number. • Add the two numbers together to get a FINAL SUM. For example, your partner might pick the even number 8 and the odd number 7 and then calculate: 𝐹𝐼𝑁𝐴𝐿 𝑆𝑈𝑀 = 5 × 8 + 10 ×7 = 110. STEP 3: Say to your friend: • I can almost sense which hand each of the coins are in. • I just need a little more information. • Was the FINAL SUM you calculated even or odd? For example, your friend might say, “The final sum is even.” 2 STEP 4: Lastly, you say: I can now see which hand each of the coins are in. The Nickel is in your ______________ hand. The Dime is in your _______________ hand. ___________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________________________________________________________ Check Your Understanding 1) What is the goal of this magic trick? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 2) When you finish STEP 3, what information do you have? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 3) What information is missing from STEP 4? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 3 Finishing the Magic Trick To be able to do the magic trick, we need to answer the question: If you know that the FINAL SUM is even or odd, how can you determine the position of the two coins? With your partner brainstorm methods to attack this problem. 4 One possible method of attack is making a table and observing a pattern. Practice the trick with different numbers. Keep track of the where the coins are and whether the FINAL SUM is even or odd. Coin in Right Hand Coin in Left Hand FINAL SUM 5 1) Is there a relationship between the position of the coins and the FINAL SUM? If so, what is it? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 2) What happens when the nickel is in the right hand? Using facts about even and odd numbers, explain why that happens. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 3) What happens when the nickel is in the left hand? Using facts about even and odd numbers, explain why that happens. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 4) Now that you know how to do STEP 4, practice the magic trick twice with your partner. Did the trick work? If not, explain what went wrong. __________________________________________________________________________________ __________________________________________________________________________________ 6 __________________________________________________________________________________ 7 Magic with Dice- Trick #1
Guessing the Total
Your Task: • Explore this dice magic trick • Investigate why and how it works • Investigate other, more advanced tricks using the same techniques What you will need: •
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Three dice One sheet of blank paper One pen One friend or spectator How to Perform the Magic Trick: 1. Hand the three dice to your friend and turn around so that you cannot see the dice. 2. Instruct your friend: • Throw the three dice and add up number of dots showing. • Write this number on the paper and call it Number 1. For example, your friend might write: Number 1 = 2+4+3 = 11 1 3. Now give your friend these instructions: • Pick up one of the dice. Add the number of dots on its bottom to Number 1. • Label this new number as Number 2. For example, your friend might write: Number 2 = Number 1 + 3 = 11 + 3 = 14 4. Now tell your friend: • Roll the die that you just picked up. • Add the number it shows to Number 2 to obtain a new number. • Label this number as Number 3. For example, your friend might write: 2 +5 = 14+5 =19 Number 3 = Number 5. Now turn around and look at the dice on the table. Even though you do not know which dice was thrown twice, you will be able to tell your friend that Number 3 must be _____________. You will investigate how to find Number 3 on the next page. 2 Investigating the Magic Trick
Answer the following questions to discover: • How to find Number 3, • How the trick actually works. 1. Practice the trick multiple times. Record the numbers showing on each die when you turn around, their overall sum and the sum, called Number 3, that is calculated by your friend. Die 1 Die 2 Die 3 Die 1 + Die 2 +Die 3 Number 3 2. Do you notice any patterns between the sum Die 1 + Die 2 + Die 3 and the sum, Number 3, calculated by your friend? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 3 3. How will the pattern you observed in #2 help you perform the magic trick? When you turn around and see Die 1, Die 2, and Die 3, how can calculate Number 3? Now that you know the secret, practice the trick. _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ 1) Why does this pattern you observed in #2 happen? Use scratch paper to explore your ideas with your group. On this page, write your explanation. __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 4 Magic with Dice - Trick #2
A Stack of Dice
Your Task: • Explore this dice magic trick • Investigate why and how it works What you will need: •
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Three dice 21 Q-­‐Tips One sheet of blank paper One pen One hat One friend or spectator How to Perform the Magic Trick: 1. Put the 21 Q-­‐Tips in your pocket. Give your friend the pen, paper, and the three dice. Turn around so that you can’t see the dice. 2. Instruct your friend: • Make a stack of three dice one on top of the other. • Add the two faces which are touching on the top and middle dice. • To this number, add the sum of the touching faces on the middle and bottom dice. • To this number, add the bottom of the lowest dice. • Write this number on your sheet of paper. For example, your friend might write: Sum = 5+ 3 +4 + 6+1 = 19 5 3. Turn around briefly and tell your friend: • Cover the dice stack with a hat (or anything else). As you turn around, be sure to note the face of the top-­‐most dice in the stack. 4. At this point, you will be able to calculate the sum your friend wrote down. (You will investigate how on the next page.) 5. Pull out that number of Q-­‐Tips from your pocket as your turn around completely. Tell your friend: I knew you would get the number ____________, and show him you are holding the correct number of Q-­‐Tips. 6 Investigating the Magic Trick
Think about it! This Magic trick uses the same techniques as the last magic trick. For the last trick, you observed: The top and bottom of a die always add to seven. Use that fact to explain this magic trick. In particular, in Step 4, how can you find the sum calculated by your friend, using only the number on the top of the stack of dice? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ What is the relationship between 21 (the number of Q-­‐Tips) and the sum that your friend calculated? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 7