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Staff Guide

Staff Guide 1 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


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.


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.


• Tricky Triangles

Start with 16 sticks arranged to form eight triangles. Remove four sticks to leave only four equal-sized triangles. 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.

• Every Line Adds to 18

Insert the numbers 1–11 so that the sum of the three numbers in any straight line is 18. 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.

• 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


needed to unlock the Wall of Fame Vault that determines eligibility into the Mindbender Society. LIBRARYIn 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. 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 Library Vault.

• Color Match Arrange six hexagons around a central hexagon so that all adjacent colors match. 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 Library Vault.

• Every Line Adds to 15

Insert numbers 1–9 so that the sum of the three numbers in any straight line (vertical, horizontal, and diagonal) is 15. 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 Library Vault.

• 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.


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. 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 Kitchen Vault.

• Disorder

Arrange the numbers 1–8 on the board so that no two consecutive numbers touch. 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 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.


MAP ROOMIn 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. 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 Map Room Vault.

• 10 Pegs in Each Line

Place pegs in each of eight boxes so there are 10 pegs in each line. 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 Map Room Vault.

• 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. 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 Map Room Vault.

• 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.


DISCO ROOMSpelling 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 ROOMMove 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 ROOMIn 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.


• 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.


• 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!


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.

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



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/ TECHNOLOGYTechnology 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

http://www.nsta.org/


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.

http://www.iteaconnect.org/


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


• 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


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.


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.


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 Every Line Adds to 15 Make a T Color Match Map Room 6 Blocks in a Box

Parlor Tricky Triangle Move the Ring Rec Room Handcuffs Tie the Knot Horseshoes Linked Hearts A Perfect Fit


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


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


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.


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:


• 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.


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. Volunteer: You are a volunteer in Mindbender Mansion. You are walking 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).


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. Volunteer: You are a volunteer in Mindbender Mansion. You are walking 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.


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:joinThe secret password you need to join is: glen

http://mindbendermansion.wikidot.com/

http://mindbendermansion.wikidot.com/system:join

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 PROCESS SKILLS AGE LEVEL

Geometry Problem Solving 5–Adult Topology Spatial Reasoning

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 32 Mindbender Mansion ©2008, OMSI


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.

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.


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.


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


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.


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.

Cut each strip all the way around the ring.


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 twist-less, 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

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.

a different result. (Try it!)


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.

http://mathworld.wolfram.com/TorusCannibal.html

http://mathworld.wolfram.com/KleinBottle.html

http://mathworld.wolfram.com/MoebiusShorts.html


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

http://books.google.com/books?id=fWM7mdhksn0C

http://dimacs.rutgers.edu/Institute/96/classroom/topology/lessons/magicring.html

http://scidiv.bcc.ctc.edu/MATH/Mobius.html

http://en.wikipedia.org/wiki/M%C3%B6bius_strip

http://mathworld.wolfram.com/Topology.html

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.


Geometry Compare/Contrast 5–Adult Symmetry Classifying Inferring

TIME REQUIRED



SUPPLIES

• 8½” x 11” paper • Pens, pencils, crayons, markers, colored pencils • Scissors • Card stock, construction paper, or some other firm paper • Tape

Twisted Tessellations 41 Mindbender Mansion ©2008, OMSI

Twisted Tesselations 42 Mindbender Mansion ©2008, OMSI

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.

http://gwydir.demon.co.uk/jo/tess/grids.htm

http://www.eaieducation.com/



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.


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.


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.


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.


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.


Examples showing rotation:

Draw a shape to cut out from one side of the square.

Cut out this shape and tape it to an adjacent side in the exact same location and orientation as the original shape.

Example of this shape tessellating. Notice how the shape rotates.

Draw a second shape to cut out.

Cut out and tape to an adjacent side in the exact same location and orientation as the original shape.

Example of this shape

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.


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/

http://library.thinkquest.org/16661/index2.html

http://gwydir.demon.co.uk/jo/tess/index.htm

http://www.tessellations.org/

http://mathforum.org/sum95/suzanne/tess.intro.html

http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html

http://www.teachers.ash.org.au/mikemath/resources/tessellations.html

http://www.clarku.edu/%7Edjoyce/wallpaper/

http://www.mcescher.com/

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!


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.


Geometry Spatial reasoning 5–Adult

Hand-eye coordination Visual memory

TIME REQUIRED



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 49 Mindbender Mansion ©2008, OMSI


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.


Suggestions for the facilitator in bold. Let visitors

speculate before offering answers to any questions. The answers at the right are provided primarily for the educator’s benefit.

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!

http://www.tanzzle.com/index.html


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.


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.

http://www.mathematische-basteleien.de/tangrams.htm



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

http://www.tangrams.ca/

http://www.tanzzle.com/index.html

http://www.ac.wwu.edu/%7Emnaylor/tangrams/tangramactivities.html



Tricky Tangrams Tricky Tangrams

Tangrams are a classic Chinese puzzle game. You can use these seven shapes to make Tangrams are a classic Chinese puzzle game. You can use these seven shapes to make

millions of pictures! millions of pictures! But wait, it’s not as simple as it sounds…. But wait, it’s not as simple as it sounds….

Do the following: Do the following:

Color these pieces however you like! Color these pieces however you like! Carefully cut them out. Carefully cut them out.

Try to: Try to:

Reassemble the square. Reassemble the square. Figure out how to make the pictures on the table. Figure out how to make the pictures on the table.

At home: At home:

Look up tangram puzzles online for more tricky fun! Look up tangram puzzles online for more tricky fun! Keep these instructions! Place your puzzle pieces and this paper in a baggie when Keep these instructions! Place your puzzle pieces and this paper in a baggie when

you are done playing. you are done playing.

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.


Topology Problem solving 5–Adult Geometry Spatial relationships Visual memory

TIME REQUIRED



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 55 Mindbender Mansion ©2008, OMSI


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.


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.

Let visitors speculate before offering answers to any questions. The answers at the right are provided primarily for the educator’s benefit.

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.


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.


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.


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


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.htmlhttp://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

http://origami.ousaan.com/library/historye.html

http://www.origami.as/Info/history.php

http://www.origami.com/index.html

http://www.origami-club.com/en/

http://www.origami-resource-center.com/index.html

http://www.origamitube.com/index.php


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

http://nuwen.net/poly.html

http://www.cs.utk.edu/%7Eplank/plank/pics/origami/origami.html

http://hektor.umcs.lublin.pl/%7Emikosmul/origami/balls.html

http://www.origamee.net/


Modular Origami: Polyhedrons

Take a square piece of paper

How to make the modules:

Fold it in half and then unfold it

Fold one edge to meet the middle crease

Fold the other edge to meet the middle crease and

unfold

Fold the top left corner down to meet the crease

Flip the paper and do the same to the opposite corner

1 2

4 3

5 6

7 8

Fold the corner down again to meet the crease And do the same to the opposite

corner

Fold the bottom left corner up to match the top left edge

Fold the top right corner down to meet the bottom right edge

Turn over to the other side


Tuck the left flap into the upper left fold Tuck the right flap into the lower right

fold

This is how your paper should look at this point.

Fold the top quarter down to meet the middle crease

Fold the bottom quarter up to meet the middle crease

9 10

11 12

13 14

15 16


Fold in half along the gap between flaps This is what your finished module should look

like

Fold the right corner to meet the bottom edge

Fold the left corner to meet the top edge

Make: 6 of these for a cube 12 for an octahedron 30 for an icosahedron

17 18

19 20


Modular Origami: Polyhedrons

You need 6 modules—it’s easiest to use 6 separate colors

How to make a cube:

Take a 5th piece and tuck it into the pocket on piece 4

Tuck the corner of piece 3 into piece 5, you now have two

corners of your cube

Take two pieces, slide a corner of one piece into a pocket in the

center square of the other piece

Take a third piece, slide one corner into the pocket of the first piece

1 2

3

1 2 1

2 3

Tuck the corner of the second piece into the pocket on the third piece to

create a pyramid

4 3

2 5

3

4

Take a fourth piece, tuck the corner into the pocket on piece 3

5

3 4

Tuck remaining corners into pockets for all pieces until you have two corners without a

pocket


Tuck one of the remaining corners into a free pocket on piece 6

2

You have now completed a cube!

6 6

6

Take the 6th and last piece, tuck one corner into a free pocket, keeping

remaining corners out.

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


Lucky Stars

Make a loose knot in one end, press the knot into a pentagon

Tuck the end of the tail into a fold on the pentagon and press flat

Fold the tail over and press the fold down, keep wrapping the tail around the pentagon and

pressing the sides down, keep it tight

Your pentagon should look like this

1 3 2

Fold the extra bit back over one side, your

paper should look like Number 3 above.

Cut a strip of paper about 1/4 inch thick

Carefully press your fingernail into each side to pop it out, repeat for all five sides

4 5

7 6

8

You should now have a star!

Active Learning Log Name:______________

Mindbender Mansion ©2008, OMSI

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!

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