calendar magic - trick #1 with dice - trick #2 !! !! %%%%%how%to%perform%the%magic%trick:% %! %

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1 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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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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      

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 5    

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           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:  

 • 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.      

         

1.      6. Unfold  your  piece  of  paper  to  reveal  the  same  number  that  your                friend  wrote  down.  

   

For  example,  your  friend  might  write:      

     

       1+  6  +11  +  16  =  34  

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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?    _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________  

   

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 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.      __________________________________________________________________________  

    __________________________________________________________________________      

__________________________________________________________________________       __________________________________________________________________________    

__________________________________________________________________________    

  __________________________________________________________________________       __________________________________________________________________________    

__________________________________________________________________________    

  __________________________________________________________________________      

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Calendar Magic–Trick #2 An Amazing Prediction

Your  Task:    

• Explore  this  Calendar  magic  trick  • Investigate  why  and  how  it  works  

 What  you  will  need:  

 

• 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:  

 • 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.  

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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.      

               

6. Now,  unfold  your  piece  of  paper  to  reveal  the  same  number  that  your                  friend  wrote  down.        

   

For  example,  your  friend  might  write:      

     

       1+  6  +11  +  16  =  34  

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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  

                                                           

     

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 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.  

 _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________  

   

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 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.    __________________________________________________________________________  

    __________________________________________________________________________      

__________________________________________________________________________       __________________________________________________________________________    

__________________________________________________________________________    

  __________________________________________________________________________       __________________________________________________________________________      

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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.  

   

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 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  ________________________________.”  

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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:        

                               

      Step  4  Square          

                               

          Practice  2         Step  1  Square:        

                               

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      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.  

    __________________________________________________________________________________  

    __________________________________________________________________________________    

__________________________________________________________________________________       __________________________________________________________________________________  

 

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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.    

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 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.  

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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  Step  8  

#  Dealt  in  Step  9  

Total  #  Dealt  

   

     

   

     

   

     

   

     

   

     

            Do  you  notice  any  patterns?         __________________________________________________________________________________       __________________________________________________________________________________    

__________________________________________________________________________________      

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 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?       __________________________________________________________________________________  

    __________________________________________________________________________________    

__________________________________________________________________________________  

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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      

 

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   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.”  

     

   

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 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!    

   

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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    

                           

   

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 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.      __________________________________________________________________________________  

    __________________________________________________________________________________    

__________________________________________________________________________________       __________________________________________________________________________________       __________________________________________________________________________________    

__________________________________________________________________________________       __________________________________________________________________________________       __________________________________________________________________________________    

__________________________________________________________________________________    

__________________________________________________________________________________      

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 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  Counted  Counter-­‐Clockwise  in  the  Circle  in    Step  1    

Number  of  Pennies  Counted  Clockwise  in  the  Circle  in    

Step  2  

Difference  between  the  Numbers  of  

Pennies  

                             

     

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 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?    __________________________________________________________________________________  

    __________________________________________________________________________________    

__________________________________________________________________________________    __________________________________________________________________________________  

     

       

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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.    

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  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.”                            

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    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?    

  __________________________________________________________________________________    

__________________________________________________________________________________       __________________________________________________________________________________  

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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.  

   

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   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  

                             

     

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 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.    __________________________________________________________________________________  

    __________________________________________________________________________________    

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__________________________________________________________________________________    

       

 

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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:  

 

• 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  

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 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.                

   

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.  

                   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.  

For  example,  your  friend  might  write:          

Number  3  =  Number  2  +5  =  14+5  =19  

For  example,  your  friend  might  write:      

     

Number  2  =    Number  1  +  3  =  11  +  3  =  14  

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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?      _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________    _________________________________________________________________________________  

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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.    __________________________________________________________________________  

    __________________________________________________________________________      

__________________________________________________________________________       __________________________________________________________________________    

__________________________________________________________________________    

  __________________________________________________________________________    

__________________________________________________________________________    

  __________________________________________________________________________        

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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:  

 

• 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  

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   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.        

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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?  

 __________________________________________________________________________    

  __________________________________________________________________________    

__________________________________________________________________________