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.

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