# Document 173626

```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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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
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
Which Hand?
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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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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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 ```