Staff Guide

Transcription

Staff Guide

Staff
Guide
Staff Guide
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Mindbender Mansion
©2008, OMSI
Staff Guide
TABLE OF CONTENTS
HOW TO USE THIS GUIDE .......................................................3
EXHIBIT OVERVIEW ..............................................................4
CLUES AND PASSWORDS ....................................................... 12
CORRELATION TO EDUCATIONAL STANDARDS ............................. 15
STAFFING, TIPS, AND TROUBLESHOOTING ...................................... 19
TRAINING OUTLINE................................................................... 22
SUGGESTED TRAINING MATERIALS LIST ........................................ 23
TRAINING SCRIPT..................................................................... 24
STAFF DUTIES
DETAILED OPENING PROCEDURES ................................... 25
DETAILED CLOSING PROCEDURES ................................... 26
HOUSEKEEPING AND EXHIBIT MAINTENANCE ...................... 26
FAQ ..................................................................... 27
ROLE PLAYING.......................................................... 27
MUSEUM ACTIVITIES
MAGICAL MÖBIUS ......................................................... 32
TWISTED TESSELATIONS ................................................. 41
TRICKY TANGRAMS ........................................................ 49
PAPERFOLDING POLYHEDRONS ........................................... 55
ACTIVE LEARNING LOG ........................................................ 67
FLOOR PLAN ...................................................................... 68
EXHIBIT COPY ................................................................... 69
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HOW TO USE THIS STAFF GUIDE
The Staff Guide to Mindbender Mansion has been written for those
responsible for training and supervising the staff and volunteers working in
the Mindbender Mansion exhibit. These materials have been developed as
a resource for the museum educator and to help ensure the consistency of
the information made available to staff and volunteers.
There is background information, answers to key puzzles, staffing tips, a
training outline, several museum floor activities, and the Active Learning
Log—an open-ended worksheet students can fill out while exploring the
exhibit.
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Mindbender Mansion
©2008, OMSI
Exhibit Overview
Enter the wonderfully puzzling world of Mindbender Mansion, an eclectic
place full of brainteasers and interactive challenges guaranteed to test the
brainpower and problem-solving skills of even the most experienced puzzlers.
Visitors to this fun and quirky mansion are invited to join the Mindbender
Society by gathering hidden clues and secret passwords scattered throughout
the various thematic rooms of the house. The clues and passwords are
revealed by solving select brainteasers and group challenges.
Visitors are encouraged to look at problems from different perspectives,
setting aside preconceived ideas to solve the individual brainteasers. They
are also encouraged to collaborate with their fellow mansion guests to meet
the group challenges that include manipulating a tilt table, forming patterns
in rolling chairs, keeping up with a conveyer belt, maneuvering a flying
machine, and disco hopscotch spelling.
Solutions to individual brainteasers, successful completion of group activities,
and discovery of hidden clues and secret passwords can be combined to solve
the ultimate challenge—the key to becoming a member of the Mindbender
Society. Visitors of all ages will enjoy challenging their minds as they try to
master each of the 40 individual brainteasers and the five, large-scale group
activities located in rooms throughout this fun and unconventional mansion!
Thematic areas and exhibit components include:
ENTRY
Start at the Entry and watch a large media screen that introduces the wacky
Mr. E., master brainteaser, puzzler extraordinaire, and current curator of the
Mindbender Society. He will explain some key features of Mindbender
Mansion and how to unlock the puzzles and become a member of the
Mindbender Society. To become a member, visitors must solve a total of
eight to 11 select brainteasers and one, large-scale group activity. Clue
cards are available at the Entry to help keep track of clues and passwords
from the puzzles that lead to membership in the Mindbender Society. There
is also a clue card in the Active Learning Log at the end of this guide.
PARLOR
In the Parlor, there are 10 individual brainteasers—three of them provide
clues toward the final challenge that determines eligibility into the
Mindbender Society.
(10) Brainteasers:
•
Make a Yellow Square
Arrange puzzle pieces to make a yellow square.
Clue reveal: When the puzzle is solved a clue is revealed—write down
this clue on the clue card to be used to unlock the Parlor Vault.
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•
Tricky Triangles
Start with 16 sticks arranged to form eight triangles. Remove four sticks
to leave only four equal-sized triangles.
•
Every Line Adds to 18
Insert the numbers 1–11 so that the sum of the three numbers in any
straight line is 18.
•
Six Pegs That Don’t Line Up
Place six pegs in holes on a square board so that no peg lines up with
another peg along a vertical, horizontal, or diagonal line.
•
Make a Green Square
Arrange puzzle pieces to make a green square.
•
Move the Ring
Move one of the rings on the rope from one side of the knot to the other,
without untying the knot.
•
15 Sticks
Starting with 15 sticks arranged in a pattern on the exhibit board, remove
six of them to leave 10.
•
String Houses
Use a rope to trace the outline of two houses without crossing or retracing
your path. One house is impossible to trace. Which one is it?
•
10 Pegs, Even Lines
Starting with 10 pegs in a pattern, move two pegs so that every row and
column has an even number of pegs.
•
Four Equations
Arrange the numbers 1–9 on the board so that four different equations
are mathematically correct.
Parlor Vault
Set the dials of the Parlor Vault to the three clues that were revealed after
successfully solving the three Parlor brainteasers: “Make a Yellow Square,”
“Tricky Triangles,” and “Every Line Adds to 18.” If successful, a video will
play where Mr. E. talks about the importance of collaboration in problem
solving. Visitors will then be entertained by a short, zany animation
introducing Mary Anderson, the real-life inventor of the windshield wiper
blade. At the end of the animation, Mr. E. will reveal a password that will be
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needed to unlock the Wall of Fame Vault that determines eligibility into the
Mindbender Society.
LIBRARY
In the Library, there are six individual brainteasers—three of them provide
clues toward the final challenge that determines eligibility into the
Mindbender Society.
(6) Brainteasers:
•
Make a T
Arrange four puzzle pieces to make a capital T.
this clue on the clue card to be used to unlock the Library Vault.
•
Color Match
Arrange six hexagons around a central hexagon so that all adjacent colors
match.
•
Insert numbers 1–9 so that the sum of the three numbers in any straight
line (vertical, horizontal, and diagonal) is 15.
•
Square or Triangle
Arrange four puzzle pieces to form a square or triangle.
•
Horse and Rider
Place the puzzle pieces so that there is one rider riding each horse
correctly (right side up and facing forward).
•
Take Away
In this game of strategy for two players, players take turns removing
pegs from the game board. The player who takes the last peg loses.
Library Vault
Set the dials of the Library Vault to the three clues that were revealed after
successfully solving the three Library Brainteasers: “Make a T,” “Color
Match,” and “Every Line Adds to 15.” If you are successful, a video will play
where Mr. E. encourages visitors to try looking at things from a different
perspective. Visitors will then be entertained by a short, zany animation
introducing Marion Donovan, the real-life inventor of the “Boater” diaper
cover. At the end of the animation, Mr. E. will reveal a password that will be
needed to unlock the Wall of Fame Vault that determines eligibility into the
Mindbender Society.
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KITCHEN
In the Kitchen, there is one, large-scale group activity (“Feeding Frenzy”)
and four, individual brainteasers. Visitors must be successful at the “Feeding
Frenzy” activity and two of the Kitchen Brain Teasers to receive clues toward
the final challenge that determines eligibility into the Mindbender Society.
Feeding Frenzy
In this large-scale activity, teamwork is necessary to successfully meet the
challenge: to fill a minimum number of TV dinner trays (with five kinds of
food) on a moving conveyer belt within the specified amount of time. Visitors
can select a level of play (slow, medium, or fast) that determines the speed
of the conveyer belt. Points are given for each TV dinner tray successfully
filled, but no points are given for trays partially filled.
Clue reveal: If a team scores enough points and the minimum number of
trays has been filled, a clue is revealed onscreen—write down this clue on the
clue card to be used to unlock the Kitchen Vault.
(4) Brainteasers:
•
Shifting Squares
Start with 16 sticks arranged to form five squares. Move only two sticks
to make four squares using all 16 sticks.
this clue on the clue card to be used to unlock the Kitchen Vault.
•
Disorder
Arrange the numbers 1–8 on the board so that no two consecutive
numbers touch.
this clue on the clue card to be used to unlock the Kitchen Vault.
•
Balancing Nails
Balance 14 nails on the head of one nail.
•
Make a Cube
Put seven puzzle pieces together to make a cube.
Kitchen Vault
Set the dials of the Kitchen Vault to the three clues that were revealed after
successfully solving the “Feeding Frenzy” activity and two Kitchen
brainteasers: “Shifting Squares” and “Disorder.” If successful, a video will
play where Mr. E. tells visitors about nutrients that are essential for keeping
a healthy brain. Visitors will then be entertained by a short, zany animation
introducing Elisha Otis, the real-life inventor of the elevator safety brake. At
the end of the animation, Mr. E. will reveal a password that will be needed to
unlock the Wall of Fame Vault that determines eligibility into the Mindbender
Society.
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MAP ROOM
In the Map Room, there is one, large-scale group activity (“Amazing Maze”)
and four, individual brainteasers—three of the Map Room brainteasers
provide clues toward the final challenge that determines eligibility into the
Mindbender Society.
Amazing Maze
In this large-scale activity, up to four visitors work together to tilt a table in
different directions, guiding a ball into several holes as quickly as possible in
the allotted time. A scoreboard keeps tally and counts down the remaining
time left in the game.
(4) Brainteasers:
•
Six Blocks in a Box
Fit six blocks together so they fit perfectly into a box and the lid can be
closed.
this clue on the clue card to be used to unlock the Map Room Vault.
•
10 Pegs in Each Line
Place pegs in each of eight boxes so there are 10 pegs in each line.
•
One Shape Fits All
From a group of differently shaped blocks, find the one block that
completely fills all three differently shaped holes as it passes through.
•
Build a Pyramid
Using two, identically shaped blocks, put them together to form a
pyramid.
Map Room Vault
Set the dials of the Map Room Vault to the three clues that were revealed
after successfully solving the three Map Room brainteasers: “Six Blocks in a
Box,” “10 Pegs in Each Line,” and “One Shape Fits All.” If successful, a video
will play where Mr. E. delivers a hilarious educational message about brain
mapping and neuroscience. Visitors will then be entertained by a short, zany
animation introducing Elijah McCoy, the real-life inventor of the steam engine
lubricator. At the end of the animation, Mr. E. will reveal a password that will
be needed to unlock the Wall of Fame Vault that determines eligibility into
the Mindbender Society.
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DISCO ROOM
Spelling Fever
In this large-scale, full-body activity, teamwork is necessary to successfully
meet the challenge: to correctly spell words within a limited amount of time
by hopping on letter squares. Start the game by touching the small screen at
one end of the dance floor. Instructions are given on a large screen above
the floor and the game begins when a randomly generated question appears
on the large screen. The challenge is to think of the answer to the question
(with help from anyone nearby) and spell it out by plotting a course down the
floor and hopping on the correct letters. Visitors must land at the far end of
the floor and press one of the letters in “FINISH” to submit their answer. If
the answer is correct, they score points and then hurry back to the starting
point to spell another word, or a team member can start spelling the next
answer to save time and increase total points.
DINING ROOM
Move and Match
In this large-scale, full-body activity, teamwork is necessary to successfully
meet the challenge. Players maneuver dining room chairs into a correct
pattern within the specified amount of time. Four players each sit in a
different colored chair in an enclosed pen. A pattern is revealed on-screen
and the four teammates work together to maneuver their chairs into the
correct pattern by using their arms to push off of one another and the pen
walls. There is a second pen, so if there are eight players each pen can play
against the clock and also the other pen.
Note: This activity is facilitated by museum staff.
REC ROOM
In the Rec Room, there is one, large-scale group activity (“Flying Machine”)
and 18 individual brainteasers.
Flying Machine
In this large-scale activity, teamwork is necessary to successfully meet the
challenge. Players move a mechanical “flying machine” around a large game
board hitting five targets in sequence within a specified amount of time. Four
players work together to move the flying machine to land on the six targets.
If a target is successfully hit, it lights up and the next target in the sequence
begins to flash.
(18) Brainteasers:
•
Four Blocks in a Box
Fit four blocks together in one box so that none of the blocks sticks out
above the top. Then try it with the other box.
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•
Triangle or Hexagon
Arrange six puzzle pieces to form a triangle or hexagon.
•
Take-Apart Cross
Separate a seemingly solid cross into two pieces and then put them
together again.
•
Make a Blue Square
Arrange the puzzle pieces to make a blue square.
•
Five-Room House
On the exhibit board is a plan of a five-room house and a rope. Pass the
rope through each and every door only once without crossing the rope
over itself or over a wall. (NOTE: This puzzle is impossible to solve—can
you figure out why?)
•
Tie the Knot
Tie or untie the knot that is in the center of the rope.
•
Linked Hearts
Separate two linked hearts and then put them back together again.
•
Make a Square
Starting with four puzzle pieces arranged in a pattern, move only one
piece to make a square.
•
Six Sticks
Arrange six sticks so that they form eight, equilateral triangles of any size.
•
A Perfect Fit
Fit four T-shaped puzzle pieces so that they lay flat within a large frame.
Then fit them into an even smaller frame.
•
Horseshoes
Remove a ring from a pair of linked horseshoes and then put the ring
back on.
•
Galloping Horse
Put three puzzle pieces together to make a galloping horse.
•
Handcuffs
Untangle the ropes without removing the “handcuffs” from your wrists.
•
Crossing the River
Help a farmer transport a fox, a chicken, and a bag of corn across a river
in a small boat—without any casualties.
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•
10-Disk Triangle
Invert a triangle made up of 10 disks by moving only three disks.
•
Two Balls in a Rocker
Move two balls that sit near the center of a rocker to opposite corners.
•
Tower of Brahma
Move a pile of disks from one peg to another peg, following some simple
rules.
•
Jumping Pegs
Start with four white pegs and four black pegs at opposite ends. Jump or
move the pegs one space at a time to switch the positions of the white
and black pegs.
WALL OF FAME
Now it’s time for visitors to see if they are eligible to become a member of
the Mindbender Society and possibly add their portrait to the “Mindbender
Society Wall of Fame.” Several framed portraits of esteemed members of
the Mindbender Society decorate this area and there is room for new
members too!
To join, visitors must enter the three to four passwords they have gathered
from the four rooms of the mansion: Parlor, Library, Map Room, and Kitchen
into the final vault at the Wall of Fame. If they are successful, they are
officially an expert problem solver and invited into the society! If they are not
successful, visitors are told to keep trying and check out the areas of the
mansion that provide the clues and passwords.
If a visitor is invited to join the Mindbender Society, they can have their
picture taken and personalize their portrait with a background, “thinking
cap,” funny hair, etc. Once they’ve finished their portrait, they can print out
their official Mindbender Society certificate with their personalized portrait
and take it home. In addition, their portrait will go up on the Wall of Fame for
all to see, in one of the four monitors available to highlight the newest
members of the Mindbender Society!
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Clues and Passwords
Here are the clues and passwords that visitors will gather throughout the
exhibit.
Library
• Make a T: Your clue is the object on the graphic panel that lights up when
the puzzle is solved.
• Color Match: Your clue is the shape that lights up on the graphic panel.
• Every Line Adds to 15: Your clue is the sum of the darkened spaces.
Parlor
• Make a Yellow Square: Your clue is the piece in the middle of the solved
puzzle.
• Tricky Triangles: Your clue is the flashing letter that lights up on the
graphic panel.
• Every Line Adds to 18: Your clue is the number in the center of the solved
puzzle.
Map Room
• Six Blocks in a Box: Your clue is the object on the graphic panel that
lights up when the puzzle is solved.
• 10 Pegs in Each Line: When solved, the clue is the number of pegs found
in each of the darkened boxes.
• One Shape Fits All: The clue is the shape that passes through all three
holes.
Kitchen
• Feeding Frenzy: If a team scores enough points and the minimum number
of trays has been filled, a clue is revealed onscreen.
• Shifting Squares: Your clue is the object on the graphic panel that lights
up when the puzzle is solved.
• Disorder: Your clue is the sum of the top and bottom numbers of the
solved puzzle.
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A correctly completed clue card will look like this:
Teamwork
Watch
Goldfish
Blender
Following is a template you can use to make new clue cards. The host
museum is responsible for supplying consumables for the exhibit, including
blank clue cards. Consumables include:
•
•
•
Printed clue cards on 8½” x 11” paper (20 lb. stock, can use recycled
paper), cut in half, at the Entry
Blank 8½” x 11” paper (20 lb. stock, can use recycled paper) for the
Mindbender Society Member Certificates at the Wall of Fame
Golf pencils for the clue cards at the Entry
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Correlation to Educational Standards
Mindbender Mansion provides connections to science, technology, and
mathematics content. The primary focus of the exhibition is problem solving,
often with a mathematical emphasis. Through exhibit activities, visitors will
practice the problem-solving skills that are used to explore the world through
scientific inquiry and mathematics.
Research has shown that students learn science and math best when
provided with a constant succession of challenges. Tasks of moderate
difficulty—hard enough to facilitate learning without being so hard as to
discourage—give students’ minds the exercise they need to develop new
skills. Problem solving is a central skill in science and mathematics and key
to understanding the process of science.
Puzzles are an excellent tool to teach and practice problem-solving skills.
Mindbender Mansion engages students in a wide range of ages by providing
hands-on experiences solving puzzles. Most of the puzzles in Mindbender
Mansion have a mathematical foundation. Sometimes the math is obvious,
with numbers and equations, other times the math is more subtle. All these
puzzles build problem-solving skills, demand creativity, build on prior
knowledge, and encourage lateral thinking.
The multiple group activities build communication and teamwork skills as
groups of visitors work together to solve puzzles cooperatively.
To help students connect the abstract puzzles they are solving in the exhibit
to real-life situations, the exhibit also features four short animations
highlighting historical inventors. Each person saw a problem and solved it by
creating a new invention.
SCIENCE
Science themes explored in Mindbender Mansion include:
• Patterns and relationships
• Communication of ideas
• Motions and forces
• Interdependence of organisms (food webs)
These concepts are found in the National Science Teachers Association (NSTA)
science content standards. More information is on the NSTA website:
http://www.nsta.org/
TECHNOLOGY
Technology themes explored in Mindbender Mansion include:
• Role of society in developing new technologies
• Influence of technology on history
• The role of problem solving in invention
• Identifying patterns
• Communication
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These concepts are found in the International Technology Education
Association (ITEA) science content standards. More information is on the
ITEA website: http://www.iteaconnect.org/
MATHEMATICS
The activities in Mindbender Mansion support a range of cognitive
mathematics-related abilities in visitors from kindergarten through adult. The
target group for Mindbender Mansion consists of children in grades 3 and
up. A secondary target group is comprised of their families since cooperative
experiences are encouraged by the activities.
Many activities will be appreciated by visitors regardless of whether or not
they are in the target groups.
Mindbender Mansion offers opportunities that provide visitors with an
engaging and stimulating experience where they:
• Solve puzzles
• Use creative thinking and problem-solving strategies
• Consider problems from different perspectives
The activities support mathematics standards and benchmarks in the two
primary compilations of standards for mathematics education: “2061:
Science for All Americans” and the National Council of Teachers of
Mathematics (NCTM).
Specifically, Mindbender Mansion addresses the following for grades 3
through 5 in the guidelines from “2061” and NCTM:
“2061: Science for All Americans”
Benchmark: Patterns and Relationships
• Mathematics is the study of many kinds of patterns, including numbers
and shapes and operations on them. Sometimes patterns are studied
because they help to explain how the world works or how to solve
practical problems, sometimes because they are interesting in
themselves.
• Mathematical ideas can be represented concretely, graphically, and
symbolically.
Benchmark: Mathematical Inquiry
• Numbers and shapes—and operations on them—help to describe and
predict things about the world around us.
• In using mathematics, choices have to be made about what operations
will give the best results. Results should always be judged by whether
they make sense and are useful.
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National Council of Teachers of Mathematics (NCTM)
There are 10 standards specified by NCTM:
• Numbers and Operations
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability
• Problem Solving
• Reasoning and Proof
• Communication
• Connections
• Representation
Activities in Mindbender Mansion support expectations for eight of these
standards in grades 3 through 5. Several of the standards are appropriate for
all grades, K–12, and are so indicated.
Numbers and Operations
• Understand numbers, ways of representing numbers, relationships
among numbers, and number systems
• Understand meanings of operations and how they relate to one another
Algebra
• Understand patterns, relations, and functions
Geometry
• Analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about
geometric relationships
• Apply transformations and use symmetry to analyze mathematical
situations
• Use visualization, spatial reasoning, and geometric modeling to solve
problems
Problem Solving (K–12)
• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Monitor and reflect on the process of mathematical problem solving
Reasoning and Proof (K–12)
• Recognize reasoning and proof as fundamental aspects of mathematics
• Make and investigate mathematical conjectures
• Select and use various types of reasoning and methods of proof
Communication (K–12)
• Organize and consolidate mathematical thinking through
communication
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•
•
Communicate their mathematical thinking coherently and clearly to
peers, teachers, and others
Analyze and evaluate the mathematical thinking and strategies of others
Connections (K–12)
• Recognize and use connections among mathematical ideas
• Recognize and apply mathematics in contexts outside of mathematics
Representation (K–12)
• Select, apply, and translate among mathematical representations to
solve problems
• Use representations to model and interpret physical, social, and
mathematical phenomena
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Staffing
It is anticipated that Mindbender Mansion will be heavily trafficked by
school groups, adult education groups, and families. For this reason, it is
recommended that there be at least 3–4 people on the floor during the
museum’s peak hours.
Suggested Minimal Staffing (staff can be trained volunteers):
• 1–2 floor staff to supervise the “Move and Match” unit
• 1 floor staff to roam between the “Flying Machine” and “Feeding
Frenzy” units
• 1 floor staff to roam between the “Spelling Fever” and “Wall of Fame”
units
• 1 floor staff to act as a floater throughout the entire exhibit helping
with the brainteasers
At peak times Mindbender Mansion can become extremely busy—four-hour
shifts might be considered to reduce stress on staff and volunteers.
It is assumed that people working on the floor have already had general
visitor service training that also covers working with young visitors, dealing
with parents, solving problems with lost children, and first aid.
Tips and Troubleshooting
Some of the units are very popular and need special attention. Here are
some suggestions for making a quality experience even better.
Feeding Frenzy
Please watch for young visitors climbing on this exhibit.
Spelling Fever
Words with more letters earn more points. Each letter is worth 16 points.
Visitors must step onto the center of the tile to get the tile to light up. We
suggest that visitors weighing less than 40 pounds hop from letter to letter
using both feet.
This is a popular exhibit. We suggest using “exit” and “line forms here” signs
with stanchions to improve the flow of visitor traffic. Create only one access
point to the podium and the two exits, one from spelling floor and one from
podium. Staff supervision is ideal.
Visitors that choose to spell inappropriate words will not be successful. We
have installed a block on inappropriate words that visitors have attempted
to spell.
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Move and Match
It is highly recommended that this activity be moderated by museum staff.
Due to the fun and competitiveness of this exhibit, visitors may not be as
careful as they should. Each chair in “Move and Match” has brakes. To
release the brakes, visitors must remain seated. Visitors are not to enter or
leave the dining room while chairs are in motion. Also, they are to keep their
feet in the chair at all times. Visitors should be at least 46 inches tall to
participate in this activity. Otherwise, they should be accompanied by an
adult (or someone taller) in their chair. This activity uses upper body
strength. Visitors that have any health concerns related to their upper body
should not participate.
When moderated, stanchion placement and crowd management are
extremely important in “Move and Match.” We suggest having a “line forms
here” sign and an “exit” sign. Due to the two entrances, visitors tend to want
to line up outside of each room. Adjust this with stanchions; create a cueing
area opposite the exit. We also recommend having two staff members
moderating this activity when experiencing high numbers of visitors.
At start up, “Move and Match” will go into moderated or non-moderated
mode based on how it was last used. The monitor in each room is operated
separately at the podium. The podium screen is split in half; each half
corresponds to the adjacent room’s monitor. To exit non-moderated mode,
touch the top left corner of each half of the screen. Visitors are more
successful if they attempt to solve the patterns with four players, but as few
as two players can solve the patterns. Note: in non-moderated mode visitors
may not realize that the chairs have brakes and that they must sit in order to
release them.
How to operate the moderated version in “Move and Match”:
The main menu screen contains the following buttons: non-moderated, lock,
instructions, practice, and start. Begin by touching instructions. The
instructions begin with the objective and move through a slide show
containing information about how to score and the rules. After instructions
press practice, the practice pattern is untimed, and no points are rewarded.
Two thousand points are rewarded for each correctly solved pattern and an
additional 100 points are given for each second remaining on the clock. Press
main menu when finished with the practice round, then press start to begin
the game. Press team wins when the visitors have correctly moved into the
pattern. The next pattern will appear on the screen in a few seconds. Once
they have worked through the three patterns, their final score will appear.
Press main menu to clear the monitor screen. During the game pause can be
pressed at anytime, press pause again to return to timed play. IMPORTANT:
after three minutes of no contact, the podium will lock. To unlock, press
anywhere along the top of the screen.
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Helpful hints for visitors playing “Move and Match”:
•
Chairs are rectangles.
•
When a chair is facing the podium or the patterns, it is on its narrow
side.
Wall of Fame
Inappropriate pictures can be removed from the Wall of Fame by turning off
the orange power switch in the cabinet below the computer to the right. Turn
off the switch, wait 20 seconds, and flip the power back on. This will turn off
the printer as well so, prior to turning off the power, wait until all printing of
certificates is complete.
Brainteasers
The following puzzles are the ones visitors most often ask for help solving.
Make sure you learn good hints to these puzzles first.
Kitchen
Balancing Nails
Shifting Squares
Disorder
Library
Make a T
Color Match
Parlor
Tricky Triangle
Move the Ring
Rec Room
Handcuffs
Tie the Knot
Horseshoes
Linked Hearts
A Perfect Fit
Map Room
6 Blocks in a Box
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Mindbender Mansion Training Outline
Introduction—10 minutes
Welcome to Mindbender Mansion
Participant sign-in
Training overview
Exhibit Overview—15 minutes
Exhibit Walk-Through—30 minutes
Staff Duties—15 minutes
Opening Mindbender Mansion—5 minutes
Closing Mindbender Mansion—5 minutes
Housekeeping—5 minutes
Frequently Asked Questions—10 minutes
Break—15 minutes
Role Playing—20 minutes
Activities—15 minutes
Practice Brainteasers—40 minutes
Closing Remarks—10 minutes
Question and Answer Period
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Suggested Training Materials List
From
•
•
•
•
•
•
the Staff Guide:
Exhibit Overview
Correlations to Educational Standards
Training Outline
Staff Duties
Activities
Active Learning Log
Mindbender Mansion Hints and Answers
Additional Resources:
1,000 Play Thinks: Puzzles, Paradoxes, Illusions and Games by Ivan
Moscovich (Workman Pub Co, 2001)
Garrett, R.M. (1987) Issues in Science Education: problem-solving, creativity
and originality. Journal of Science Education. 9 (2) 125–137
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Training Script
Introduction—10 minutes
•
•
•
Welcome to Mindbender Mansion
Participant sign-in
Training overview: Briefly go over what will be covered
Exhibit Overview—15 minutes
What is Mindbender Mansion about? What are its goals?
•
In Mindbender Mansion, visitors will explore an eclectic place full of
brainteasers and interactive challenges and become members of the
Mindbender Society.
•
Mindbender Mansion was designed to promote “family learning.”
Activities are intended to appeal to a broad age range and encourage
group interactions. That is why you’ll find activities for all ages throughout
the exhibit.
•
Visitors join the Mindbender Society by gathering hidden clues and
secret passwords scattered throughout the various rooms of the
mansion. The clues and passwords are revealed by solving select
brainteasers and group challenges.
•
Mindbender Mansion provides visitors with the opportunity to
practice inventive thinking, problem solving, and communication skills.
How does the exhibit support classroom teachers?
•
Mindbender Mansion provides connections to science, technology,
and mathematics content. The primary focus of the exhibition is
problem solving, often with a mathematical emphasis. (See
Correlations to Educational Standards.)
•
Through exhibit activities, visitors will practice the problem-solving
skills that are used to explore the world through scientific inquiry and
mathematics.
•
The Mindbender Mansion exhibit and related educational resources
were developed with specific links to national math, science, and
technology standards.
Staff Guide
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Exhibit Walk-Through—30 minutes
•
•
•
•
Tour of the building and/or exhibit hall (or provide information about
when and where Mindbender Mansion will be installed).
Orientation to essential information (e.g., restrooms, drinking
fountains, emergency exits, etc.)
Walk through (or discuss) all nine rooms. Review how to use clue
cards, which brainteasers in each room give clues, and how to open
clue vaults. Also review how to get on the Wall of Fame. Finally explain
the objective of each large interactive component. (See the Exhibition
Overview and Component Descriptions for more details.)
Discuss different approaches that staff can take to help visitors that
are challenged on brainteasers. (See Role Play.)
Opening Mindbender Mansion—20 minutes
Make sure computer activities and videos are working.
Walk through the exhibit and check that Spelling Fever, Feeding Frenzy,
Move and Match, Flying Machine, Amazing Maze, Wall of Fame, entry video,
and clue vaults (located in Kitchen, Parlor, Library, and Map Room) are
functioning correctly. To test, start each activity, listen and look for sounds
and visuals to appear.
The following can be fixed on the floor by education staff*:
Troubleshooting:
• If Feeding Frenzy has red sign denoting contact staff, open panel
behind computer and check inside that all food is clear from edges
of tray and conveyor belt, press the orange button to reset.
•
If Wall of Fame is frozen, reboot computer by pressing the green
button on computer in cabinet, wait for computer to shutdown, wait
an additional 10 seconds, and turn on computer.
•
If clue vaults are frozen or if the knobs are malfunctioning open
vault either from front or rear and turn off orange switch on power
strip, wait 10 seconds, and turn back on. If this doesn’t fix the
problem call exhibit repair. Do not open parlor vault, call exhibit
repair.
*any repairs beyond these are to be performed by exhibit repair personnel.
Check for maintenance issues.
Check printer at Wall of Fame, print off certificate to check printer toner
and wheels. Add paper as needed. Solve the following puzzles to make
sure brainteasers light up to reveal clues:
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•
•
•
•
Library: Make a T
Color Match
Parlor: Shifting Triangles
Kitchen: Shifting Squares
Map Room: 6 Blocks in a Box
Make sure exhibit components are in place.
• Restock clue cards and pencils at entry. Also return pencils from Wall
of Fame to entry.
• Stools are not to be put in the Kitchen or the Map Room for safety
reasons. Visitors will move stools to wherever they are needed.
Children tend to take stools and small chairs to Feeding Frenzy and
the Amazing Maze, please discourage this activity for safety, but
encourage the adult supervising them to help them to see or
participate in the activity without the stools.
Closing Mindbender Mansion—10 minutes
Make sure exhibits are clean.
Remove any miscellaneous clue cards or pencils from exhibits.
Gather and replace exhibit components in appropriate areas.
• Restock paper in printer.
• Restock clue card paper if necessary.
• Check all brainteasers for missing pieces and return them to the
appropriate location.
• Make sure all brainteasers are left unsolved.
Check for maintenance issues.
Housekeeping—5 minutes
Make sure that materials and equipment (brainteasers, pencils, clue
cards, books, games, and exhibit stools) are available for use in specific
exhibit areas—however, remember that small children engaged in
exploration are not concerned about where something “belongs.”
Specifics:
•
Try to keep stools at appropriate stations (under exhibits and out of
the Map Room and Kitchen).
•
Restock paper in the entry.
•
Several times daily, pick up: abandoned clue cards and pencils and
games pieces off the floor.
•
Unsolve brainteasers.
•
Try to keep the activity pieces at their appropriate stations.
•
If busy, monitor the arrangement of stanchions around the Dining
Room and Spelling Fever. See detailed floor plan.
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Frequently Asked Questions
Q: How do I become a Member of the Mindbender Society?
A: Grab a clue card and a pencil at the entry. Look for the yellow circles that
denote clue-giving brainteasers. Solve each challenge to receive your
clues, mark your clue card, and enter your clues into the clue vault to get
your password. Write each password down on your clue card. Get at least
three passwords and enter them at the Wall of Fame.
Q: Can you show me how to solve this brainteaser?
A: I’d love to help you with that brainteaser; these puzzles are made
deceptively simple so that we have to solve them in an unusual way. They
present us with an opportunity to “think outside the box.” I can provide
you with a hint or two to help you solve it. (Some brainteasers need more
frequent support than others. We suggest giving your volunteers/staff
practice time on the brainteasers. Also refer them to the Mindbender
Mansion Hints and Solution Manual.)
Break—15 minutes
Role Play—20 minutes
Scenario 1
Visitor: You are a visitor that is stuck on a brainteaser. You WANT hints. Do
the following: stare at the volunteer, look like you are about to give up, and
finally ask for help.
Volunteer: You are a volunteer in Mindbender Mansion. You are walking
around the hall and you notice the visitor. Do not help the visitor until he/she
asks for help. (Of course in real life, we would ask visitors if they needed help
when we noticed them looking at us or if they looked like they were
struggling).
Scenario 2
Visitor: You are a visitor that is stuck on a brainteaser. You DO NOT want
hints. Please do the following actions to display that you do not want help:
with eyes focused on puzzle, don’t acknowledge the volunteer’s presence and
put your back towards the volunteer.
around the hall and you notice the visitor struggling with a brainteaser.
Attempt to ask the visitor if she needs help once she has her back to you.
(It’s okay to be told no, the best response to this would be, I’m here to help
if you ever get stuck).
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Scenario 3
Visitor: You are a visitor that is stuck on a brainteaser. You WANT the
ANSWER. Please do the following actions to display that you want the
answer: keep asking for clues, say that you are horrible at puzzles and that
you dislike them, and ask for the solution.
around the hall and you notice the visitor struggling with a brainteaser. Help
the visitor, but DO NOT give the answer away. (Visitors can have time
constraints, use your best judgment in this situation, but never walk up to a
visitor and give the answer away immediately.)
Activities—15 minutes
See Activities for Mindbender Mansion
Practice Brainteasers—40 minutes
Solving brainteasers in the exhibit on your own or with others is an essential
part of training. Being able to relate to the visitor as they are solving these
challenging puzzles is important. Use the Mindbender Mansion Hint and
Answer Guide to help in this process as needed.
Closing Remarks—10 minutes
•
•
Question and answer period.
Thank you.
Staff Guide
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Mindbender Wiki
We know that we haven’t discovered the best possible way to do each of the
following demonstrations. What you find here is our best version so far.
We invite you to modify and adapt the demonstrations to best meet the
needs of your museum. More than that—we invite you to share what you
find!
A wiki about Mindbender Mansion is at
http://mindbendermansion.wikidot.com
The wiki has copies of this manual, the Teachers’ Guide and the Hints and
Answers Guide. You can edit the wiki and add your own ideas about good
puzzle demonstrations, hints for the brainteasers, exhibit maintenance, or
anything else. Just create a wikidot account and go to the Join the Wiki page:
http://mindbendermansion.wikidot.com/system:join
The secret password you need to join is: glen
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Staff Guide
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Staff Guide
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Magical Möbius
Description: Visitors observe the amazing characteristics of the Möbius strip.
Learning Objectives: Visitors will learn about the unique geometry of the
Möbius strip.
SCIENCE TOPICS
Geometry
Topology
PROCESS SKILLS
AGE LEVEL
Problem Solving
Spatial Reasoning
5–Adult
TIME REQUIRED
Advance Preparation
Set Up
Activity
Clean Up
30 minutes
2 minutes
30 minutes
5 minutes
SUPPLIES
•
•
•
•
Scissors
Tape or glue stick
Lengths of paper cut about 3 inches wide and 12 inches long. Adding
machine tape, butcher paper, and 11”x17” copy paper would all be good
choices. Other lengths and widths are fun to play with, like really huge lengths
of butcher paper.
Markers, crayons, pens, or pencils (it is useful to have at least two colors for
the demonstration).
SAFETY PRECAUTION: Always supervise children with scissors.
Magical Möbius
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ADVANCE
PREPARATION
Make materials for visitors.
• Cut paper into strips approximately 3”x12”. Label ends with letter or numbers,
if desired. (See photo.)
Prepare materials for demonstration.
• Pre-make some cylinders and some Möbius strips.
o For cylinders, match up corners A and C and tape or glue the ends of
the paper. (See photo.)
o For Möbius strips, match up corners A and D so there is a half twist in
the paper and tape or glue the ends together. (See photo.)
Paper strips
Cylinder
Möbius strip
SET UP
•
•
Set out materials for visitors to access.
Organize demonstration materials for visitors.
INTRODUCING THE
ACTIVITY
Let visitors
speculate before
offering answers to
any questions. The
answers at the
right are provided
primarily for the
educator's benefit.
Magical Möbius
Ask visitors the following questions in bold.
Possible answers are shown in italics.
There are many ways to do this activity, this is just one
idea.
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Hello! I have something very cool here to show you.
It’s magic, it’s math, it’s a Möbius strip! Who here
has heard of a Möbius strip?
Visitors raise hands. Some have seen a Möbius strip
before. Some may start to hypothesize wildly about the
Möbius strip.
If you have seen this before, please keep the answers
to yourselves for now, thanks!
August Möbius was a German mathematician from
the eighteen hundreds who discovered many useful
and interesting concepts. One of the most unusual
and amazing is the Möbius strip. I am about to
demonstrate some of the more entertaining things
one can do with a Möbius strip without the use of
advanced mathematics. All I need are some scissors,
tape, and paper!
At this point, you can start the demonstration.
DOING THE
ACTIVITY
A Möbius strip is a surface with only one side. I’ll show you how to make a
Möbius strip. Then we’ll talk about the unusual characteristics it has.
Show your audience the pre-made examples of a cylinder and a Möbius strip. Let
the audience examine them closely. Show the audience HOW to make a Möbius
strip by creating a new cylinder and a new Möbius strip.
Show the cylinder.
How many sides does this object have?
Visitors can notice there are two sides, one inside the cylinder and one outside.
Show the Möbius strip.
What about this one?
Visitors should notice it is slightly different than the cylinder. They may still think it
has an inside and outside. The next activity will prove it has only one.
Magical Möbius
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Activity 1:
Take a marker or pen and draw on the outside surface of the
cylinder. It will bring you back to where you started and there
will be a pen mark on only one side of the paper. You can draw
a second line in a different color on the inside of the cylinder to
emphasize the two sides of the cylinder.
Take a marker or pen and draw on one surface of the Möbius
strip. It will meet back up at where you started too, but there will
be pen marks on all surfaces of the paper. This is because a
Möbius strip has only one side! It will also take twice as long to
finish drawing the line.
If visitors have a hard time understanding the demonstration, you
may need to repeat it.
How are the cylinder and Möbius strip the same?
They both are made from paper. They both have just one line drawn on them.
(Or one line in the first color.)
How are they different?
The Möbius strip has a line that is twice as long. The cylinder has paper on one
side with no line drawn on it. (Or a different line, in another color.)
Activity 2:
Demonstrate what happens when you cut the Möbius strip:
This is the cool part! If I take this cylinder and cut it in half along the line I
drew, what will I end up with?
It will make two smaller cylinders.
What if I cut the Möbius strip?
I don’t know! It will make two Möbius strips?
Cut the cylinder in half, following the line you drew. You will
have two separate cylinders.
Cut the Möbius strip in half along the line you drew. You
will have a very long loop of paper with TWO full twists in it.
Not only that, this will be a ONE sided loop. You can prove
this by drawing along one side, repeating what you did in
Magical Möbius
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Activity 1. (You may want to use a different color to avoid confusion.)
What happened to the cylinder? What happened to the Möbius strip?
Answers will vary
Activity 3:
What do you think will happen if I cut the Möbius strip in
half again?
Answers will vary.
Proceed to cut the Möbius strip in half again: you will end up
with two linked single sided strips, draw a line around the middle again to prove
this. (With wide enough paper you can keep cutting these loops in half, however,
soon you will have a big, tangled pile of streamers! This is fun, but it’s hard to see
what is really going on.)
Activity 4:
Another trick of the Möbius strip, and the most perplexing to watch, is cutting the
strip, not in the middle, but in thirds.
Based on what you have seen so far, what do you think will happen if I cut
this Möbius strip, not in the middle, but about a third of the way in?
Answers will vary.
The illustration shows the numbers 1, 2,
and 3, with lines. This helps people see
what is happening to the paper,
especially at the end. Start cutting along
one side, keep cutting until you meet
back at the point you started from. You
will pass this point on the OTHER side
of the strip halfway through your cutting.
You will end up with a Möbius strip linked to a loop
with two twists in it. What you have done is cut the
edge off the Möbius strip. If you show the audience
the longer loop, they will see the numbers 1 and 3,
while the 2 is on the Möbius strip.
Conclude the demonstration portion of the activity and allow visitors to make and
experiment with their own Möbius strip.
Magical Möbius
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OPTIONAL
EXTENSIONS
Möbius or “No”bius?
Here are a few additional twists to put on the original activity. In addition to these,
encourage visitors to experiment on their own.
If you want to trick your audience, have a strip of paper with three slits cut in
each end (thirds) and braid them. When you cut each third apart, you get three
intersecting rings, but they are not Möbius strips and neither was the original
loop. It is a trick and nothing more. Ask them what they think will happen before
cutting and then ask them at the end whether or not this is a Möbius strip and
why or why not, let them examine it.
Start with a joined cylinder
Make three lines
Cut along lines to make three
strips
Cut the “1” strip along the
middle
Take the top section of strip “1” and cross
it over strips “2” and “3.” Take the bottom
section of strip “1” and cross it under strips
“2” and “3,” tape together.
Magical Möbius
Cut each strip all the
way around the ring.
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You now have three
interlocked rings.
The original set up has no twist in it, just braiding
paper, the end result of three loops are also twistless, even if they are connected. By braiding the
paper in a particular way, you just set the rings up to
be connected, once they are cut apart.
You can try making strips with more twists in them to
see what the results are. A Möbius strip has only the
one half twist. Others may be one sided objects, but they are not a Möbius strip.
They will exhibit similar and unusual results.
For example: Put three half twists in a strip of paper, tape the ends together, and
cut along the outer third—you get a trefoil knot in the loops.
Other topological extensions:
James A Neilson’s “Magic Band”: This is similar to the “No”bius. Except that it
has two full twists in the band before taping and the braiding is slightly different.
The result is three separate bands, each linked to the other two bands. One is a
Möbius strip; the other two are single sided surfaces with different numbers of
twists in the band. All directions are the same as the “No”bius except for the
following:
Start with a strip
of paper and put
two twists in it
before taping the
ends together.
Take the top “1” strip,
cross it over the “2”
strip. Take the bottom
“1” strip and cross it
under the “2” strip and
reconnect the “1” strip.
This is how it should
look. Order is
important. If you
link the “1” strip
around the “2” strip
backwards, you get
a different result.
(Try it!)
Magical Möbius
After cutting through
each of the strips, you
end up with three rings,
each joined to another
ring. It can be tricky to
tease apart. One ring is a
Möbius strip. Use the
pen trick to find it.
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Cannibal torus ring: A cannibal torus ring starts with two tori linked together,
like a chain. One torus has a hole in its side (think of a hole in the side of an inner
tube). The torus with the hole can swallow the other torus by turning itself inside
out through the hole in its side. The hole has to stretch considerably to
accommodate this change, but it does not rip or break. In the end, you have a
torus inside a torus.
http://mathworld.wolfram.com/TorusCannibal.html
Klein bottles: Klein bottles are only fully realized in four dimensions,
but people do make 3-D versions. A Klein bottle is the shape you would
get if you turned a torus ring into a Möbius strip. Hard to wrap your head
around! You can cut a Klein bottle in such a way as to get one or two
Möbius strips.
You can purchase representations of Klein bottles for display.
http://mathworld.wolfram.com/KleinBottle.html
Möbius shorts: This figure is topologically equivalent to a Klein bottle with a hole
in it and distinct from a Möbius strip. Cutting the strips along their midline
produces a square. At first it appears that the cut version has two twists in it, but
you can untwist it. Weird. There is little study of Möbius shorts, although it can be
safely said they would be hard to wear.
http://mathworld.wolfram.com/MoebiusShorts.html
BACKGROUND
Mathematician Möbius
August Ferdinand Möbius (1790–1868) was from Germany and a student of the
astronomer and mathematician, Carl Friedrich Gauss. Astronomy was a more
popular topic in his time; mathematics was more of a secondhand hobby. His
extensive publications on math and astronomy included papers on Barycentric
calculus, parameterization, pandromic rings, variations on the four-color theory of
maps, and the Möbius function.
Topology:
Topology is the mathematical study of shapes and what properties of space are
preserved under deformation. Möbius strips fall into a topological category known
as homeomorphisms. These are functions that stretch without tearing or sticking
together. The cannibal torus is an excellent example of this.
Magical Möbius
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Book on Möbius: (The only book you really need, fascinating read!)
The Mobius Strip: Dr. August Mobius's Marvelous Band in Mathematics, Games,
Literature, Art, Technology, and Cosmology
By Clifford A. Pickover
Published by Thunder's Mouth Press, 2006
ISBN 1560258268, 9781560258261
244 pages
See some of it here:
http://books.google.com/books?id=fWM7mdhksn0C
Websites:
More information on the Möbius strip and further exploration of the mathematical
concepts:
The Magic Ring—Möbius Strip
http://dimacs.rutgers.edu/Institute/96/classroom/topology/lessons/magicring.html
The Möbius Strip—A simple informative worksheet
http://scidiv.bcc.ctc.edu/MATH/Mobius.html
Wikipedia article on the Möbius Strip
http://en.wikipedia.org/wiki/M%C3%B6bius_strip
Information on topology:
http://mathworld.wolfram.com/Topology.html
Magical Möbius
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Twisted
Tessellations
Description: Visitors will create tessellating patterns they can color.
Learning Objectives: Visitors will learn about patterns and shape repetition, which
shapes tessellate, which do not.
SCIENCE TOPICS
Geometry
Symmetry
PROCESS SKILLS
AGE LEVEL
Compare/Contrast
Classifying
Inferring
5–Adult
TIME REQUIRED
Advance Preparation
15 minutes
Set Up
Activity
Clean Up
5 minutes
45 minutes
5 minutes
SUPPLIES
•
•
•
•
•
8½” x 11” paper
Pens, pencils, crayons, markers, colored pencils
Scissors
Card stock, construction paper, or some other firm paper
Tape
Twisted Tessellations
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ADVANCE
PREPARATION
Prepare pattern shapes: Cut out shapes
on firm colored paper and laminate if
desired. Make shapes that tessellate
(squares, rectangles, diamonds,
6-pointed stars, etc.) and shapes that do
not tessellate (octagons, pentagons,
circles, 5-pointed stars, etc.). Making all
of the shapes in a variety of colors will
allow for fun pattern making. We made most of the shapes in this image using
the Microsoft Word Auto Shape tool.
You can find some grids that are easy to print out and copy here:
http://gwydir.demon.co.uk/jo/tess/grids.htm
If you would prefer to buy geometric manipulatives try this site:
http://www.eaieducation.com/
Prepare materials for the tracing tessellations:
Cut squares from card stock or other firm paper in advance. (We recycle
laminated paper and signs for this.) These will be for making tracing
tessellations. (Illustrated in “Doing the Activity” below.)
A 3” x 3” square is a good size. The size can vary but should be large enough
for small hands but small enough to fit a maximum number of copies on an
8 ½” x 11” sheet of paper.
Images of tessellating patterns: You may want to print
out examples of tessellating patterns. Consider using
some from nature, such as honeycomb, columnar
basalt, and pavement brick patterns. You can also find
images of brickwork, tile work, and wallpapers. You can
also use examples of patterns that are NOT
tessellations to compare and contrast.
SET UP
•
•
•
Place writing and coloring materials, scissors, tape, and paper on table.
Have tessellating shapes out in separate piles, stacks, or containers.
Have squares for making tessellations available for tracing activities.
Twisted Tesselations
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INTRODUCING THE
ACTIVITY
Ask visitors questions in bold.
Possible answers are shown in italics.
Let visitors
speculate before
offering answers to
any questions. The
answers at the
right are provided
primarily for the
educator’s benefit.
Have different shapes laid out on a table, invite people over
to make patterns from the shapes. Challenge them with the
following:
What shapes do we have here? How many can you
name?
Which shapes are similar, which are different?
Which of these shapes can make a repeating pattern—
using only one shape—which leaves no spaces and
doesn’t overlap?
Which shapes will do that? Which ones won’t?
How are they the same? Different?
Can you make a repeating pattern with just one shape,
which leaves no gaps and has no overlaps?
Yes, no, I don’t know…
Can you find other shapes that do this?
Squares, equilateral triangles, hexagons, parallelograms…
Can you make a repeating pattern with two or more
shapes?
Yes, no, maybe…
Which shapes work for this?
Squares, octagons, triangles, parallelograms, etc.
Are there any shapes that you can’t make a repeating
pattern with no matter the combination?
Yes, I don’t know, no…
Which shapes do not make a repeating pattern?
5-pointed stars, circles…
Introducing tessellations:
What we are doing here is called tessellation.
Tessellation is making patterns, which repeat over and
over again, using just a few shapes. Which shapes did
you use that would make patterns that repeat?
Squares, hexagons, parallelograms, rectangles, etc.
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We can even make our own shapes that tessellate using
those basic shapes, like squares and triangles, as a
starting point. See these tiles here?
Show images of tessellations that are not a regular shape.
(Example: scale pavers in photo.)
Have you ever heard of M.C. Escher? He’s a famous
artist from the nineteen hundreds who was known for
his tessellation art and other optical puzzle art. (Show
example of M.C. Escher’s tessellating artwork.)
Tessellations can be very simple or very complicated,
but they all start out with basic shapes. (Escher’s
metamorphosis pieces are especially good at demonstrating
this.)
We are going to make our own tessellating shapes using
just a square, are you ready?
Yeah!
DOING THE
ACTIVITY
Activity 1: Exploring tessellating patterns
Help visitors make patterns with the cutout shapes to explore the idea of
tessellating patterns. Why are some patterns tessellations and others not?
Optional: visitors can copy examples of tessellations supplied by the
facilitator. After playing with the shapes, move on to the next part of the
activity: Making tessellations!
Activity 2: Translation
Translation tessellations are when a piece of one side of a shape is
moved in its exact orientation to the opposite side of the shape. When you
tile them, you keep the shape in the same position every time you copy it.
• Give each visitor their own square. Have scissors and markers or pens
out to share.
• Demonstrate translation; show visitors how to make a translating
shape. (See photos.)
• Once you have made an example, use it to trace onto a piece of paper
to show visitors how your pattern repeats.
• Aid visitors in creating and tracing their own tessellating patterns.
• Allow them to decorate their patterns and keep their stencil.
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Examples showing translation:
Draw a shape to cut out
on one side of the square.
Cut out the shape and tape
it to the opposite side of the
square in the exact same
location/orientation.
Example of this shape
tessellating.
Create another shape
(This one is on the same
side as the first shape.)
Cut this shape out and
tape it on the opposite
side of the square in the
exact same location as
the original shape.
tessellating.
This shape is cut out of
the top side of the
square—
and placed on the bottom
side in the exact same
location/orientation as
the original shape.
tessellating.
Activity 3: Rotation
Rotation tessellations are ones in which a piece from one side is placed
on an adjacent side, in the same orientation. When you tile them, these
shapes will rotate.
•
•
•
•
•
Give each visitor their own square. Have scissors and markers or pens
out to share.
Demonstrate rotation; show visitors how to make a rotated shape. (See
photos.)
Once you have made an example, use it to trace onto a piece of paper
to show visitors how your pattern repeats.
Aid visitors in creating and tracing their own tessellating patterns.
Allow them to decorate their patterns and keep their stencil.
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Examples showing rotation:
Draw a shape to cut out
from one side of the
square.
Draw a second shape to
cut out.
Cut out this shape and
tape it to an adjacent side
in the exact same
location and orientation
as the original shape.
Cut out and tape to an
adjacent side in the exact
same location and
orientation as the original
shape.
tessellating. Notice how
the shape rotates.
tessellating. Notice how
the shape rotates.
BACKGROUND
INFORMATION
Tessellating patterns exist everywhere in everyday life as well as in M.C.
Escher’s famous tessellating artwork. Mosaics and tile, honeycomb,
columnar basalt, and bricklaying are some examples.
Tessellating shapes fill the space they occupy with no overlaps or gaps.
Tessellating patterns have been part of art and culture of world peoples
since ancient times. The word tessella is Latin and means “small square,”
from the shapes used for making mosaics in ancient Greece and Rome.
Today, whether or not they can articulate the reasons, people continue to
be fascinated by tessellations and to find ways of incorporating them into
the patterns of daily life.
There are two kinds of tessellating patterns covered in this activity.
Regular tessellations can be made with just three shapes: squares,
equilateral triangles, and hexagons. Regular tessellations are ones in
which a single shape can fill the whole plane with no gaps or overlaps.
Semi-regular tessellations are ones in which two or more shapes can fill
the plane with no gaps or overlaps. This includes combinations like
squares and octagons, or dodecagons and triangles.
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Although simple shapes will tessellate, the cool part of this activity is the
making of unique shapes out of basic shapes. In this activity, when a
piece of one side is cut out and placed onto another side, you can be
doing two kinds of manipulation: translation and rotation.
Translation is when you take a piece out of one side of the shape and
paste it to the opposite side of the shape.
Rotation is when you take a piece out of one side of the shape and move
it to one of the sides next to it.
Online Resources:
Totally Tessellated
http://library.thinkquest.org/16661/index2.html
Tessellations
http://gwydir.demon.co.uk/jo/tess/index.htm
Tesselations.org
http://www.tessellations.org/
The Math Forum @ Drexel: Tessellation Tutorials
http://mathforum.org/sum95/suzanne/tess.intro.html
Tantalizing Tessellation
http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html
Teacher Resources: Tessellation
http://www.teachers.ash.org.au/mikemath/resources/tessellations.html
Extras:
Wallpaper Groups:
http://www.clarku.edu/~djoyce/wallpaper/
M.C. Escher
http://www.mcescher.com/
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Make Your Own Puzzle!
Draw a picture in the puzzle below. When you are done,
take it home and carefully cut out the pieces.
Try to put your picture back together!
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Tricky Tangrams
Description: Visitors will manipulate tangram puzzle pieces to create new shapes
and construct their own tangrams to take home.
Learning Objectives: Visitors will learn strategies to solve shape and
spatial puzzles.
SCIENCE TOPICS
Geometry
PROCESS SKILLS
Spatial reasoning
AGE LEVEL
5–Adult
Hand-eye coordination
Visual memory
TIME REQUIRED
Advance Preparation
15 minutes
Set Up
Activity
Clean Up
5 minutes
45 minutes
5 minutes
SUPPLIES
•
•
•
•
•
•
Tangram sets x 4 (make your own or purchase sets)
Copies of tangram worksheets
Tangram puzzle sheets
Crayons
Scissors
Baggies (to transport tangram pieces home)
Tricky Tangrams
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ADVANCE
PREPARATION
Make copies of worksheet A onto cardstock or construction paper if you are
having visitors make their own tangram sets.
To make your own tangram sets: copy the worksheet tangram square onto
colored construction paper or card stock. Cut out each shape and laminate.
Tangram sets are also easily found in toy stores and online.
Find tangram silhouettes you wish to use online or from a book. Here is one site
that allows use of their silhouettes for educational and classroom purposes to get
you started: Tannzle: http://www.tanzzle.com/index.html
Size of pieces: create a few tangram puzzle sets that are the same size as the
silhouette. Working directly on the silhouette helps young learners because it is
easier to work on a picture than to work from a picture.
SET UP
•
•
•
Place tangram sets out on table.
Place copies of puzzles to solve out on table.
If using worksheets:
o Have crayons, scissors, and baggies out on table.
INTRODUCING THE
ACTIVITY
Let visitors
speculate before
offering answers to
any questions. The
answers at the
right are provided
primarily for the
Suggestions for the facilitator in bold.
Sample visitor answers in italics.
Tangrams are popular. Most people will have
encountered tangrams at some point in their lives. It’s a
familiar puzzle.
As an assisted demo, draw people in with a challenge:
Do you think you can help me solve this puzzle? I
have these simple geometric shapes and need to
make a dog (or other diagram). I could use a hand!
Tricky Tangrams
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If you are having visitors make their own tangrams, the
lure of crayons and scissors is usually enough to draw a
curious crowd!
Once you have an audience, you can introduce
tangrams.
A sample introduction:
Hi, I have this amazing puzzle that is so old, we don’t
know for sure when it was invented! It’s from China
and it’s still puzzling people today. Does anyone
know what this is called? Have you played with this
game before?
No, yes, Tangrams!
Yes, this is Tangrams.
Show a set, unassembled.
How many pieces are there?
Seven, I don’t know, a lot…
What shapes do we have here?
Square, triangles, parallelogram, rhombus…
Specifically: one square, two large triangles, one medium
triangle, two small triangles, and one parallelogram.
How many different shapes do you think we can
make with these seven pieces?
A whole lot, a few, I want to make a boat!
How do these pieces fit together?
Allow visitors to explore what sides fit together from the
different shapes. Also, they should see if putting two or
more pieces together can make another shape. For
instance, the two small triangles can be put together to
make a parallelogram or a medium triangle.
People have been making tangram silhouettes for a
long time, there are many figures to figure out! We
have a few here, they look simple, but, sometimes,
they are very tricky.
Ask visitors if they have seen or worked with tangrams
elsewhere in the exhibit; many of the Mindbender
Mansion puzzles are tangrams.
Tricky Tangrams
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Shall we try some puzzles? Awesome! Let’s do it!
Tangram worksheet activity:
We’re going to make our own tangram sets that you
can take home with you! Color the pieces however
you like and then we will cut them out…
Tangrams are also a good candidate as an unassisted
activity; you can leave out tangram puzzles and pieces
for people to work on, without staff assistance.
DOING THE
ACTIVITY
Tangram silhouettes can, indeed, be very challenging. It’s a good idea to make
different silhouette sets for different levels of difficulty when choosing patterns to
work with. Make sure you have the solutions on hand! Develop your own color
scheme for tangram sets and answers, so materials at the different levels of
difficulty can be distinguished easily.
Offer clues and suggestions to solving puzzles before giving answers away (e.g.,
place one piece in the right spot to get the visitor started).
Ideas for leading this activity:
• Talk about the history of the game.
• Use silhouettes surrounding themes, like holidays, seasons, animals,
people, etc., and tie in with time of year or other things going on in the
museum.
• Have a race to solve a picture.
• Make up their own tangram picture, trace it, challenge a friend! (Make sure
they also trace their answers!)
• Try to make some of the 13 possible convex shapes (you can find these
shapes here: http://www.mathematische-basteleien.de/tangrams.htm)
If doing the worksheet activity, make sure kids get a baggie to take their pieces
home with them.
Tricky Tangrams
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BACKGROUND
INFORMATION
History:
Tangrams originated from China. Little is known about their early origin, but they
became popular in the West in the eighteen hundreds. The earliest known book
for patterns is from 1813.
Book Resources:
Tangrams: 330 Puzzles
By Ronald C. Read
Published by Courier Dover Publications, 1965
ISBN 0486214834, 9780486214832
152 pages
Tangram Puzzles: 500 Tricky Shapes to Confound and Astound
By Chris Crawford
Published by Sterling Publishing Company, Inc., 2002
ISBN 080697589X, 9780806975894
96 pages
Tangram Puzzles: Describing and Comparing Attributes of Plane Geometric
Shapes
By Colleen Adams
Published by The Rosen Publishing Group, 2004
ISBN 0823989763, 9780823989768
24 pages
Web Resources:
Tangrams
http://www.tangrams.ca/
Tannzle
http://www.tanzzle.com/index.html
Tangram activities: by grade level
http://www.ac.wwu.edu/~mnaylor/tangrams/tangramactivities.html
Tricky Tangrams
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Tricky Tangrams
Tangrams are a classic Chinese puzzle game. You can use these seven shapes to make
millions of pictures!
But wait, it’s not as simple as it sounds….
Do the following:
Color these pieces however you like!
Carefully cut them out.
Try to:
Reassemble the square.
Figure out how to make the pictures on the table.
At home:
Look up tangram puzzles online for more tricky fun!
Keep these instructions! Place your puzzle pieces and this paper in a baggie when
you are done playing.
Tricky Tangrams
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Paperfolding
Polyhedrons
Description: Visitors bend a two-dimensional object (paper) to make a
three-dimensional object.
Learning Objectives: Visitors will learn geometrical shapes and basic topology.
SCIENCE TOPICS
Topology
Geometry
PROCESS SKILLS
Problem solving
Spatial relationships
Visual memory
AGE LEVEL
5–Adult
TIME REQUIRED
Advance Preparation
30 minutes
Set Up
Activity
Clean Up
5 minutes
50 minutes
10 minutes
SUPPLIES
•
•
•
Origami paper: 4” x 4” or 6” x 6” squares, ½” x 12” strips (for stars)
Sample of complete origami constructions: a cube, an octahedron, an
icosahedron, lucky stars, etc.
Origami diagrams: Modular Polyhedron and Lucky Star diagrams attached to
this activity.
ADVANCE
PREPARATION
Have paper cut into squares in advance or buy origami paper. Good sizes
for small fingers and novice folders are 4” x 4” or 6” x 6.” Note: cutting your
own paper tends to end up with imperfect squares that can create
imperfect results. Origami paper is best.
Paperfolding Polyhedrons
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Choose simple origami diagrams for small children. Many origami folds
are beyond their manual dexterity and can be frustrating. Begin with the
ones included here.
Have a few origami books on hand for self-discovery. (See resources list
at the end of the document for some recommended books.) Visitors can
pursue their own diagrams at their own skill level while others are guided
by you.
Practice the origami!
“When the paper folds the mind unfolds.” Author unknown.
Practice the instructions for each of the main origami designs in this
activity. All the main projects for this activity are beginner–intermediate
diagrams. A familiarity with origami is useful but not necessary.
SET UP
•
•
•
Have paper available.
Place sample origami constructions out for visitors to look at.
Place books and diagrams out for visitors to view.
INTRODUCING THE
ACTIVITY
Let visitors
speculate before
offering answers to
any questions. The
answers at the
right are provided
primarily for the
Welcome visitors to the activity; explain you are exploring
geometry (the shape of things) and topology (the study of
how space can be transformed through stretching and
bending and folding) through origami or paper folding. Ask
visitors if they would like to turn a simple square of paper, or
pieces of paper, into one of the samples on the table.
Would you like to learn how to turn six pieces of paper
into a cube? A strip of paper into a star? Would you like
to learn how to make a hopping frog? Or a cup you can
drink out of?
Show examples of the items.
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DOING THE
ACTIVITY
This activity is good for quiet times. People love origami! It’s a great
activity to do when you and your visitors can really spend time on it
together.
There are several ways to do this demo:
• Have multiple diagrams out for people to make and offer instructions
and help if they get stuck on the diagram.
• Pick one diagram and work on making it with visitors.
• Make polyhedrons. The cube takes some time to construct because
there are many pieces to assemble.
We strongly recommend doing the polyhedrons separately from the
origami unless you have more than one staff person running this activity.
The polyhedron cube has several simple steps, but still takes a bit of time
and patience. People, especially young children, often need help with
tricky origami folds. It can be challenging to help two or more groups at the
same time.
Origami:
There are many good books and websites that have information on
origami, and we have included our favorites in the resources listed below.
We pulled diagrams from these websites and books that we felt were easy
to teach and fun to do and made copies of those diagrams available to
visitors.
Origami diagrams that are easy to learn and fun to make include cups,
cranes, water bombs (or balloons), jumping frogs, tulips and animal faces.
Modular origami:
Modular origami takes one folded
shape, in this case a parallelogram, and
fits it into complex 3-D geometric
objects. It’s sort of an origami puzzle
where all the pieces are the same.
There are a number of ways to make
modular origami. The diagram included
with this activity is an easy one to learn
and teach. Information on other forms of
modular origami can be found in books and Internet resources.
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The parallelogram module can also be used to make cubes or stellated
octahedrons and icosahedrons.
It takes a little practice to see how the modules fit together, but the end
results are very rewarding. The cube is the quickest and simplest form to
make. If visitors have the time to make the octahedron or icosahedrons
while you are there to help them, encourage them to do so. It’s a very cool
experience.
Lucky Stars:
Lucky stars are popular with kids and easy to make. These stars are made
using a form of paper folding called strip folding. You can make a number
of objects with strips, including modular origami.
Giant Origami:
Another fun variation could be to make giant squares out of butcher paper
and to work together in groups to make giant cranes and other figures.
BACKGROUND
INFORMATION
Origami and mathematics:
Origami is a tangible way to play with and introduce the ideas of geometry
and topology. You begin with a two-sided piece of paper. Depending on
the folder’s skill, he or she can end up with infinite shapes out of that piece
of paper. In the case of modular origami, you end up with full blown, 3-D
geometric models.
To demonstrate topology, walk visitors though a simple origami diagram,
like a cup. Have them make the cup and then unfold it. The unfolded cup
with return to being a two-sided piece of paper but will have creases in the
paper that made up the folds of the cup. This is the crease pattern. Some
origami artists use crease patterns to fold origami instead of diagrams.
You can use these creases to discuss how surfaces can bend and
become other shapes without cutting or tearing.
Origami History:
Paper folding can be traced back to many Asian cultures. Origami
originates from traditional Japanese folding, origami-tsuki. Origami-tsuki
was a way of folding documents to prevent unauthorized copies being
made, kind of an early security measure. It extended into making gift
wrappings, or tsutsumi. Noshi, which was often done with strips of
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seaweed or dried fish instead of paper are little attachments for gifts that
mean “good wishes.”
However, origami also has roots in Europe. There were paper folders
throughout history from east to west sharing and blending ideas. Modern
origami is a hybrid and gained popularity in the eighteen hundreds and
more recently in the 1950s.
For more on the history of origami:
http://origami.ousaan.com/library/historye.html
http://www.origami.as/Info/history.php
Origami Resources on the Net:
Origami.com:
You can search a database for all kinds of diagrams, many are very tricky.
http://www.origami.com/index.html
Origami Club:
Check out the pages titled Fun Origami and Easy Origami for good, simple
diagrams
http://www.origami-club.com/en/
Origami Resource Center:
Excellent resource for all kinds of paper folding. This site has some great
basic diagrams.
http://www.origami-resource-center.com/index.html
Origami Tube (videos):
Watch and learn!
http://www.origamitube.com/index.php
Suggested Origami Books to Purchase or Check Out from the
Library:
Origami Design Secrets: Mathematical Methods for an Ancient Art
By Robert J. Lang
Published by A K Peters, Ltd., 2003
ISBN 1568811942, 9781568811949
585 pages
Origami 1-2-3
By David Petty
Published by Sterling Publishing Company, Inc., 2002
ISBN 0806955112, 9780806955117
128 pages
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Wings and Things: Origami That Flies
By Stephen Weiss
Published by Macmillan, 1984
ISBN 0312882289, 9780312882280
128 pages
Modular Origami Resources on the Net:
Origami Polyhedra:
http://nuwen.net/poly.html
Jim Plank’s Origami Page:
A resource for how to make complicated modular origami
http://www.cs.utk.edu/~plank/plank/pics/origami/origami.html
Modular Origami—Balls and Polyhedra:
This site includes images of complicated modular origami that people
have made and links to the base modules that they used to make them.
http://hektor.umcs.lublin.pl/~mikosmul/origami/balls.html
MM’s Modular Mania:
This site includes diagrams for some cool modular origami.
http://www.origamee.net/
Books to Purchase or Check Out from a Library on Modular Origami:
Polyhedron Origami for Beginners
By Miyuki Kawamura
Published by Japan Publications Trading, 2002
ISBN 4889960856, 9784889960853
99 pages
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Modular Origami: Polyhedrons
How to make the modules:
1
2
Take a square piece of paper
Fold it in half and then unfold it
3
4
Fold the other edge to meet the
middle crease and
unfold
Fold one edge to meet the
middle crease
5
6
Fold the top left corner down to
meet the crease
Flip the paper and do the same to the
opposite corner
7
8
Fold the corner down again to
meet the crease
And do the same to the opposite
corner
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10
9
Fold the bottom quarter up to meet the
middle crease
Fold the top quarter down to meet the middle
crease
11
12
Fold the top right corner down to meet the
bottom right edge
Fold the bottom left corner up to match the
top left edge
14
13
Tuck the right flap into the lower right
fold
Tuck the left flap into the upper left fold
16
15
Turn over to the other side
This is how your paper should look at
this point.
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18
17
Fold the left corner to meet the top edge
Fold the right corner to meet the
bottom edge
19
20
This is what your finished module should look
like
Fold in half along the gap between flaps
Make:
6 of these for a cube
12 for an octahedron
30 for an icosahedron
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Modular Origami: Polyhedrons
How to make a cube:
2
1
Take two pieces,
slide a corner of one piece into a pocket in the
center square of the other piece
You need 6 modules—it’s easiest to
use 6 separate colors
2
1
1
3
2
3
Tuck the corner of the second piece
into the pocket on the third piece to
create a pyramid
Take a third piece, slide one corner into
the pocket of the first piece
4
2
3
4
3
Take a fourth piece, tuck the
corner into the pocket on piece 3
3
5
Take a 5th piece and tuck it into the
pocket on piece 4
4
5
Tuck the corner of piece 3 into
piece 5, you now have two
corners of your cube
64
Tuck remaining corners into pockets for all
pieces until you have two corners without a
pocket
Mindbender Mansion
©2008, OMSI
6
6
2
Take the 6th and last piece, tuck one
corner into a free pocket, keeping
remaining corners out.
Tuck one of the remaining corners into a free
pocket on piece 6
6
Take the other remaining corner and
tuck it into a pocket on piece 6,
there is one corner left, find its pocket
and tuck it in place
You have now completed a cube!
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Lucky Stars
1
3
2
Make a loose knot in one end,
press the knot into a pentagon
Cut a strip of paper about 1/4
inch thick
Fold the extra bit back over one
side, your
paper should look like Number 3
above.
4
5
Fold the tail over and press the fold down, keep
wrapping the tail around the pentagon and
pressing the sides down, keep it tight
Tuck the end of the tail into a fold on
the pentagon and press flat
7
6
Your pentagon should look like
this
8
Carefully press your fingernail into each side to
pop it out, repeat for all five sides
You should now have a star!
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Active Learning Log
Name:______________
Which puzzle is your favorite? Why? Without giving them the answer, what hint
would you give a friend to solve this puzzle?
How did you use teamwork or cooperation to solve a puzzle?
Which puzzle was the hardest for you? How did you solve it?
Draw a picture of the answer of a puzzle you solved:
This is your clue card for Mindbender Mansion. Throughout the mansion
there are special puzzles that will give you clues when you solve them. In certain
rooms, find the three clues and then go to the vault. Put in your clues to get a
password and write it down.
Once you have at least three passwords, you can go to the Wall of Fame and
join the Mindbender Society!
Mindbender Mansion
©2008, OMSI

Staff Guide

Transcription

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