Chapter 1. Chapte r 2. Chapter 3. Chapter 4. Chapter 5. Chapter 6. Chapter 7.

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Chapter 1. Chapter 2. Chapter 3. Chapter 4.Chapter 5.Chapter 6.Chapter 7.

NumberArithmetical operationsFraction Decimal TimeMeasurementGeometry

Chapter 8.Chapter 9.Chapter 10.Chapter 11.Chapter 12.Chapter 13.Chapter 14.Chapter 15.Chapter 16.Chapter 17.Chapter 18.Chapter 19.

Amazing numberTetrisSecret codeMagic SquareTraversable diagramsTower of HanoiEnglish words puzzleMathematical equations

puzzleSudokuTangramThe golden ratioThe toothpick puzzles

General Mathematics

12 Puzzles and games

Contents ………………………………………………………………........................................ 목 차

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01Chapter

Number

A number is for counting and measuring.

A symbol of a number is a numeral

Type of numbers

Natural numbers

Integers Rational numbers

Natural numbers

Counting numbers one, two, three, four ……, ten ….

Place value

Each digit in a number has a value based on its place in the number.

The 3 is in the millions place. The 7 is in the hundred thousands place.The 6 is in the ten thousands place.The 5 is in the thousands place.The 1 is in the hundreds place.The 4 is in the tens place.The 7 is in the ones place.

Integers

Integers (Whole numbers)

Positive numbers : 1, 2, 3, 4…..

Zero : 0

Negative numbers : -1, -2, -3, -4 …

3,765,147

Rational numbers

A rational number can be expressed as a fraction. numerator denominator ( Not 0 as a denominator ) Some fraction can make up one integer number ;

Two different fractions may correspond to the same rational number ;

62= 13

3- 4 2 == - 23

63=1

2 =24

84

mn

= 2

These sentences are typical expressions and students should learn and memorize them!

A symbol which represents a number is called a numeral. 수를 나타내는 기호를 숫자라고 한다 .

Each digit in a number has a value based on its place in the number. 수의 각 숫자는 고유의 자리 값을 갖는다 .

Negative numbers are numbers that are less than zero. 음수는 0 보다 작은 수이다 .

If the value of m is greater than n, then the value of the fraction is greater than 1. m 값이 n 보다 크면 분수 값은 1 보다 크다 .

Mathematic English Expression To Learn


02Chapter

Arithmetical operations

Additions

Sum or total

12+ 719

Definition : Add two or more numbers to find a sum or total.

Write : 12 + 7 = 19

Read : Twelve plus seven equals nineteen. Twelve plus seven is equal to nineteen. Twelve plus seven is nineteen.

A farmer planted 78 acres of soybeans and 62 acres of corn. Last year, 30 of the acres now used for corn were used for soybeans. How many acres of corn did the farmer have last year?

Seongjun has coins of 100, 50 and 10 won. Their total quantity is 7 and its value is 290 won. What coins and how many each does he have?

Ingyeong spent 20,000 won for two new shirts and 35,000 won for a pair of jeans. She has 3,000 won left over. How much money did she take for shopping?

Subtraction

difference

12- 7 5

Definition : Subtract one number from the other number to find a difference.

Form : Subtract 7 from 12.

Write : 12 - 7 = 5

Read : Twelve minus seven equals five. Twelve minus seven is equal to five. Twelve minus seven is five.

Combined, the movies "Titanic" and "Gone with the Wind" won 19 Academy Awards. "Titanic" won 3 more awards than "Gone with the Wind". How many awards did each movie win?

Sangwon's flight left at 9:00. It took him one and a half hours to check in at the airport. His house is an hour drive from the airport. At what time did Sangwon leave his house to get to the airport?

Jooyeon did a piano class and an English class for total one and a half hours. The English class was 10 minutes longer than the piano class. How long was each class?

Multiplication

product

12× 784

Definition : Multiply number with the other number to find the product.

Form : Multiply 12 and 7.

Write : 12 × 7 = 84

Read : Twelve times seven equals eighty four. Twelve times seven is equal to eighty four. Twelve times seven is eighty four.

The Empire State Building in New York is hit by lightning about 100 times a year. The building opened in 1931. About how many times was it hit by lightning by the year 2008?

Every day there are 40 flights to Busan and 50 flights to Jeju from Seoul. Each plane holds about 130 passengers. How many people can fly to Busan and Jeju from Seoul each day?

Pluto travels around the sun at a speed of 10,600 miles per hour. How far does Pluto travel in 8 hours?

Division

reminder

112 84

Definition : Divide a number by the other number to find the quotient and remainder.

Form : Divide 12 by 8.

Write : 12 ÷ 8 = 1.5

Read : Twelve divided by eight equals one point five. Twelve divided by eight is equal to one point five. Twelve divided by eight is one point five. Twelve over eight is one point five.

quotient4

Julie used 48 shells to make 6 necklaces. She used the same number of shells for each necklace. How many shells were on each necklace?

Mexico City is one of the fastest growing cities in the world. If the population is increased by 15,183 every week, how many more people would be in Mexico City every day?

A frog's heart beats about 1,800 times per hour. About how many times does a frog's heart beat per minute? (1 hour = 60 minutes)

Comparison

Definition : Compare two or more numbers.

Form : The symbol < means "is less than". The symbol > means "is greater than". The symbol = means "is equal to".

Write and Read : 5 < 7 Five is less than seven. 7 > 5 Seven is greater than 5. 5 = Five is equal to ten-second. 10

2

Add two or more numbers to find a sum or total. 두 개 혹은 그 이상의 수를 더해 합이나 총계를 구한다 .

Subtract one number from the other number to find a difference. 한 수에서 다른 수를 빼 차를 구한다 .

Multiply number with the other number to find the product. 한 수와 다른 수를 곱하여 값을 구한다 .

Divide a number by the other number to find the quotient and remainder. 한 수를 다른 수로 나누어 몫과 나머지를 구한다 .



03Chapter

Fraction

Cardinal numbers : one, two, three, … , ten, … (How many things are) Ordinal numbers : first, second, third, … , tenth, … (When a thing occurs)

four parts in all

34

Definition : A fraction names part of a whole.

Form :

Write :

Read :

Read a numerator in a cardinal number and a denominator in ordinal number.

three yellow parts

denominator

numerator

34

12

14

three - quarters three – fourthsthree over four

one - half one over two

one - quarterone – fourthone over four

A proper fraction : a numerator is smaller than a denominator. For example : or

An improper fraction : a numerator is greater than or equal to a denominator. For example : or

A mixed fraction : a whole number except zero and a proper fraction. For example : or A mixed fraction can be written as an improper fraction. For example :

712

35

231

Proper fraction, Improper fraction and Mixed fraction

36

12 7

53

66

571 1

32

231 5

3= 132 7

3=

To add or subtract fractions, you might need to use equivalent fractions which have the same of denominator. are equal to . They are equivalent fractions. In order to add to , might to be changed to .

48

24

3 8

24

Equivalent fraction

4 8

24

To simplify a fraction, divide both the numerator and denominator by the same greatest number possible. In order to simplify , both the numerator and denominator divided by 4 and get .

1216

Simplified fraction

34

Stan hiked km on Saturday and km on Sunday. His 2-day goal was to hike 30 km. Did he reach his goal?

One honeybee makes teaspoon of honey during its lifetime. How many honeybees are needed to make teaspoon of honey?

In the frog-jumping contest, the winner jumped m. The second-placed frog jumped m. What was the difference in the length of their jumps?

3417

122

112

1211

1 2

152

A fraction names part of a whole. 분수는 전체의 부분이다 .

A proper fraction is a fraction with a numerator that is smaller than the denominator. 진분수는 분자가 분모보다 작은 분수이다 .

A mixed fraction can be written as an improper fraction. 대분수는 가분수로 표시될 수 있다 .

To simplify a fraction, divide both the numerator and denominator by the same greatest number possible. 분수를 간단하게 하기 위해 분자와 분모 동시에 나눌 수 있는 수 중 가장 큰 수로 같이 나누어 준다 .



04Chapter

Decimal

Definition : Like fractions, decimals show part of a whole.

Form : 0.4

Write : 0.4 0.79

Read : four tenths point four

seventy nine hundredthspoint seventy ninepoint seven nine

Place value

A place value chart help you understand how to read and write decimals.

To read a decimal that has a whole number part,First, read the whole number part.Second, read the decimal point as and.Third, read the decimal part as a whole number.Then name the place value of the last digit.Read 35.206 as thirty five and two hundred six thousandths.

Read 35.206 simply as thirty five point two-o- six.

35.2061

23

4

1 2 3

4

Rounding decimal is to estimate the number.

Round 31.2 to the nearest one

31.2 is closer to 31 than to 32. Therefore, 31.2 rounds down to

31.

31.2 31

Round the numbers to two decimal places.

12.026 12.03

Rounding decimal

31 31.2 32

Mia used 18.5 cm of wire to make a bracelet. Then she made 2 earrings using 4.75 cm of wire for each one. She had 26.38 cm of wire left over. How much wire did she start with?

Mangi's model train set now has 7.5 m of tracks. After he bought it, he added 4 m of tracks. But it was too long for the room. He then took off 2.7 m. How many meter of tracks came with Mangi's train set when he bought it?

Everyday 274,000 carats of diamonds are mined. One carat is 0.2 grams. The Cullinan Diamond is the largest diamond ever discovered. It is 3,106 carat. How many grams does the Cullinan Diamond weigh?

Like fractions, decimals show part of a whole. 소수도 분수처럼 전체의 부분을 나타낸다 .

Read 0.79 as seventy nine hundredths. 0.79 는 seventy nine hundredths 라고 읽는다 .

Read 35.206 as thirty five and two hundred six thousandths. 35.206 은 thirty five and two hundred six thousandths 라고 읽는다 .

31.2 is closer to 31 than to 32. Therefore, 31.2 rounds down to 31. 31.2 은 32 보다 31 에 가깝다 . 그래서 31.2 를 반올림하면 31 이 된다 .



05Chapter

Time

A day is divided into hours, minutes, and seconds.

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60

seconds

The clock shows the time.

Write : 4 : 35

Read : thirty five minutes after four twenty five minutes before five four - thirty five

Time

Elapsed time is the amount of time that passes from the start of an event to its end.

Elapsed time

These clocks show that 4 hours and 35 minutes elapsed between 5:00 and 9:35.

To find when an event ended, add elapsed time to start time

Start time 5 : 00 + Elapsed time 4 : 35 End time 9 : 35

A schedule is a list or table to show when events happen.

Schedule

Flight schedule from SeoulDestination Departs Arrives

Jeju 7:15 8:15Tokyo 8:30 11:45

Hongkong 6:40 10:20LA 9:00 19:20

Use the schedule to answer.

1) How long is the flight from Seoul to Hongkong?

2) Which is the shortest flight on the schedule?

3) If it takes 90 minutes to check in for a flight, What time should you arrive at the airport for the flight to LA?

4) If it takes 45 minutes to drive to the airport and 90 minutes to check in for a flight, what time should you leave from house for Tokyo?

A year is divided into months, weeks, and days.

Calendar

Use the calendar to write each day and date.1) 3 days after Jan 30, 2009 Monday, Feb 2, 2009 2) 5 days before Feb 3, 2009 3) 2 weeks before Feb 24, 2009 4) 5 days after the last Friday in Feb, 2009

The calendar below shows Jan, Feb and Mar of the year 2009.

7 days = 1 week

52 weeks = 1 year

12 months = 1

year

Soccer activity ended at 7:00. The team stretched for 10 minutes and practiced for 40 minutes. Then they played a game for 35 minutes. What time did the soccer practice start?

Yoonkyung got home from shopping at 4:30. She spent 1 hour and 15 minutes in the department. Then she did her grocery shopping for 30 minutes. What time did she start shopping?

It takes Jupiter about 11 years and 10 months to orbit, or to go around, the sun. Saturn takes about 17 years and 7 months more than Jupiter to orbit the sun. About how long does it take Saturn to orbit the sun?

A day is divided into hours, minutes, and seconds. 1 일은 시간 , 분 , 그리고 초로 표시된다 .

Elapsed time is the amount of time that passes from the start of an event to its end. 경과시간은 어떤 일의 출발 시점에서 끝나는 시점까지 시간의 양이다 .

A schedule is a list or table to show when events happen. 시간표는 언제 일이 일어나는가를 보여주는 표이다 .

A year is divided into months, weeks, and days. 1 년은 월 , 주 , 그리고 일로 나누어진다 .



06Chapter

Measurement

1 foot(ft.) = 12 in.1 yard(yd.) = 3 ft.1 mile(mi.)=1,760 yd.

Length

1 cm = 10 mm1 m = 100 cm1 km = 1,000 m

1 in. = 2.54 cm1 ft. = 30.48 cm1 yd. = 91.44 cm1 mi. = 1.61 km

In USA Metric system Conversion of units

Customary length units in USA and Canada : inches, feet, yards and miles.

Length units in Korea and other countries : millimeters, centimeters, meters and kilometers (Metric System)

The speed of highway in the US is 60 mi. per hour and the speed of highway is in Korea is 100 km per hour. Where and how fast do cars run?

Sangwon is 153 cm tall and Bill is 5 feet tall. Who is taller?

The ostrich and the emu are the two largest birds. An emu is usually 1/2 the size of an ostrich. The sum of their heights is 150 inches. How tall is the average ostrich?

1 pound (lb.) = 16

oz.

1 ton (T.) = 2,000

lb.

Weight

1 g = 1,000 mg1 kg = 1,000 g1 ton = 1,000 kg

1 oz. = 28.35 g1 lb. = 453 g 1 T. = 906 kg


Customary weight units in USA and Canada : ounces, pounds, and USA tons

Weight units in Korea and other countries : milligrams, grams, kilograms and metric tons (Metric System)

A hot dog has about 1/4 the amount of protein as 3 ounces of hamburger. Together, they have about 25 grams protein. How many grams of protein are in a 3 oz. hamburger?

What is difference between 1 ton in the US and 1 metric ton?

Mia's weight is 45 kg and Julie's weight is 90 lb. Who is heavier?

1 cup (c.) = 8 fl. oz.1 pint (pt.) = 2 c.1 quart (qt.) = 2 pt.1 gallon (gal.) = 4 qt.

Capacity

1 cc = 1 mL1 L = 1,000 mL1 kL = 1,000 L

1 c. = 0.237 L1 pt. = 0.473 L 1 qt. = 0.946 L 1 gal. = 3.784 L


Customary capacity units in USA and Canada : cups, pints, quarts and gallons

Capacity units in Korea and other countries : milliliters, liters and kiloliters (Metric System)

fl. oz. means fluid ounce to measure the volume of liquid and 1 fl. oz is equal to 29.59 cc.cc (cubic centimeters) is metric unit. It is equal to 1 mL.

NOTE

There are 2 pints bottle and a liter bottle. Which bottle is bigger?

The gas price is $ 2.25 per gallon in the US and it is 1,300 won per liter in Korea. Which country has more expensive gas? (Assume $ 1 is 1,300 won)

A water bottle of 16.9 fl. oz. in the US is used for the most popular size of drinking water. Is it the same size of a water bottle in Korea?

110 1100 11,000 11,000,000 11,000,000,000

Example of metric system

The customary units that are used to measure length are inches, feet, yards and miles in the US. 미국은 일상 생활에서 길이나 거리 단위로 인치 , 피트 , 야드 그리고 마일을 주로 사용한다 .

Milligrams, grams, kilograms, and metric tons are used to measure weight in the metric system. 미터법에서는 밀리그램 , 그램 , 킬로그램 그리고 미터법 톤으로 질량 단위를 나타낸다 .

How many grams of protein are in a 3 oz. hamburger? 3 온스 햄버거에는 몇 그램의 단백질이 있는가 ?

cc (cubic centimeters) is metric unit. cc (3 제곱 센티미터 ) 는 미터법 단위이다 .



07Chapter

Geometry

A point is an exact location in space.

A coordinate grid is a graph with horizontal and vertical

lines.

Plotting points on a coordinate grid

A

Plot a point (2,3)

1. Start at 0.2. Move 2 spaces to the right.3. Move 3 spaces up.4. Plot a point.

A line is an endless straight path.

A line segment is a straight path between two points.

A ray is an endless straight path starting at one point.

Lines, Rays, and Line segments

Read : line AB or line BAWrite : AB or BA

Read : line segment RS or line segment SRWrite : RS or SR

Read : ray BGWrite : BG

Lines that cross at one point are intersecting lines.

Lines that intersect to form four 900 angles are perpendicular lines.

Lines that never intersect are parallel lines. They are always the same distance apart.

NOTE

A B

R S

B G

An angle is two rays with a common endpoint.

Angles are measured in degree (0).

Read : angle ABC or angle CBAWrite : ABC or CBA

Angles

Plane

A plane is a flat surface that extends in all direction.It is named by four points.

Plane LMON

A right angle is exactly 900. An acute angle is less than 900.

An obtuse angle is greater than 900.

A

CB

L M

N O

Name of diagrams

a quadrangle (a tetragon)

a square (a regular tetragon)

a rectangle

a circle an oval a cone

a triangle

a right-angled triangle

an isosceles triangle

a pentagon a hexagon an octagon

Perimeter is the distance around a figure.

To find the perimeter of a figure, add the lengths of its sides.

Perimeter

Area of a rectangle

Perimeter

6 cm

4 cm

6 cm4 cm

6 cm+ 4 cm20 cm

The formula, A = l × w , means the area of a rectangle equals the length times the width.

1 cm1 cm

This is 1 square unit. Count the number of square units to find the area of a figure.

The area of this figure is 12 square units.4 cm × 3 cm = 12 cm2

l

w

Volume of a rectangle solid

The formula, V = l × w × h , means the volume of a rectangular solid equals the length times the width, and times the height.

1 cm1 cm

This is 1 cubic unit. Count the number of cubes in the top layer.Count the number of layers. Then multiply.

The volume of this rectangular solid is 36 cubic units.4 cm × 3 cm ×3 cm = 36 cm3

1 cm

One day his teacher asked the class to find the sum of all the numbers, 1 through 100. While the other children sat there busily scratching out sums and adding more sum, Gauss looked off in a world of his own. His teacher scolded him to get to work to find an answer. But He already figured it out in his head.

Gauss's anecdote

A coordinate grid is a graph with horizontal and vertical lines. 좌표는 수평축과 수직축을 갖는 그래프이다 .

Lines that intersect to form four 900 angles are perpendicular lines. 4 개의 900 각도를 만드는 직선을 수선이라 한다 .

To find the perimeter of a figure, add the lengths of its sides. 도형의 둘레를 알기 위해 도형 각 변의 길이를 더한다 .

The formula, A = l × w , means the area of a rectangle equals the length times the width. 공식은 A = l × w 이다 . 즉 직사각형의 면적은 가로와 세로의 곱이다 .



08Chapter

Activity 1. Amazing number

Triangle numbers

Can you guess what they are?

Square numbers

Can you guess what they are?

The triangle numbers are 1, 3, 6, 10, 15, 21, 28, 36 and so on.

The Square numbers are 1, 4, 9, 16, 25, 36 and so on.


Amazing numbers

Can you think of a way in which triangle numbers relate to square numbers?What happen when you add any triangle number to the next higher triangle number?Triangle

numbers ?

1 3 6 10 15 21 28 4 9 16 25 36 49

Q1

Can you think of a way in which odd numbers relate to square numbers?

Q2

1+3+5+7+9+11=?1+3+5+7+9=?1+3+5+7=? 1+3+5=?1+3=?1

They were mostly interested in geometry, the math of shape of things. 그들은 기하학 즉 어떤 모양에서 나오는 수에 대해 많은 관심을 가졌다 .

To begin, look at the first dot in the lower left corner. 먼저 왼쪽 하단의 첫 번째 점을 보자 .

The number of dots in each succeeding triangle is 10, 15, 21, 28 and 36. 연속되는 각각의 삼각형이 갖는 점의 수는 10, 15, 21, 28 그리고 36 이다 .

Can you think of a way in which odd numbers relate to square numbers? 홀수와 사각수 사이에는 어떤 관계가 있을까 ?



List of worldwide highest-grossing films

Rank Movie name Worldwide Gross

1 Titanic $1,845,034,189

2 The Lord of the Rings: The Return of the King

$1,119,113,000

3 Pirates of the Caribbean: Dead Man's Chest $1,066,179,725

4 The Dark Knight $996,826,853 5 Harry Potter and the Philosopher's Stone $976,475,550 6 Pirates of the Caribbean: At World's End $960,996,492 7 Harry Potter and the Order of the Phoenix $938,468,864 8 The Lord of the Rings: The Two Towers $926,287,4009 Star Wars Episode I: The Phantom Menace $924,317,558 10 Shrek 2 $919,838,758

-To be continued -

11 Jurassic Park $914,691,118 12 Harry Potter and the Goblet of Fire $896,016,159

13 Spider-Man 3 $890,871,626

14 Harry Potter and the Chamber of Secrets $878,988,482

15 The Lord of the Rings: The Fellowship of the Ring

$871,368,364

16 Finding Nemo $864,625,978

17 Star Wars Episode III: Revenge of the Sith $850,000,605

18 Spider-Man $821,708,551

19 Independence Day $816,969,268

20 Shrek the Third $797,641,069

21 Harry Potter and the Prisoner of Azkaban $795,900,000

Highest grossing films by year

Year Movie name Worldwide Gross

2000 Mission: Impossible II $546,388,1052001 Harry Potter and the Philosopher's Stone $976,475,5502002 The Lord of the Rings: The Two Towers $926,287,400

2003 The Lord of the Rings: The Return of the King $1,119,113,000

2004 Shrek 2 $919,838,7582005 Harry Potter and the Goblet of Fire $896,016,159

2006 Pirates of the Caribbean: Dead Man's Chest $1,066,179,725

2007 Pirates of the Caribbean: At World's End $960,996,4922008 The Dark Knight $996,826,853

09Chapter

Activity 2. Tetris

Tetris is one of the most well known games. It has several types, for example, video game or wooden block game etc.

The name of Tetris com from Greek numerical prefix "tetra-" because the all shape of blocks has 4 unit blocks.

What is Tetris?

Tetris

Components : Tetris board and blocks Goal : Who is winner to assemble first the given Tetris. How to play :

1) All students spread out all blocks of Tetris on the desk.2) A teacher calls "start".3) The student who completed his / her blocks on Tetris board

raises his / her hand.


Tetris is one of the most well known games. 테트리스는 가장 잘 알려진 게임 중 하나이다 .

He derived its name from the Greek numerical prefix "tetra-". 그는 그리스어로 숫자 4 를 뜻하는 접두어 "Tetra" 를 인용하여 게임의 이름을

"Tetris" 라고 하였다 .Electronic Gaming Monthly's 100th issue in 2007 had Tetris in the first place as "Greatest Game of All Time".

2007 년 잡지 월간전자게임 100 회 특집에서 테트리스는 역사상 가장 위대한 게임으로 선정되었다 . The student who completed his / her blocks on Tetris board raises his / her hand.

테트리스 블록을 다 맞춘 학생은 손을 든다 .


Harry Potter series

Harry Potter is a series of seven fantasy novels written by British author J. K. Rowling. The books chronicle the adventures of a teenage wizard Harry Potter, together with Ron Weasley and Hermione Granger.

Harry Potter and the Philosopher's StoneHarry Potter and the Chamber of Secrets Harry Potter and the Prisoner of Azkaban Harry Potter and the Goblet of Fire Harry Potter and the Order of the Phoenix Harry Potter and the Half-Blood Prince Harry Potter and the Deathly Hallows

1 권

2 권

3 권

4 권

5 권

6 권

7 권

Logic, Strategy, and Problem solving

10Chapter

Activity 3. Secret code

Probability is the chance of a certain result coming up. You know that when you flip a coin, there is one chance out of two.

Probability

Many games involve lots of thinking and the use of strategy. A player must think logically. Sometimes a player must anticipate what an opponent will do and take that into account in a game.

Many games involve a variety of mathematical issues and thinking skills that are useful in problem solving. Some of games are merely games of chance in which probability is the center of all the game action.

Secret code

Components : Play board and color pawns and hint pawns (black & white)

Goal : Try to break opponent's secret code. How to play for beginner : Refer to the book.

For example of attack and defense

One color and place matched

One color and place matched, two color only

matched

Two color and place matched, one color only

matched

Four color and place matched (secret code)


Many games involve a variety of mathematical issues and thinking skills that are useful in problem solving.

대부분 게임들은 그 해답을 풀기 위해 다양한 수학적 사고와 논리를 필요로 한다 .Whether it is the roll of dice or the flip of a coin, probability is the chance of a certain result coming up.

주사위를 굴리거나 동전을 튕겨 어떤 결과가 나오는 가능성을 확률이라고 한다 .Many games involve lots of thinking and the use of strategy.

대부분 게임은 많은 사고와 전략을 요구한다 .The attacker will take a note of his turns he needed to break the secret code.

공격자는 몇 번의 공격으로 비밀코드를 알았는지 기록한다 .These sentences are typical expressions and students should learn and memorize them!

Method of magic square

11Chapter

Activity 4. Magic Square

Nine smaller squares (3 rows, 3 columns)

The sum of across : 15The sum of down : 15The sum of diagonal : 15

The simple magic square

Magic Square for 1-25

Components : Magic square board and numbered chips (1-25) Goal : Who is winner to make first the magic square with 1-25

numbered chips? How to play :

1) All students spread out all numbered chips (1-25) of magic square on the desk.2) A teacher calls "start".3) The student who completed magic square raises his hand.


Historians believe the first magic square was from ancient China before 2000 BC.

역사 학자들은 마방진은 기원 전 2000 년경에 중국에서 시작된 것으로 믿고 있다 .The simplest magic square is made up of nine smaller squares, three across and three down.

가장 간단한 마방진은 가로 3 줄 , 세로 3 줄 총 9 개의 정사각형 조각으로 구성된다 . It takes a lot of time to make a magic square if you have to choose numbers by trial and error.

마방진을 만들기 위해 임의의 숫자를 골라 시행착오를 한다면 엄청난 시간이 소요될 것이다 .Using the number sequence 1 through 9, begin with 1 in the top middle square.

1 부터 9 까지 숫자를 이용하고 , 1 을 첫 줄 가운데 칸에 놓고 시작한다 .These sentences are typical expressions and students should learn and memorize them!

Solution of traversable diagrams

12Chapter

Activity 5. Traversable diagrams

What is traversable diagrams?

The path of diagram is a series of lines and vertices.Some diagrams are traversable, it can be traced the entire set of lines going through each arc or line only once without lifting your pencil.

Euler found that traversable diagrams can have no more than two odd vertices.


Traversable diagrams

Find out the traversable diagrams.Q1

Is there a way to cross each bridge only once and traverse the entire path?

Q2


The path of diagram is a series of lines and vertices (or points where lines meet).

도형의 패스는 선과 , 선이 만나는 꼭지점으로 이루어진다 .He studied the problem of diagram to figure out why some were traversable and some were not.

그는 어떤 도형은 한 붓 그리기가 가능하고 , 어떤 도형은 한 붓 그리기가 불가능한가에 대해 연구하였다 .A vertex is a point on the diagram at which lines and or arcs intersect.

꼭지점이란 도형에서 직선이나 곡선이 만나는 점이다 .Euler found that traversable diagrams can have no more than two odd vertices.

오일러는 한 붓 그리기에서 도형에 2 개 이하의 홀수 꼭지점이 있어야 한다는 사실을 발견하였다 .


Roles of Tower of Hanoi

13Chapter

Activity 6. Tower of Hanoi

What is Tower of Hanoi?

The Tower of Hanoi is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod.

Only one disk should be moved at a time. Move the upper disk from the stack and sliding it onto another

rod. No disk may be placed on top of a smaller disk.

Tower of Hanoi

Components : Main board, 3 rods and 8 different size of disk Goal : Successfully move the Tower of Hanoi onto the other rod. How to play for beginner : Refer to the book. For 3 disks, we need 23-1 = 7 movement.


The Tower of Hanoi is a mathematical game or puzzle. 하노이 탑 쌓은 수학적 게임이며 퍼즐 놀이이다 .

The objective of the game is to move the entire stack to another rod, obeying the following rules.

이 게임의 목적은 다음의 규칙을 지키면서 한 막대 기둥의 모든 디스크를 다른 막대 기둥으로 그대로 옮기는 것이다 .Only one disk should be moved at a time.

한번에 한 개의 디스크를 옮긴다 .The exact number of moves that this solution requires can be calculated by: 2h − 1.

이 게임에서 문제를 풀기 위한 정확한 디스크의 이동 수는 2h – 1 로 계산된다 .


Key factors of the game

14Chapter

Activity 7. English words puzzle

What is English words puzzle?

English words puzzles are a process of entertainment and education for not only language skills, but also brain activities.

Swiftness of thought (quick thinking) Well-developed vocabulary (words knowledge) Excellent language skills (comprehension and spelling)

English words puzzle (2 to 4 persons)

Components : 1 game board, about 80 letter pieces and 1 dice. Goal : To form more words. How to play : Refer to the book.


English words puzzles are a process of entertainment and education for not only language skills, but also brain activities.

영어 단어 맞추기 퍼즐은 언어 이해력 및 두뇌 활동을 위한 오락과 교육 과정이다 . These skills are generally thought to be much more improved with continued play.

게임 실력은 게임을 계속적 반복함으로 향상될 수 있다 . Put letters of sticker on all of the pieces.

모든 조각에 알파벳 스티커를 붙인다 .The final winner will be the one who has more letter pieces.

최종 승리자는 획득한 글자 조각 수가 많은 사람이다 .


Key factors of the game

15Chapter

Activity 8. Mathematical equations puzzle

What is Mathematical equations puzzle ?

Mathematical equation puzzles are a process of entertainment and education for not only mathematical skills, but also brain activities.

Quick process of thought (fast thinking) Well-developed numerical sense (mathematical analysis) Excellent mathematical skills (ability of calculation)

Mathematical equation puzzle (2 to 4 persons)

Components : 1 game board, 80 pieces of numbers and mathematical signs, and 1 dice.

Goal : To form more mathematical equations. How to play : Refer to the book.


Mathematical equation puzzles are a process of entertainment and education for not only mathematical skills, but also brain activities.

수학 수식 맞추기 퍼즐은 수학적 이해력 및 두뇌 활동을 위한 오락과 교육 과정이다 .Turn all numbers and mathematical signs facing down, so that no one can see them and place them on the game board.

모든 조각의 앞면이 밑으로 가게 뒤집어 아무도 볼 수 없게 하고 게임판 위에 올려 놓는다 .When all numbers and mathematical signs are exposed, the game is over.

모든 숫자와 수학기호 조각이 위로 뒤집어지면 게임은 종료된다 .Winner is the one who formed the most mathematical equations.

게임의 승리자는 수식과 답을 많이 가져온 사람이다 .These sentences are typical expressions and students should learn and memorize them!

16Chapter

Activity 9. Sudoku

How to play Sudoku

Place the digits 1 through 9 in the cell.

Each digit only once in each square.

Each digit only once in each row and column.

☞ For more puzzle, look on the internet, in the newspapers and magazines, and in bookstores.


Sudoku

Q1 Q2

Q3 Q4


One of most popular games is Sudoku in the world. 세상에서 가장 인기 있는 게임 중 하나는 수도쿠이다 .

This puzzle was developed later in Japan with the name of Sudoku. 이 퍼즐이 후에 일본에서 수도쿠라는 이름으로 발전되었다 .

The small squares are called cells. 작은 정사각형을 셀이라 한다 .

A vertical line of nine cells is called a column. 9 개 셀의 수직선을 열이라고 한다 .


17Chapter

Activity 10. Tangram

What is tangram?

It is consisted of seven pieces.

More than 1,600 shapes developed.

Tangram can create images of

animals,

people, and objects.


Tangram

Q1

Q2

Make following polygonal shapes.

Can you figure out how to make animals?


The tangram is a square that is divided into seven pieces. 칠교놀이는 정사각형이 7개의 조각으로 나누어져 있다 .

An isosceles triangle is a triangle with two equal sides. 이등변 삼각형은 같은 길이의 두 변을 갖는 삼각형이다 .

In addition, there is one square and one parallelogram. 그리고 1 개의 정사각형과 1 개의 평행사변형이 있다 .

Over the years, more than 1,600 shapes have been developed using the tangram puzzle to create images of animals, people, and objects.

오랜기간 동안 , 칠교놀이를 이용하여 동물모양 , 사람모양 , 그리고 물체모양 등 약 1,600 개 이상의 형상이 개발되었다 .


18Chapter

Activity 11. The golden ratio

The golden rectangle is based upon the "golden ratio". The beauty of the rectangle and the related ratio is seen in the architecture, art, and nature. Many artists, such as, Leonardo da Vinchi, have used it in their paintings. The face of da Vinchi's "MonaLisa“ used the golden rectangle.

AB : BC = AC : AB X : 1 = X + 1 : X X2 – X – 1 = 0 X = = 1.618

Explanation

Golden ratio

The golden ratio of width to length is 1 : 1.618

A B C

X 1


The golden ratio

Can you make a golden rectangle without measuring?

Make a square ABCD and bisect the square with line segment JK. Make an arc using a compass.

The center of the arc is K and radius KB.

HintA J B

D K C


The golden rectangle is a rectangle of a certain shape that, through history, has been considered very pleasing to the eye.

황금 사각형은 역사적으로 사람의 눈을 즐겁게 해주는 모양의 사각형으로 간주되었다 . The golden rectangle is based upon the "golden ratio".

황금 사각형은 " 황금 비 "를 기본으로 한다 .The ratio of width to length is approximately 1 : 1.618.

세로와 가로의 비율은 1 : 1.618 이다 . Mathematically, you write and calculate it as below.

수학적으로 풀어 쓰면 아래와 같다 .


19Chapter

Activity 12. The toothpick puzzles

What is toothpick puzzles

Toothpick puzzles allow you to exercise these skills and focus your thinking. Because the toothpick acts like a kind of line segment, doing these puzzles exercises your skill in seeing the relationship between geometric designs and shapes. You can play anytime anywhere with anyone


Tangram

Q1

Q2

Look at the five squares formed by the toothpicks below. Can you move two toothpicks to turn five squares into four squares?

Can you make two squares and four triangles from eight toothpicks?

Q3

Q4

Seven toothpicks make a triangle with a base of three toothpicks and two equal sides of two toothpicks each. Can you move three toothpicks to turn one triangle into three triangles?

Can you move only one toothpick to make the following equation correct?

Q5 Arrange twelve toothpicks in a hexagon with six triangles. Move four toothpicks to create three triangles from the original design.


You rely less on straight memorization and more on your ability to think clearly and logically.

단순한 기억력이 필요한 것이 아니라 분명하고 논리적인 사고가 필요하다 .Toothpick puzzles allow you to exercise these skills and focus your thinking.

이쑤시개 퍼즐은 사고력 향상에 도움이 된다 .Can you move two toothpicks to turn five squares into four squares?

2 개의 이쑤시개를 이동하여 5 개의 정사각형을 4 개의 정사각형으로 만들 수 있는가 ?Arrange twelve toothpicks in a hexagon with six triangles.

12 개의 이쑤시개를 이용하여 6개의 삼각형을 갖는 정육각형을 만들자 .These sentences are typical expressions and students should learn and memorize them!

Chapter 1. Chapte r 2. Chapter 3. Chapter 4. Chapter 5. Chapter 6. Chapter 7.

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