Contents ………………………………………………………………........................................ 목 차 Chapter 1. Chapter 2. Chapter 3. Chapter 4. Chapter 5. Chapter 6. Chapter 7. Number Arithmetical operations Fraction Decimal Time Measurement Geometry General Mathematics 12 Puzzles and games 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 number Tetris Secret code Magic Square Traversable diagrams Tower of Hanoi English words puzzle Mathematical equations puzzle Sudoku Tangram The golden ratio The toothpick puzzles www.magicblock.co.kr
01 Chapter Number A number is for counting and measuring. A symbol of a number is a numeral Natural numbers Type of 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. 3,765,147 Positive numbers : 1, 2, 3, 4….. Integers Zero : 0 Integers (Whole numbers) Negative numbers : -1, -2, -3, -4 …
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 ; m n 3 3 6 2 - 4 2 = 1 = 3 = - 2 2 4 8 4 1 2 6 3 = 2 = =
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 0보다 작은 수이다. • If the value of m is greater than n, then the value of the fraction is greater than 1. • m값이 n보다 크면 분수 값은 1보다 크다. Mathematic English Expression To Learn These sentences are typical expressions and students should learn and memorize them! These sentences are typical expressions and students should learn and memorize them!
02 Chapter Arithmetical operations Additions 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. 12 + 7 19 Sum or total
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 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. 12 - 7 5 difference
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 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. 12 × 7 84 product
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 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. 1 12 8 4 quotient 4 reminder
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. Mathematic English Expression To Learn These sentences are typical expressions and students should learn and memorize them!
03 Chapter Fraction 1 2 1 4 3 4 Definition : A fraction names part of a whole. Form : Write : Read : Read a numerator in a cardinal number and a denominator in ordinal number. 3 4 numerator three yellow parts denominator four parts in all one - half one over two three - quarters three – fourths three over four one - quarter one – fourth one over four • Cardinal numbers : one, two, three, … , ten, … (How many things are) • Ordinal numbers : first, second, third, … , tenth, … (When a thing occurs)
Proper fraction, Improper fraction and Mixed fraction • 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 : 3 5 7 12 3 6 5 3 12 7 6 6 5 7 1 3 2 3 1 2 1 5 3 1 3 2 3 7 3 = 2 1 =
Equivalent fraction • 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 . 2 4 4 8 2 4 2 4 3 8 4 8 Simplified fraction • 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 . 12 16 3 4
3 4 1 2 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? 17 11 1 12 1 2 1 2 2 1 5 2
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. Mathematic English Expression To Learn These sentences are typical expressions and students should learn and memorize them!
04 Chapter Decimal Definition : Like fractions, decimals show part of a whole. Form : 0.4 Write : 0.4 0.79 Read : seventy nine hundredths point seventy nine point seven nine four tenths point four
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. 1 35.206 2 3 4 1 2 3 Read 35.206 as thirty five and two hundred six thousandths. Read 35.206 simply as thirty five point two-o- six. 4
Rounding decimal • 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 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. • 0.79는 seventy nine hundredths라고 읽는다. • Read 35.206 as thirty five and two hundred six thousandths. • 35.206은 thirty five and two hundred six thousandths라고 읽는다. • 31.2 is closer to 31 than to 32. Therefore, 31.2 rounds down to 31. • 31.2 은 32 보다 31에 가깝다. 그래서 31.2를 반올림하면 31이 된다. Mathematic English Expression To Learn These sentences are typical expressions and students should learn and memorize them!
05 Chapter Time 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
Elapsed time Elapsed time is the amount of time that passes from the start of an event to its end. 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
Schedule A schedule is a list or table to show when events happen. 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?
Calendar 7 days = 1 week 52 weeks = 1 year 12 months = 1 year A year is divided into months, weeks, and days. The calendar below shows Jan, Feb and Mar of the year 2009. Use the calendar to write each day and date. • 3 days after Jan 30, 2009 Monday, Feb 2, 2009 • 5 days before Feb 3, 2009 • 2 weeks before Feb 24, 2009 • 5 days after the last Friday in Feb, 2009
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. • 1일은 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. • 1년은 월, 주, 그리고 일로 나누어진다. Mathematic English Expression To Learn These sentences are typical expressions and students should learn and memorize them!
06 Chapter Measurement Length • 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) In USA Metric system Conversion of units 1 foot(ft.) = 12 in. 1 yard(yd.) = 3 ft. 1 mile(mi.)=1,760 yd. 1 in. = 2.54 cm 1 ft. = 30.48 cm 1 yd. = 91.44 cm 1 mi. = 1.61 km 1 cm = 10 mm 1 m = 100 cm 1 km = 1,000 m
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?
Weight • 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) In USA Metric system Conversion of units 1 g = 1,000 mg 1 kg = 1,000 g 1 ton = 1,000 kg 1 oz. = 28.35 g 1 lb. = 453 g 1 T. = 906 kg 1 pound (lb.) = 16 oz. 1 ton (T.) = 2,000 lb.
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?
Capacity • 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) In USA Metric system Conversion of units 1 cc = 1 mL 1 L = 1,000 mL 1 kL = 1,000 L 1 cup (c.) = 8 fl. oz. 1 pint (pt.) = 2 c. 1 quart (qt.) = 2 pt. 1 gallon (gal.) = 4 qt. 1 c. = 0.237 L 1 pt. = 0.473 L 1 qt. = 0.946 L 1 gal. = 3.784 L NOTE 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.
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?
Example of metric system 1 10 1 100 1 1,000 1 1,000,000 1 1,000,000,000
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 (3제곱 센티미터)는 미터법 단위이다. Mathematic English Expression To Learn These sentences are typical expressions and students should learn and memorize them!
07 Chapter Geometry Plotting points on a coordinate grid • A point is an exact location in space. • A coordinate grid is a graph with horizontal and vertical lines. 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
Lines, Rays, and Line segments Read : line AB or line BA Write : AB or BA Read : line segment RS or line segment SR Write : RS or SR Read : ray BG Write : BG • 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. A B R S G B NOTE 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.
Angles An angle is two rays with a common endpoint. Angles are measured in degree (0). Read : angle ABC or angle CBA Write : ABC or CBA A B C A right angle is exactly 900. An acute angle is less than 900. An obtuse angle is greater than 900. Plane L M A plane is a flat surface that extends in all direction. It is named by four points. Plane LMON 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