## Spatial Relationships

Knowing where you are with respect to other objects, distinguishing between two similar objects, and finding similarities between two objects are examples of skills in spatial relationships. In general, having good spatial-relationship skills means that you are comfortable and working well with the three-dimensional world. Kinesthetic learners usually have wonderful spatial-relationship skills. They seldom get lost. They know where their keys are! They function well with their bodies. Often, they are fine athletes. They make fine quilters. They generally possess the body/kinesthetic intelligence Gardner tells us about. Those of us without a native ability in this area require training to develop spatial-relationship skills. This section provides an introduction to and exercises in spatial relationships (SR).

First, consider inductive reasoning with objects. This will carry over from the previous section and tie in spatial skills. You will use a table of objects as your "space." Each section of your table contains a special character, a #. If you would like to name this object, and some of you will find no need to do so, you may call it a burst. Notice that the location of the # varies in each cell.

 * * * * * * * * *

Each # occupies a different combination of top, middle, bottom, left, center, and right of the cell. No two % are in the same location within the cell. You now will observe a sequence of squares and predict the next location of the # in each square. Use T, M, or B to identify the vertical location, and L, C, or R to identify the horizontal location of the #. In the following figure, the # is located as:

 TL TC TR MR BR

Predict where the next two # would go based on the pattern established. It appears that the # is moving across the top row (TL, TC, TR), down the right column (TR, MR, BR). You may predict that the pattern looks as it appears in the following table. However, you may have identified another pattern altogether!

 TL TC TR MR BR BC BL

Visit the Web site www.mentalagility.com for an interactive version of this exercise.

A second type of spatial relationship is rotation of an object. You will consider this in two dimensions—that is, on a flat surface, such as this page, and also in three-dimensional space. This is very difficult, and you may find yourself wanting to stop before you arrive at a solution. The advice we can offer that will help you to grow new brain cells is: Keep going! Press on! There is an answer, and you can find it!

2D Spatial Relationships

Look at the floor plan in Figure 7-5. Which of the other floor plans is a rotation of it?

 — y

\

s

Figure 7-5 Floor plans

The answer is letter b. To convince yourself, trace the original plan (you might use the tissue paper that came in a gift box), place it over each of the other plans, and rotate it until it completely matches one of them. To match plan a, c, or d, flip your tracing paper over and rotate it until it matches plan a, c, and d. They are the rotations of the mirror image of the original plan.

3D Spatial Relationships

Now consider one of a pair of dice, a die. Use Figure 7-6. Which of the four dice matches the die on the left when rotated?

Figure 7-6 Match dice

The answer is letter a. It may help to visualize this process:

1. The die on the left was first rolled so that the 6 pips

2. Then it was turned 90 degrees to the left.

It also may help to find a pair of dice and try to set them up to match the picture. As a kinesthetic learner, you will want to turn them in your hands to help verify this result.

Did you notice that all dice are alike in the placement of the pips? That's a standardization you may not have been aware of! Now notice that the dice in options b, c, and d in the exercise are not even regulation dice. How can you tell? Hint: Try to arrange a die to resemble the dice in b, c, and d.

Another nifty fact about dice is that the opposite sides always add up to seven. That means that the 1 is opposite the 6, the 2 is opposite the 5, and the 3 is opposite the 4. Using this extra fact, along with strategies you learned in the earlier example, find the die on the right that is a copy of the die on the left in Figure 7-7.

Figure 7-7

Did you select c? Visualize the rotation of the die on the left to match the die lettered c. First turn the die 180 degrees clockwise until you can see the 1 on the front. Then roll it over on its side, so that the 5 is on top. Now the die matches view c. This will take some practice. Use the die if that helps.

You also could solve this puzzle by eliminating incorrect dice. You can eliminate both dice a and d, because they have adjacent (not opposite) faces that add up to seven pips. Additionally, die b has an incorrect face. The two pips on the top face are in the wrong corners. Check this with a regulation die if you like.

Interestingly enough, men generally perform better at this type of activity than women, so women will require a bit more practice to be just as agile with spatial relationships.

Visit the Web site www.mentalagility.com for an interactive version of this exercise.

Here are some practice exercises for you. Choose the letter of the die that is a rotation of the die on the left.

 s • 1 • 1 • / /- - • 1 • • / • • • r • • • 9 V • » • /
 • :¡ • • i • • r • • • • / • • V •
 • I» 1 • : • • • • • 9 • 1 • • • ? • •

You'll find the answers at the end of this chapter. Spatial Relationships Exercises

To increase spatial abilities, try to draw a floor plan of your home. After that, sketch a map of your neighborhood. Plan a party where the main activity is a scavenger hunt where you design the field of play. Assemble a model of a vehicle or building that you have admired. In fact, design an activity yourself that will suit your interests. The key components are that you will have to think in three dimensions and create a physical object from parts. The result will be a combination of visual and kinesthetic learning.

### ANAGRAMS AND ANAGRAMPS

This is a language exercise. Recall that the visual learning style makes good use of the printed word. Playing word games, in general, will help your language-processing skills and develop your visual learning style.

An anagram is a word created from another word by rearranging all of the letters in the first word. For example, tar is an anagram of rat. Art is also an anagram of rat and tar. Danger is an anagram of gander. Try to identify anagrams in the following list.

Identify Anagrams

Are these words anagrams? Yes No

In this table, lines 1, 3, 4, and 5 contain anagrams. Line 2 contains homonyms, words that sound alike. Line 6 contains opposites.

Now that you know what anagrams are, you can try to make some of your own.

What is an anagram of the word pit?_

What is an anagram of the word bear?_

Possible answers include tip and bare. Did you think of tip and bare? If so, good for you! Go on to the section named Play AnaGramps. If not, let's do some more.

### Bonus Exercise

Notice that bare is also a homonym for bear. Try to find more anagrams that also sound like the original word. This extra exercise will help you work on your auditory skills as well.

Let's choose the word ear. If you rearrange the letters, you can make new words. Some words you can make are era and are. You also could rearrange the letters to spell rea or Rae or aer. But these are not words in English. Sometimes Rae can be a woman's name, and aer means air in Irish. Rearrange these letters to make anagrams:

What is an anagram of the word spot?_

What is an anagram of the word garden?_

Two of the ones we found for spot were tops and pots. Did you find a third? For garden, we can use the anagrams from earlier: danger and gander.

Play AnaGramps

Now you're ready to play the game. This game is a completion task. Each blank in each sentence can be filled with anagrams.

Sample: I saw a star in the sky as I was walking last night.

### AnaGramps

Complete each sentence with an anagram of the word in italics (remember that the sentence must make sense). Try more than once to fill these blanks before checking the answers at the end of this chapter. Each search will strengthen your mind.

1. Pirates used to rove_the bounding sea.

2. My friend Thelma retired to a cottage in a tiny _by the sea.

Now fill in the blanks with two anagrams.

4. The _river is so long and straight that it looks like a_on the map.

5. She traveled_and far to_a living.

_to startle you.

7. It is hard to_to a_movie. That's why they used title frames.

8. Eve was duped by the_to_Adam with the forbidden fruit.

9. _Gonzalez could really_during his siesta.

10. The mother bird finally_her chicks out of the_.

11. I pricked my finger on the thorn of a_and, boy, is it ever_!

12. You will need a military _ if you march through that_.

13. I _ the children to stay close and not to

14. At_I turn on the lights so I won't miss a

15. Read this_for me. I want to be sure it has the right_.

Now that you have the hang of it, try to make up some anagram examples to share with friends. Teach another person how to play AnaGramps, and then trade puzzles.

You can find an anagram by listing all the possible arrangements for a word and then examining each one to determine whether it is a word. For example, crate can be rearranged to form 120 possible words. Here are a few

 acert acetr acrte acret acter actre aecrt aectr aertc aerct aetcr aetrc caert caetr carte caret cater catre ceart ceatr certa cerat cetar cetra arect aretc arcte arcet artec

We made 29 arrangements and found only three words! This plan of attack can be exhausting and not much fun. The

CROSSWORD PUZZLE: A Learning style Puzzle

ACROSS

 1 Choose from a list 30 Swiss mountains 64 Visual organ 4 Forever youthful 32 Tip over 65 Belonging to me 11 Smear test 33 Not far 66 Payable 14 Porcine card game for 34 Shortens skirt 67 Narcissistic children 37 Pares 69 Lack of presence 17 Michael Jordan's 40 Flat thin narrow strip 72 In harmony with nickname 42 A gourd rattle 76 Concluding remarks 18 Chloride (I AM TRUE 44 Keep 78 Soiled anagram) 47 Writing fluid 79 Peanut candy 19 Many "l's" 49 Neurons and glial cells 80 One billion years 21 Run 52 Set up 81 Groove 22 Auditory learner's "to" 53 Hydrogen compounds 82 Gave temporarily 23 Ancient Roman 55 Concious mental state 83 Haute couture magistrate 57 Finish 86 Metal or bamboo rods (A REPORT anagram) 58 Poly ending (STEER 89 Seed house 24 Alone anagram) 92 Astray 25 Article 60 "A drink with jam and 94 Yours and mine 26 Scrooge's lament bread..." 95 Tiny disagreement 28 Toss out 61 Money first 96 Lives in 30 across
 98 Driving aid 119 Grab 134 Nimbleness 99 Concerning the brain 120 Blend 135 Contents of 89 102 Small twitch 121 Wrongly accused across 103 Title 123 For sooth 136 Possess 104 Follows 126 E in HOMES 137 Kinesthetic 106 Fence portal 128 in Hierarchy between acquisition 109 Central idea Baron and Knight 138 Handworker? 112 Belts 131 Tall flightless bird 139 Arid 114 Sandwich fish 132 Conflicts 116 Noted 133 Father DOWN 1 Promise 39 Clip 85 Pull 2 Holy 41 Arbor native 87 Pause 3 Tread heavily 43 Consented 88 Engrave 4 Holds fluid for injections 44 Took a seat 89 Fruit desert (UP A ELM anagram) 45 Top card in the deck 90 Poem 5 Auditory output of a 46 By way of 91 Performed brook 48 Last in hierarchy of 128 93 Spread around 6 Equal Rights across 97 Dropsy Amendment (abbrev.) 50 Selected at random 100 Visual activity 7 Prevaricate 51 Product of 55 across 101 Tardy 8 Consumed 54 Spirit 105 Persuades 9 Cookers 56 Princess of Wales 107 Knotted hat 10 Sequential 59 Refine metals 108 Promise 11 Annoyer 62 Fishing gear 110 Worn out 12 Before now 63 Plunges 111 Died for a cause 13 White bears 66 Passageways 113 Shoot 14 Tap gently 68 Corners 115 Mountaintop nest 15 Solid water 70 Prickly pod 117 Correct 16 Bauble 71 Wet snow 118 Pause 20 Serious 72 Evaporate (A TABLE 120 Encounter 21 Choir step anagram) 122 Obligation 27 Two footed 73 Brain condition result- 123 Another of 22 across 29 Crustacean ing from alcohol abuse 124 Uncooked 31 Passage 74 Smallest 126 Vase 35 Stirred, not shaken 75 Devil 127 Anger 36 Body of knowledge 77 Not apt 129 Mature, wise, arrived 38 Citrus 84 Not in 130 Naught

key is to work on developing a strategy that reduces the work and increases the fun. Notice that the bulk of these "words" do not form English words. You can improve your search by developing strategies using what you know about English words. For example, many words start with tr, but none with rt Find a word starting with tr.

This is the type of activity your brain thrives on. When you design your own strategies for playing a game, you exercise your brain in a way it has never been exercised before. Think a while and see whether you can find another strategy for improving your ability to identify an anagram of a word. By the way, trace is an anagram of crate. Did you find others?

Anagrams can be extended to complete phrases. By rearranging the letters of Albert Einstein, Stephen Choi created the anagram Ten elite brains. Using a software program named Anagram Genius, Wendy A. Keen found nice ration size to be an anagram of a senior citizen. Type in The best things in life are free, and the program produces the anagram Nail-biting refreshes the feet! We found these anagrams at http://www.anagramgenius.com. You can visit the Web site and get a list of anagrams for your name! You also might enjoy the Anagram Hall of Fame at the Web location http://www.wordsmith.org/anagram/hof. html. Samples there include dormitory and dirty room, as well as senior moment and I'm not Emerson.

^^ We would like to hear about your strategies for finding ^^ anagrams. Go to this book's Web site at http://www. mentalagility.com. Access the Anagrams and Ana-gramps menu item and send us your ideas. We'll post new strategies for other readers to read and use. You also will find an option on the Web page for letting us know about AnaGramps you have created. We'll post the first ones we receive from each reader.

This is an interesting note for math lovers on the possible number of arrangements of a set of letters in a word. The number of arrangements of letters in a word of all different letters is calculated by a formula known as a factorial. Suppose that there are five letters in a word. Imagine five blanks:_____. Where might you place the first letter? You have five choices. Then there are only four places left for the second letter, three for the third letter, two for the fourth letter, and then only one place remains for the last letter. Multiply 5 x 4 x 3 x 2 x 1. The result is 120. Mathematicians devised shorthand for writing out this problem: 5!. The exclamation point is read as "factorial." 5! is read as "5 factorial." So 4! = 4 x 3 x 2 x 1. And 7! is 7 x 6 x 5 x 4 x 3 x 2 x 1. If no letters are repeated, the number of possible rearrangements for a word with n letters is n!

WORD FIT! A FILL-IN PUZZLE

In this puzzle you have all of the words. To solve the puzzle, put all the words in their proper location. (Hint: Since there are only two 8-letter words, try to place them first.)

3 LETTERS 4 LETTERS 5 LETTERS

 ADO ABET ALIGN ALL AIRY AMASS ALP ASIA ARISE BAY AXON CLING EBB CLIP DIALS EGO EASY ENACT EVE EBBS FILAR FAT ENDS PEEPS GAP ETCH PIXIE GIN EYED PRIME ITS FLAP PRONE LIE GLUE SLANT LOB LOBE STOLE MAN NAVE THESE MOB NEAT TYPED PEN NILE WIPED SEE OBOE SUE OLEO TED OMEN TOE PEAS RODE SINS SLAB TOOT

6 LETTERS 7 LETTERS 8 LETTERS

ACCEPT APPEARS MIRABILE

ENCORE COSINES SLIPCASE

IRENIC FRONTAL

MATTER IRANIAN

PAEANS SNEERED

SANDAL TOOTERS

SOIREE

TISANE

WISEST

YEOMEN

WORD UP!

Find the message hidden in these letters. Rearrange the letters below and place them in the grid to make a sentence. We'll give you a hint! The letters are already in the correct columns.

ETA I NGAAADNO STEORKEG I NO? VFRTS TOPTT H R T

BEK I DCENGEHOLER CHNN I E I THORYML . OORS YOUY'OU U S S T

### MIND MATCHES

Many words are used in technical ways that are related to the original etymology of a word. The etymology of a word is similar to its pedigree. It describes the origin of the word, in what languages it was used, and how its meaning has changed over the years.

The object of this game is to match each word with its origin. Some matches are more obvious than others. This game develops your verbal comprehension, which is one of the skills tested on an IQ test. For this game, we encourage you to use a dictionary. You will find many wonderful new words in your dictionary as you try to solve this puzzle. Answers are at the end of this chapter.

Match each brain-related use of the following terms with their word origins.

 I. _homunculus a. glue-like 2. _circadian b. juncture 3. _hippocampus c. a half of the celestial sphere of stars and planets 4. _rehearsal d. rounded body parts S. _ neurons e. bark 6. _hemisphere f. nerves 7. _auditory g. relating to time B. _temporal h. a little human 9. _lobes i. opposite of anesthetic 10. _thalamus j. chamber II. _reticular system k. to cultivate again 12. _limbic system l. related to hearing 13. _glial m . about a day 14. _kinesthetic n. border area of the cortex IS. _synapse o. sea horse 16. _cortex p. similar to a pouch or a

woman's drawstring bag woman's drawstring bag t

### THE CALENDAR

The calendar is a tool we use every day, and it is so common you probably don't ever think much about its origins. It helps to think about it as a human creation. This set of exer-J| cises helps to develop your verbal fluency. An almanac is a handy tool for this job.

"Remember that time is money." — Benjamin Franklin The Vocabulary of the Calendar

Look in an almanac to find out the etymology, or the origins of the words, for the following terms: calendar, day, week, month, year, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, January, February, March, April, May, June, July, August, September, October, November, December.

### Calendar Reform

Currently we follow the Gregorian calendar. Use an almanac to find out how our current calendar was developed. If you are interested in genealogy, you know about the calendar reform of 1582 finally adopted by the British in 1752. If not, find out about calendar reform. Try to determine why there are 12 months of uneven numbers of days. It seems like an arbitrary decision for breaking up the 365 days.

Calendars of Other Cultures

Investigate the Chinese calendar. How is it like the Gregorian calendar? How is it different? Investigate other calendars for other groups.

How Many Calendars Do You Ever Need?

Have you noticed that many years have the same arrangements of dates? For example, the calendar for the year 2000 is the same one we used in 1972. How many different calendars do you need to keep around so that you always have a correct version? When is the next time you will be able to use the 1999 calendar again? Answers for this question are at the end of this chapter.

### Day of the Week Calculation

Ever wonder on what day of the week you were born? Find out the day of the week for any date after 1753. Use the following calculation. We will demonstrate with February 6, 1897. The last column is provided for you to work this calculation on a date of your choosing.

 Steps Step # Sample Values Your Values Write the day of the month. 1 6 Write the month. 2 2 Write the year. 3 1897 If the month is January or February, add 1 to the number in step 1. 4 7 If the month is January or February, subtract 1 from the number in step 3. 5 1896 Write the first two digits of the number in step 5. 6 18 Divide the number in step 6 by 4. (Toss the remainder.) 7 4 Multiply the number in step 3 by 5. 8 9485 Divide the number in step 8 by 4. (Toss the remainder.) 9 2371 Add 1 to the number in step 5. 10 1897 Multiply the number in step 10 by 13. 11 24661 Divide the number in step 11 by 5. (Toss the remainder.) 12 4932 Add the numbers in steps 9 and 12. 13 7303 Subtract the number in step 7 from the number in step 13. 14 7299 Add the number in step 6 to the number in step 14. 15 7317 Add the number in step 1 to the number in step 15. 16 7323 Subtract 1 from the number in step 16. 17 7322 Divide the number in step 17 by 7. Keep only the remainder. 18 0

The number in step 18 tells you on which day of the week 2/6/1987 fell. Use this table to determine the name of the day of the week:

 Remainder Decimal part of answer (if you used a calculator) Day of the Week 1 0.14285714... Sunday 2 0.28571428... Monday 3 0.42857142... Tuesday 4 0.57142857... Wednesday 5 0.71428571 ... Thursday 6 0.85714285... Friday 0 0 Saturday

So, February 6, 1897 was on a Saturday. Try this calculation with a date of your choice.

### Number of Days in Each Month

You may recall the jingle for remembering the number of days in each month. "Thirty days hath September, April, June, and November. All the rest have 31, except February." This is an example of a mnemonic device. This works very well for an auditory learner. However, a kinesthetic or visual learner may experience difficulty remembering the order of the months in that device. A visual learner may remember the number of days in a month by remembering what a calendar looks like. For a kinesthetic learner, there is another way to remember the number of days in a month. It uses your hands as a tool. Make a pair of fists, as shown in Figure 7-8.

Notice that your knuckles form peaks and valleys. Start at the left hand, first knuckle, and recite the months of the year, in order, using peaks and valleys. When you run out of knuckles on your left hand, go to your right hand for August on the first knuckle. Continue until you reach December. Notice that all of the months you named by a knuckle have 31 days. Those you named by a valley do not. All of those months, except February, have 30 days. Most people remember about February.

As an exercise, explain this calendar mechanism to someone. Tell him it is a great mnemonic device—a handy digital device, solar powered, and pocket-sized.

A Very Spatial Puzzle

Copy these patterns to a piece of cardstock or a 3"x 5" card. Cut out the pieces and rearrange the smaller pieces to make the big square. Hint: Flip the puzzle pieces over if it helps.

THE HOUSE THAT JACK BUILT

For this exercise, you'll use Figure 7-9. An ancient Chinese puzzle called tangrams will improve your kinesthetic learning

skills. The puzzle pieces, or tans, all are cut from a square. Then the tans are arranged in shapes by puzzle masters. A silhouette is drawn and given to a puzzler to solve. The puzzler rearranges the seven tans to match the arrangements.

You can learn ancient puzzle techniques. Using a blank piece of paper, trace Figure 7-9. Cut out all seven tans. Spend some time noticing the seven pieces. Some are alike, some are very different. For your first puzzle, put the seven tans back into a square. Don't peek at the diagram on this page!

After you master the square puzzle, you can move on to a set of puzzles. This is a puzzle made to match the characters in a famous old nursery rhyme, The House That Jack Built.

This is the House that Jack built.

This is the Malt that lay in the House that Jack buil

This is the Rat that ate the Malt that lay in the House that Jack built.