Math Fair Guidelines - KSECksec.ca/wp-content/uploads/2015/03/KMEPPuzzles.doc · Web viewSudoku are suitable for Kivalliq math classrooms because: They develop logic, reasoning

KMEP Presents

Classroom Puzzles

Kivalliq Math Education Panel

Kivalliq School Operations 2011

Team Work

Communication

Concentration

Logical Reasoning

Problem Solving


AcknowledgementsThe document Classroom Puzzles was compile, adapted, and developed by the 2006 Kivalliq Math Education Panel Kivalliq School Operations acknowledges and thanks the following teachers for their time and commitment to this project.

Kristen Sawyers Inuglak School Whale CoveEva Angoo Leo Ussak School Rankin InletTaras Humen Rachel Arngnammaktiq School Baker LakeBertha Iglookyouak Rachel Arngnammaktiq School Baker LakeJim Kreuger Kivalliq School Operations Baker Lake

For more puzzles check out the following web resources:

www.puzzles.com/ www.puzzles.ca/linklist.html )

Preface

Puzzles should be a challenging part of your daily routine. They may be given to your class as a group problem solving exercise or developed into centres. Puzzles help to develop the following skills in you class:

reading problem solving logical reasoning lateral thinking perseverance concentration teamwork and communication

Knowing the answer is not a necessary requirement to using a puzzle in your classroom. In many ways, not knowing the answer helps the teacher to challenge the students to find the solution and show the whole class. If answers are known, teachers should not provide them to their students as this practice could reduce students’ efforts to find the answers themselves.

Math Puzzles of this type, can also be sent home with your students for their parents’ help. Homework like this will get the whole family involved. An electronic version of this document can be found in the First Class System:

Kivalliq ConferencesKivalliq MathMath Month

Jim KreugerBaker Lake--February 11, 2011

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http://www.puzzles.ca/linklist.html

http://www.puzzles.com/

Classroom Puzzles

Table of Contents

Stick Puzzles.......................................................................................................2Coin Puzzles........................................................................................................3Number Pattern Puzzle.......................................................................................6Building Polygons................................................................................................6Thelon Puzzle I....................................................................................................6Thelon Puzzle II...................................................................................................7Wild Tic-Tac-Toe.................................................................................................7Measuring Cups..................................................................................................7Pentominoes........................................................................................................7Rush Hour...........................................................................................................9Tangram ............................................................................................................9Simple Sudoku..................................................................................................10KenKen Puzzles................................................................................................12Topological Puzzles...........................................................................................14

Handcuff Puzzle Puzzles..........................................................................15Hand Cut...................................................................................................16Thumb Trap..............................................................................................17Catch Me If You Can.................................................................................18Ring On a String........................................................................................19Linking Paper Clips...................................................................................20Hand to Hand Switcheroo.........................................................................21Tie a Knot Challenge.................................................................................22Looped String Puzzle................................................................................23Mobius Madness.......................................................................................24

Math Wuzzles....................................................................................................26

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Stick Puzzles

Sticks IUse popsickle sticks or tooth picks to make the shape on the left. Remove the smallest number of sticks to leave four little triangles.

Sticks IIUse popsickle sticks or tooth picks to make the shape on the right. There are four small squares. Move as few sticks as possible to make three small squares. All sticks must be used.

Sticks IIIUse popsickle sticks or tooth picks to make the shape on the left. There are four small squares here. Remove as few sticks as you can to Ieave two squares.

Sticks IVUse popsickle sticks or tooth picks to make the shape on the right. Move four sticks and make three non-overlapping parallelograms that are exactly the same.

Sticks VUse popsickle sticks or tooth picks to make the shape on the left. Move three sticks and make two non-overlapping quadrilaterals that are exactly the same.

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Classroom Puzzles

Coin Puzzles

Sliding Pennies I Six pennies are placed on the table to form a triangle as shown. By sliding one penny at a time, move them to form the shape on the far right. You can only move one penny at a time, without disturbing any other penny. When you move a penny, it has to be moved to a position where it touches two others.

The pennies have to stay flat on the table at all times.

Sliding Pennies II Place six pennies on the table in two rows as shown on the far left. The object is to turn these two rows into the coin circle shown in the right figure in only three moves.

A move consists of sliding one coin to a new position, where the moved coin has to touch two other coins.

Coin SquadTake four coins of the same size or four two-colour counters and make a square as shown in the far left square in the illustration; two coins - heads up in the top row, and the other two - tails up in the bottom row.

The object is to make another square with two coins heads up on one diagonal and with two coins tails up on the other - as shown in the right square in the illustration.

This should be performed in the shortest possible number of moves.

A move consists of sliding a pair of the two adjoining coins to a new place. You have to slide the coins only orthogonally; it means that you are not allowed to rotate the pair of coins while you move it. The final square not necessarily needs to be formed exactly at the same spot as the start square was.

Tip the CupMake the depicted cup with eight coins of the same size as shown in the illustration. The object is to move only two of them in a new position to get the cup standing upside-down.

You're allowed to move the coins as you wish but at the end the cup has to have exactly the same shape only rotated at 180 degrees from its start position.

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ExchangeTake six two-colour counters of the same size and arrange them in the capital L altering colours as shown in the illustration - left position.

The goal is to make another L with all the two colour counters having their heads and tails exchanged as shown in the right position of the illustration. It should be performed in the fewest possible number of moves.

A move consists of sliding a pair of the two adjoining two colour counterss to a new place. You have to slide the two colour counterss only orthogonally; it means that you are not allowed to rotate the pair of two colour counterss while you move it. The final L not necessarily has to be formed exactly at the same spot as the start L was.

Sort the Counters

Arrange five two-colour counters (or coins) as shown above on the left.

The problem is to rearrange their positions to those shown on the right side of the diagram in the fewest possible number of moves.

A move consists of placing the tips of the first and second fingers on any two touching counters, always of the different colours, then sliding the pair to another spot along the imaginary line shown in the illustration. The two counters in the pair must touch at all times. The counter at left in the pair must remain at left; the counter at right must remain at right. Gaps in the chain are allowed at the end of any move except the final one. After the last move the counters need not necessarily be at the same spot on the imaginary line that they occupied at the start.

Pile FourPlace eight counters in a row as shown in the illustration. The object is to make from all the counters four stacks of two counters each and it should be done in four moves only.

Every move consists of jumping of a coin over any two counters (no matter lying flat or in a stack) in one direction, and stopping on the top of the next counter.

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Classroom Puzzles

Jumping Counters

The three red counters and the three yellow counters have to change positions. The red counters can only be moved to the right and the yellow ones can only be moved to the left. A counter can move into an empty square if it is beside the empty square. A counter can jump over a different coloured counter as long as there is an empty square to land in. A counter cannot jump over two counters or over a counter of the same colour.

Try acting this puzzle out with boys and girls instead of red and yellow counters.

Triangles IWhen the centers of any three counters lie in the corners of an equilateral triangle of some size, such counters form an equilateral coin triangle. How many equilateral coin triangles of different sizes can you count in the figure?

The object of the puzzle now is to remove the minimum number of counters so that no equilateral triangles remain. In other words, centers of any three counters among those that remained don't lie in the corners of an equilateral triangle.

Triangles IIMove the coins dragging them. Change the triangle into a square by moving the minimum of the coins.

How many coins will you need to move to do this?

Simple NimNim is a very old puzzle game that can be played many different ways. The rules given here are for a simple version of the game. Arrange fifteen counters to form a triangle, like the one shown here. Players take turns removing one, two, or three counters from the triangle. The player who removes the last counter or counters from the table, wins the game. Does the same player win all of the time? To understand the game and winning strategies, play the game with only 6 counters. Who wins this version? Increase the

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counters to 10 and play until you understand the strategy. Now try the game with twenty-one counters

Number Pattern Puzzle

Write the numbers 1 through 8 in the circles so that no two numbers inside the circles joined by a line differ by 1. For example, if you put a 5 in the bottom circle, you cannot put a 4 0r a 6 in any of the circles in the row directly above it because those three circles are joined by lines.

Building PolygonsYou are given many squares and equilateral triangles. All with the same side length. Your challenge is to arrange the squares and triangles to produce poly gons of 3, 4, 5, 6, 7, 8, 9, 10, 11, & 12 sides. Some examples are given below.

Thelon Puzzle IA trapper comes to the Thelon River with a Ptarmigan, a Dog, and some Berries. To cross the river there is a small boat, with only room enough for the trapper and one of his items. He will have to make several trips across the river to transport all of his items. However, he can not trust his dog to be alone with the ptarmigan, for the dog is hungry and might eat it. Also he could not trust the ptarmigan to be alone with the berries for the ptarmigan is hungry and might eat them. How can the trapper get all of his items safely across the river?

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3 sides 4 sides 5 sides 6 sides or 6 sides

Classroom Puzzles

Thelon Puzzle IIA mother, father and two children want to cross the Thelon River in a small boat that can only carry one adult or 2 kids at a time. Both kids are good rowers, but how can the whole family reach the other side of the Thelon River?

Wild Tic-Tac-Toe This game is the same as ordinary tic-tac-toe, except that at each turn the player can choose to play an X or an O. You win if you get three X's in a row, or three O's in a row. If the first player doesn't make any mistakes, he or she can always win.

Measuring CupsYou are given a 3-ounce measuring cup and a 5-ounce measuring cup. Using only these two cups, explain how you could measure out the following amounts.

1 ounce 2 ounces3 ounces 4 ounces5 ounces 6 ounces7 ounces 8 ounces9 ounces 10 ounces100 ounces

Pentominoes(www.numeracysoftware.com)

Ask to connect 5 multilink cubes together in as many different 2-dimensional arrangements as possible. This is a very worthwhile activity because it raises the important question of what we mean by ‘different’. It is likely that many pupils will duplicate at least one of the arrangements, with one being a reflection or rotation of another. They will have constructed the SAME SHAPE but in a DIFFERENT ORIENTATION. This can be the focus of valuable discussion with individuals and the entire class.

There are 12 different pentomino arrangements as illustrated below.

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http://www.numeracysoftware.com/


Once pupils have produced the complete set they can be used in various follow-up activities:

Line Symmetry – ask pupils to draw the lines of symmetry on all of the pentominoes.

Rotational Symmetry – ask pupils to identify those pentominoes that have rotational symmetry.

Perimeter – Sort the twelve pentominoes according to the length of their perimeters.

Tessellation – Which of the pentominoes will tessellate? Tessellating the pentominoes is far more interesting and challenging than tessellating simple regular shapes!

If your class has a set of plastic pentominoes they can be used in a puzzle centre. See if you students can arrange the pentominoes to make the following solid rectangles.

6 x 10 5 x 12

4 x 15

3 x 20

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Classroom Puzzles

Rush Hour

IntroductionRush Hour® is one of the most elegant and fun sliding block puzzles to come on the market in years. It's designed to challenge players of all ages all around the World. Rush Hour® teaches logical progression, problem solving and sequential-thinking skills.

The ObjectYour goal is to drive your red car out of the playing grid and escape to freedom… To do so, set up the traffic on a game grid to match one of 40 playing cards, then shift all blocking cars and trucks out of your way, and you win!

Play GameRush Hour® is a genuine puzzle phenomenon with legions of fans. There are some great places on the Web dedicated to this most successful sliding block puzzle of these years. We'd like to introduce here some of them. Good Luck!

www.puzzles.com/products/rushhour.htm www.woodlands-junior.kent.sch.uk/Games/rush/rushHour_test.html

Tangram

IntroductionTangram is an ancient Chinese puzzle, consisting of 7 geometric shapes that are moved around to make a surprising number of different pictures.

The ObjectYour goal is rearrange the seven puzzle pieces to make a given picture, like the ones below.

Play GameTangrams may be made from paper or cardboard or purchased from math resource suppliers

www.tangrams.ca/

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QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor




An example Sudoku puzzle on the next page. Don’t Cheat!


Simple Sudoku(www.krazydad.com/ sudoku or www.sudoku.com or www.sudokuforkids.com/)

Sudoku puzzles were first published in the US in the 1970s and are sometimes known as "Number Squares". They have been popular for many years in Japan, where the name "Sudoku" (meaning "single number") was coined. The current craze was started late in 2004 when a UK newspaper started publishing the puzzles.

The ChallengeThe aim of the puzzle is to insert numbers in the boxes to satisfy only one condition: each row, column and 3x3 box must contain one each of the digits 1 through 9. There is a unique solution, which can be found by logical thinking.

This means that — The digits to be entered are 1, 2, 3, 4, 5, 6, 7, 8, 9.

This is a row, 9 cells wide. A filled-in row must have one of each digit. That means that each digit appears

only once in the row. There are 9 rows in the grid, and the same rule applies to each of them.

This is a column, 9 cells tall. A filled-in column must have one of each digit. That means that each digit appears only once in the column. There are 9 columns in the grid, and the same rule applies to each of them.

This is a box on the right, containing 9 cells in a 3x3 layout. A filled-in box must have one of each digit. That means that each digit appears only once in the box. There are 9 boxes in the grid, and the same applies to each of them.

You can't change the digits already provided in the grid.You have to work around them.

Every puzzle has just one correct solution.

Sudoku in the ClassroomSudoku are suitable for Kivalliq math classrooms because:

They develop logic, reasoning skills and brainpower.

They are fun. They are great time-fillers for a spare

moment, in the classroom or at home.

Sudoku puzzles are perfect for classroom use, as time-fillers for children who finish early, as whole class activity, or as "homework".

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http://www.sudokuforkids.com/

http://www.sudoku.com/

http://www.krazydad.com/sudoku

Classroom Puzzles

Sudoku: Try one out!

The solution to this puzzle is on the preceeding page, but try not to look .

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KenKen Puzzles

KenKen is a new puzzle phenomenon that’s sweeping the world! Educational, and fun, KenKen is a great way to exercise your brain and sharpen your mathematical tools at the same time! Invented by Japanese math teacher Tetsuya Miyamoto in 2004, KenKen has joined Sudoku & crosswords as the most popular newspaper puzzles in the world.

RulesAlthough the difficulty may vary from puzzle to puzzle, the rules for playing KenKen are fairly simple.

1. The size of the puzzle determines the numbers that may be used. Ex: a 3x3 puzzle uses the numbers 1-3; a 4x4 puzzle uses the numbers 1-4; a 5x5 puzzle uses the numbers 1-5, etc.

2. The same number may not be repeated in any row or column.

3. The numbers in each cage (a heavily outlined square or set of squares) must combine (in any order) to produce the target number in the top corner of the cage using the mathematical operation indicated (+ - x ÷).

4. Cages with just one box should be filled in with the target number in the top corner. These are “freebies” and are the best place to begin your solution.

5. A number may be repeated within a cage as long as it is not in the same row or column.

KenKen in the ClassroomThe key math skills utilized in solving a KenKen puzzle are addition, subtraction, multiplication, division, factoring and logic. By grade four most students have mastered the four mathematical operations and have the innate logic necessary to solve a simple KenKen, but have not developed the perseverance to complete a puzzle. Teachers who introduce simple puzzles via the overhead projector or blackboard and work through student solutions together with the class have been successful in helping students to develop strategies and perseverance to enjoy KenKen puzzles.

Example 3x3 KenKen LogicLook at the corner cage marked 18xFactor tree for 18

The only possibilities for these three squares are 2, 3, & 3. The 3s cannot be in the same row or column so they must go in as shown on the right.

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These are solutions to the example puzzles on the following page.

2 x 9

3 x 32 x 3 x 3

2 3

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Classroom Puzzles

Example KenKen Puzzles(answers on the preceeding page)

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Topological Puzzles

Topology, as a branch of mathematics, can be formally defined as "the study of qualitative properties of certain objects (called topological spaces) that are invariant under certain kind of transformations (called continuous maps), especially those properties that are invariant under a certain kind of equivalence (called homeomorphism)." In simpler terms, topology is concerned with properties of geometric objects that are not affected by elastic distortions. These properties include number of holes, dimensionality, and boundaries that remain unchanged when the object is distorted in any way by such things as twisting, shrinking, or stretching. Topology has sometimes been called "rubber sheet geometry

Topological puzzles are well suited to a hand-on approach and include: knot puzzles, bridge crossing puzzles, mobius strips, wire puzzles, and string puzzles

The mathematical explanation for many of the puzzles presented here is quite complex, but should not dissuade you from using them in your math class. Puzzles are fun and can initiate curiosity-fuel problem solving, which is authentic and most satisfying when successful. Solving these puzzles will require perseverance and lateral thinking to arrive at the “aha moment” These examples are well suited to both math centers and regularly scheduled puzzle periods. They also make excellent topics for math projects and displays at math fares.

The example puzzles included here are not original and have all been culled from math web sites and blogs. I have included the links to the primary source or sources under each activity title. In compiling this document, I became aware of some excellent websites that offer teachers a wide range of quality activities. These sites include:

http://www.aimsedu.org/Puzzle/categories/topological.htmlhttp://mathsyear7.wikispaces.com/http://mathforum.org/http://www.gamesmuseum.uwaterloo.ca/http://www.cut-the-knot.org/Curriculum/index.shtmlhttp://britton.disted.camosun.bc.ca/jbstringring.htmhttp://mathcentral.uregina.ca/index.php

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http://mathcentral.uregina.ca/index.php

http://britton.disted.camosun.bc.ca/jbstringring.htm

http://www.cut-the-knot.org/Curriculum/index.shtml

http://www.gamesmuseum.uwaterloo.ca/

http://mathforum.org/

http://mathsyear7.wikispaces.com/

http://www.aimsedu.org/Puzzle/categories/topological.html

Classroom Puzzles

The Handcuff Puzzlehttp://mathssquad.questacon.edu.au/the_ handcuffs _ puzzle .html

http://www.aimsedu.org/Puzzle/linkLoops/linkloops.pdf

This is a classic puzzle that has been around for at least 250 years. It is very challenging, but it does give teachers a chance to get students up and moving. Its solution depends on lateral thinking and topology.

How to Make the Puzzle1. Cut two pieces of cord or rope about 1.5 metres long2. Tie a small loop (big enough to slide your hand through) in each end of each rope.

The Set-upFor this puzzle you need two people and enough room to move around. 1. Give one rope to the first person and ask them to slip one hand into each loop so that

the rope acts as a large pair of handcuffs.2. With the rope handcuffs on, ask the person to hold his or her arms outstretched.3. Take the second rope and loop it around the rope handcuffs

on the first person.4. With the second rope linked to the first, ask the second

person to slip the loops of the second rope onto his or her hands. The result should resemble the adjacent diagram.

The ChallengeThe two people must disentangle themselves without removing the handcuffs or cutting/untying the rope.

The Solution1. Pinch your rope in the middle and move it to one of the forearms

of your connected partner. 2. Slide your pinched rope towards the wrist of your partner and

under the loop.Grab your rope on the other side of the loop and pull it up and over

the hand of your partner.3. Now pull your rope back under your partner’s loop and you will

be free.

The gap between the loops and your wrists makes this solution possible. People rarely solve this puzzle without a little help but let your students have some fun trying before hints or a solution are offered.

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QuickTime™ and a decompressor


http://www.aimsedu.org/Puzzle/linkLoops/linkloops.pdf

http://mathssquad.questacon.edu.au/the_handcuffs_puzzle.html


Hand Cuthttp://www.arvindguptatoys.com/arvindgupta/stringgames.pdf

You will need a willing student to perform this puzzle trick.

1. Hold the loop of string in both hands. Place the right hand string on top and make a small loop inside the big loop. Place the small loop over a student’s wrist.

2. Insert you hands into the big loop to make the starting position of most string games. (String across the palms between the thumbs and little fingers)

3. Now use your right middle finger to hook the string from your left palm and your left middle finger to hook the string from your right palm.

4. The trap has been set! Release the strings held by your little fingers and thumbs and pull your hands apart

quickly.

5. Magically, the string has passed through the students wrist!

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Classroom Puzzles

Thumb Traphttp://www.arvindguptatoys.com/arvindgupta/stringgames.pdf

Pay attention and catch your thumbs!

1. Put the string in the thumbs and little fingers of both hands (starting position). Give the loop a twist to make a cross in the middle. (Note: that the string that passes from the thumb on your left hand to your little finger on your right hand must cross over top the other string and not underneath)

2. Hook the left palm string with your right index finger and the right palm string with your left index finger.

3. Put your thumbs over and into the forefinger loops as shown in the diagram.

4. Hold the string underneath your thumbs and release the index and little finger strings of both hands.

5. Bend your hands inwards and then pull apart as far as they will go.

6.

If you’re quick and if you followed the instructions carefully, you will catch your thumbs!

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Catch Me if you Can!http://www.arvindguptatoys.com/arvindgupta/stringgames.pdf

If your not careful you will get caught!

1. Hold the loop of string in both of your hands and make a small loop within the larger loop. Make sure that the right hand string is on top of the of the small loop.

2. Place the top of the loops between your teeth and place your right index finger into the small loop downwards from the top.

3. Holding the large loop in your left hand, swing the right index finger over and around the long right hand string and up into the large loop as shown.

4. Touch your nose with your right hand finger.

5. Release the strings from between your teeth and pull the large loop away. Presto! The strings magically dissolve and your finger and you are left holding your nose!

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Classroom Puzzles

Ring on a Stringhttp://www.arvindguptatoys.com/arvindgupta/stringgames.pdf



1. Thread one end of your loop through a ring and pull it until the ring is centered.



2. Loop the string across both palms between your thumb and little finger on each hand (starting position).



3. Pick up the left palm string with your right middle finger and your right palm string with your left middle finger.



4. With some fanfare, release the string from all of your fingers except your right middle finger and your left thumb and pull your hands apart.

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Linking Paperclips Puzzlehttp://bencdean.home.comcast.net/~bencdean/school/Unit%2010.pdf

At first this trick seems perplexing, yet after careful observation it is reduced to another topology trick that works because of transference of curves.

Materials: • 2 to 8 large paper clips• strip of paper (~ 4 cm x 26 cm)• rubber band

ProcedurePart 11. Curve the strip of paper into an S-shape.

Attach two paper clips as shown in the diagram on the right.

2. Pull sharply on the ends of the paper to straighten it out. What happens to the paperclips?

Part 21. Place the strip of paper through a rubberband so that it is

between the two paperclips as shown in the adjacent diagram. What happens to the paperclips when you pull?

Part 31. This time link the two paperclips together with a paperclip

chain. Can you predict what will happen when you pull? Try it out.

The SolutionThe above topology tricks works because of transference of curves. The paper strip is curved so that both sides of each paperclip touch only one side of the paper strip.

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http://bencdean.home.comcast.net/~bencdean/school/Unit%2010.pdf

Classroom Puzzles

Hand to Hand Switcherooby Dave and Michelle Youngs

http://www.aimsedu.org/Puzzle/switcharoo/switch1.html

Introduction:This puzzle is a magic trick that requires no slight of hand, just a little dexterity and practice. It is an application of topological principles. In this trick, two AA batteries are switched back and forth between hands without dropping them. This is not as easy as it might seem since the objects must start off being held as shown in the first illustration and end up being held as shown in the second illustration. There are two challenges here: moving from figure 1 to 2 and from figure 2 to 1. Before you do this activity with students, you should master the trick yourself. It is best to learn the trick by watching someone do it, but I will offer these instructions instead.

Instructions:1. Place two AA batteries in your hands (+ side up) as pictured in the first diagram.2. Rotate your right hand about 90o and place your right thumb on the bottom of the

battery in your left hand and your right middle finger on the top (+ side). 3. While pinching the right battery between your thumb and index finger and the left

battery your right thumb and middle finger, slowly rotate your right hand counterclockwise until you can grab the battery in your right hand with your left thumb on the bottom and middle finger on the top (+ side).

4. Slowly pull your hands apart and rotate them into the position shown in the second diagram.

5. Once you have figured out how to do it, practice the trick until you can make the switch smoothly without thinking about what you are doing. Then figure out how to go backwards from figure 2 to figure 1. At this point, you are ready to introduce it to your students.

Presentation:Show students the switch several times, and then give them the batteries (piece of chalk will also work fine) and let them try it for themselves. It is unlikely that your students will succeed in making the switch after only a few tries, so encourage them to be persistent. Show your students the switch in slow motion as many times as they request—after all, you want them to be able to perform the trick. When one or two students are successful, encourage them to show others how to do the trick. Once students have mastered the trick they can try to explain how it works and challenge their friends and family with it!

Why it Works.This trick involves yet another example of the topological principle of transference of curves.

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http://www.aimsedu.org/Puzzle/switcharoo/switch1.html


Tie a Knot Without Letting Go of the Ropehttp://bencdean.home.comcast.net/~bencdean/school/Unit%2010.pdf

Challenge your class to grab a piece of rope with one end in each hand and tie a knot without letting go of the rope. Sound impossible? Follow the instructions given below to successfully complete the challenge.

Step 1 Place a piece of rope or string in front of you on a table or a desk.

Step 2 Fold your arms across your chest.

Step 3 With your arms still folded, grab the left end of the rope with your right hand and the right end of the rope with your left hand.

Step 4 Hold the ends of the string and unfold your arms. The string should now have a knot in it.

This trick works because of a principle in topology called transference of curves. Your arms had a knot in them before you picked up the string. When you unfolded your arms, you transferred the knot from your arms to the string.

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Feynman's Plate Trickhttp://zetahype.wordpress.com/

Stretch you right arm out, palm up with a plate on it. Try to rotate your palm clockwise about the vertical axis while keeping it facing up at all times. (do not drop the plate) You will notice that it takes a continuous 720 degrees rotation rather than a 360 degrees rotation to bring your arm back to its original state. This is an illustration of the remarkable fact that an object rotated through 360 degrees might not always come back to its original state. The second rotation effectively undoes the first and eliminates any twist in the arm.

This famous topological insight of physist Paul Dirac has since taken many forms and legends: the Phillipine wine glass trick (which involves sustaining a wineglass placed on the aforementioned palm), the Feynman Plate trick or the Dirac belt trick.

http://zetahype.wordpress.com/

http://en.wikipedia.org/wiki/Richard_Feynman


Classroom Puzzles

Looped String Puzzlehttp://bencdean.home.comcast.net/~bencdean/school/Unit%2010.pdf

http://www.youtube.com/watch?v=cYGJbsHu2rU

Here is a classic looped string puzzle made from things found around the classroom. The looped string puzzle is a disentanglement puzzle with a solution similar to the Buttonhole Puzzle. Although it is not so difficult, it can be time consuming. Some students will have a natural ability to solve such puzzles. If you have one in your class, make him or her your puzzle expert.

Materials: • pair of children’ scissors• piece of string• button (larger than the holes in the scissor handles)

Instructions:1. Thread the string though the holes in the button and tie the ends

together to form a loop.

2. Turn the scissors on its side and thread the string loop through the bottom hole (from behind) and then through the top hole (from behind).

3. Pull loop through the top hole and then back down through the bottom hole. As you pull the loop, the button will move up towards the loop.

4. Grab the button and pull it through the loop.5. Pull down on the button and the loop will slowly move up and knot

itself around the top scissor handle. The puzzle is no ready for your students to take apart!

Challenge:To remove the string & button without cutting, breaking or forcing.

Solution:The solution is essentially the assembly instructions in reverse order (from diagram 4 to 1).1.Turn the scissors sideways with the knot on the top and the button

dangling through the bottom hole.2. Pull the bottom of the knot loop down and feed it through the

bottom hole. This action will pull the button up towards the loop.3. Feed the button through the loop and pull. The string and button

should be free of the scissors.

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http://www.youtube.com/watch?v=cYGJbsHu2rU



Mobius Madnesshttp://mathforum.org/sum95/math_and/moebius/moebius.html

http://www.aimsedu.org/Puzzle/mobius/mobius2.html

The Mobius loop is a topological surface first discovered by German mathematician August FerdinandMöbius in 1858.. A mobius loopcan be constructed by giving one end of a strip of paper a half twist before connecting it to the other end. The result is a confounding surface which has only one side and one edge. Practical applications of the Mobius loop includes machine belts which are given half a twist so that all surfaces wear evenly and extent the life of the belt.

How to Make a Mobius Loop.1. Take a strip of paper and colour one side.2. Give it a half twist (turn one end over).3. Tape the ends together.

Mobius Investigation I1. After you make your mobius strip, take a pencil

and begin to draw a line along its length on the inside of the loop. Keep going until you meet you original pencil mark. What side of the loop are you on now? How many sides does the mobius strip have?

2. What will happen if you cut the mobius loop along the line you just made? Now take a pair of scissors and cut along your line. Was your prediction correct? What happened?

3. What do you think will happen if you cut it down the middle again? Try it as see

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http://www.aimsedu.org/Puzzle/mobius/mobius2.html

http://mathforum.org/sum95/math_and/moebius/moebius.html

Classroom Puzzles

Mobius Investigation II1. Cut two identical strips of paper that are about

11 inches long and one inch wide.2. Place one strip on top of the other, holding at

the end between your thumb and first finger. 3. Give the strips a half twist and bring the end

together.4. Tape the ends, together -top to top and bottom

to bottom. You should now have two Möbius loops nested right next to each other.5. Take a pencil and place it between the two loops.6. Move the pencil around the loop one time until it returns to the place you began.



Answer these questions after you have made your loops and followed steps 1 - 6 1. What direction is the tip of the pencil facing now?2. Is this the same or different than the direction it was facing when you began? 3. Move the pencil around the loop one more time. Now what direction is it facing?4. Pull the two loops apart. What happens?5. How can you explain this?

Teacher Notes:Mobius Investigation II presents an interesting variation of the Mobius loop in which two apparently disconnected loops turn out to be joined together. Students will be challenged to explain this phenomenon as they explore topology using the Mobius loop. This investigation works best if you construct a model in front of the class, move the pencil between the two loops to show that they are not connected, and then try to pull them apart, showing that they are, in fact, connected. When moving the pencil between the two loops, you will find that after one rotation the pencil will be facing the opposite direction than it was when you started. It is necessary to make two complete rotations to return the pencil to its original orientation. This realization is an important part of explaining the puzzle, and students should be allowed to make the discovery for themselves without having it pointed out to them. Once you have demonstrated the puzzle for the class, give students the necessary materials and have them construct their own version of the puzzle. It is better if the paper students are using is plain so that it is more of a challenge to distinguish between front and back.

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Math Wuzzles

A Wuzzle is a word puzzle that is solved by decoding the position or placement of letters and pictures to reveal a math term.

For example

Answer: One in a million!

As a team solve as many of the following Wuzzles as you can in 5 minutes.

__________________Deci

Decimal Decimal Decimal Decimal… __________________

TER10%EST __________________

ANGLEANGLEANGLE __________________

__________________

numbernumbernumbernumbernumbernumber __________________

__________________

__________________

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Classroom Puzzles

__________________

__________________

__________________

__________________

__________________

__________________

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Math Wuzzles(Answers)

Forty (4-Tee)

Deci

Decimal Decimal Decimal Decimal… Never ending decimal

TER10%EST Ten percent interest

ANGLEANGLEANGLE Triangle

Long division

numbernumbernumbernumbernumbernumber Repeating number

Equal

Seventeen

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Classroom Puzzles

Multiply

Random numbers

Descending order

3 degrees below zero

Primetime

2-D drawing

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O R D E R


Rounging up

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Documents

Math Fair Guidelines - KSECksec.ca/wp-content/uploads/2015/03/KMEPPuzzles.doc · Web viewSudoku are suitable for Kivalliq math classrooms because: They develop logic, reasoning