The Essence of Mathematics Skills Textbook- Math Primary_2

151 Exercise 9 a. Read the plan of a flower and vegetable garden plot that belongs to Sukjai and answer the following questions: N scale 1 cm : 9 meters (1) What is the shape of Sukjai‟s land? (2) Which direction is the vegetable plot oriented on the land and what is its width in metres? (3) What is the length of the longest side of the flower plot in metres? (4) What kind of plant is grown on the west side of the land, vegetables or flowers? (5) What is the width of Sukjai‟s land? b. Read the plan and answer the questions. A group of scouts take a long distance walk from the school to a temporary camp at the bottom of a hill having a direction plan as follows: scale 1 cm : 100,000} Read the plan and answer the questions. (1) Which direction did the scouts travel and what is the distance to the temple? (2) What is the distance between the camp and the school in kilometres?

152 c. Read the plan and answer the questions. Beverage School shop Flower shop Home scale 1 cm : 500 m (1) Which directions are to be taken in order to reach the flower shop and what is the total distance travelled? (2) In which direction from the school is the flower shop and what is the distance between them? (3) In which direction from the flower shop is the beverage shop and if we travel from the flower shop to the school, should the distance be nearer or farther than travelling from the flower shop to the beverage shop? d. Sketch a plan that shows travel route from your home to a near-by temple. Topic 6: Money 6.1 Writing and reading an amount of money Money is used as a medium in trade and exchange. The monetary unit used in Thailand is the Baht which consists of the following sub-units: 1 baht = 100 satang or 1 baht = 4 quarters 1 quarter = 25 satang There are two kinds of money as follows: 1) Coin money: The common types are 1 quarter coin or 25 satang 2 quarters coin or 50 satang 1 baht coin 2 baht coin 5 baht coin 10 baht coin

153 2) Banknotes: The common types are Ten baht note Twenty baht note Fifty baht note One hundred baht note Five hundred baht note One thousand baht note The writing and reading of Thai money 5 satang written: 0.05 baht read: five satang. 25 satang written: 0.25 baht read: twenty five satang or one quarter in spoken language 50 satang written: 0.50 baht read: fifty satang or two quarters in spoken language 75 satang written: 0.75 baht read: seventy five satang or three quarters in spoken language 1 baht and 25 satang written: 1.25 baht read: one baht and twenty five satang or one baht and one quarter or five quarters in spoken language 2 baht and 50 satang written: 2.50 baht read: two baht and fifty satang or two baht fifty or ten quarter in spoken language 15 baht and 65 satang written: 15.65 baht read: fifteen baht and sixty five satang A dot shall be used between the baht and satang when writing an amount of money. 6.2 Comparison of money values and exchange of money Money values comparison: Coins and banknotes have different values from the lowest to the highest, i.e. 25 satang, 50 satang, 1 baht, 2 baht, 5 baht, 10 baht. For banknotes, the order from the lowest to the highest values are 20 baht, 50 baht, 100 baht, and 1000 baht Coin and banknote exchange: We can exchange money such as a five baht coin to 5 one baht coins, a ten baht coin to 10 one baht coins or 2 five baht coins. Similarly, a banknote can be changed to coins or smaller notes such as a fifty baht banknote to 2 twenty baht banknotes and 2 five baht coins. Example: Given 3 five hundred, 9 one hundred, 5 fifty, 10 twenty and 20 ten baht banknotes, how much total money do we have? Method: 3 five hundred baht notes worth 500 × 3 = 1,500 baht worth 100 × 9 = 9 one hundred baht notes 900 baht worth 50 × 5 = 250 5 fifty baht notes baht worth 20 × 10 = 200 10 twenty baht notes baht

154 20 ten baht notes worth 10 × 20 = 200 3,050 baht baht 1,500 + 900 + 250 + 200 + 200 baht = Total: Answer: 3,050 baht 6.3 Problems in daily life Money exchange occurs frequently because the price of goods is not matched with the type of money. For example, when buying 37 baht of goods with a one hundred baht note there will be a change of 63 baht consisting of notes and coins. Example: Mukda has 1 five hundred baht note that she spent as follows: buy 2 Method: kilograms of pork which cost 108 baht, 3 kilograms of chicken which cost 94.50 baht, buy 2 kilograms of sugar which cost 25.50 baht, and 3 bottles of fish sauce which cost 55.50 baht. How much does she have left? 108.00 baht Buy pork 94.50 + baht Buy chicken Subtotal 202.50 baht Buy sugar 25.50 + baht Subtotal 228.00 baht Buy fish sauce 55.50 + baht Subtotal 283.50 baht Mukda had 500.00 - baht Total spent 283.50 baht Total money left 216.50 baht Answer: 216 baht 50 satang Note: For the addition or subtraction of money in a decimal form, the decimal points of the addend and the augend or the minuend shall be set in a straight column before normal addition or subtraction operations can be performed and the decimal point of the result must also have the same number of digits as the augend or minuend amount.

155 Example: Metta sold 7 kilograms of Snake-head fish for 63 baht 75 satang per kilogram. How much money did she make? × 63.75 Method: Metta sold 1 kilogram of Snake-head fish for 7 baht Sales volume kilograms 446.25 Therefore, sales amount baht Answer: 446 baht 25 satang Note: The multiplication of money in a decimal form can be done similarly with the multiplication of integers but the result must have the same number of decimal digits of the initial amount plus those of the multiplying amount. For example, from example 3, the initial amount has 2 digits but the multiplying amount has no digit, therefore the result has only 2 digits. Example: Thongbai bought 5 baskets of coal at a cost 233 baht 75 satang. What is the price of coal per basket? 233.75 baht Method: 5 Total cost of coal baht Thongbai bought coal basket baht Therefore each basket cost 5 )233.75 46.75 Answer: 46 baht 75 satang Note: The division of money in a decimal form can be done similarly to the division of integers but the result must have decimal digits equal to the initial amount. Summary Money 1. Money is used as a medium for trading and exchange of goods. Currently, Thailand uses the “Baht” as a monetary unit and units of small change are called “Satang”. 2. In writing an amount of baht and satang, a dot is placed between the baht and satang amounts. For example, 19 baht 45 satang is written 19.45 baht. For reading, the full amount shall be read as 19 baht 45 satang. 3. For addition or subtraction of money in a decimal form, the dot must be set in the same position before the addition or subtraction operation the same as ordinary numbers. 4. The multiplication of money in a decimal format can be done in the same manner as the multiplication of integers but the product must have the same number of digits as the initial number plus the digit of the multiplying number.

156 5. The division of money in a decimal form can be done in the same manner as the division of integers but the result must have the same number of decimal digits as the initial amount. Exercise 10 Show the method used: (1) Give the oldest child 18.50 baht, the second child 16.50 baht, the third child 15 baht, and the youngest child 12.50 baht. What is the total amount given to all the children? (2) A vendor‟s earnings consist of 1 fifty baht note, 4 twenty baht notes, 7 ten baht notes, 7 five baht coins and 9 one baht coins. How much did she earn? (3) When buying 2 hats at a cost of 25 baht each, 1 pen at a cost of 65 baht, one pair of shoes at a cost of 135 baht with a five hundred baht note, how much is the change? (4) When buying 8 shirts which cost 35 baht 50 satang each, if the vendor gives a 10 baht discount total, how much money to be paid? (5) If you buy one 24 kilogram bucket of Sapodilla which cost 384 baht and resale it at 21 baht per kilogram, how much is the profit? 6.4 Writing and reading the income-expense account Companies, partnerships, shops or trading organizations are required to keep 5 kinds of accounts in compliance with the Accounting Act, i.e. cash, accounts receivable and accounts payable, purchases and sales, assets, and income and expenses. Accounting not only helps facilitate auditors in terms of tax collection but also helps business entities realize their actual business status. A person with a busy daily work schedule, particularly dealing with income-expense operations, usually keeps his own daily income-expense account to remind him of expenses for convenient future reference similar to Mr. Chumpon‟s income-expense record below. Income-expense record of Mr. Chumpon From 1 June 2010 to 7 June 2010 Date Item Income Expense Balance 1 June 10 500 Money from Mother 500 - 300 2 June 10 250 3 June 10 Buy 1 shirt - 200 300 4 June 10 Buy books - 50 275 5 June 10 125 6 June 10 Income from paper 50 - 200 7 June 10 75 bag folding Buy snacks - 25 Buy trousers - 150 Sell flowers 75 - Buy shoes 125

157 Cash account The cash account represents the amount of cash received and paid each day as well as the details of the transactions and names of payers and payees involved. Transactions in the cash account can be divided into two categories: “Income” which is commonly recorded as “Accounts receivable” on the left side and “Expenses” which is commonly recorded as “Accounts payable” on the right side. Example of cash account (For the 3-day accounting period) Exercise 11

158 a. Determine whether the following items are an income transaction (accounts receivable) or an expense transaction (accounts payable). (1) Goods purchase 1,500 baht (2) Loan interest payment 300 baht (3) House repairs 500 baht (4) Balance brought forward 1,250 baht (5) Transportation of goods 120 baht (6) Wholesale of goods 2,000 baht (7) Textbooks sale 3,000 baht (8) Student shoes sale 450 baht (9) House rental 500 baht (10) Plant seeds sale 1,200 baht (11) Food sale 1,800 baht (12) Water utility 160 baht (13) Electricity utility 230 baht (14) Cooking service fee 1,350 baht (15) Cook‟s salary 800 baht b. Prepare the cash account of Aroy Restaurant based on the following transactions: On 1 May 2010 Balance brought forward is 2,335 baht; food sale is 3,500 baht; fresh food purchase is 1,200 baht; electricity expense is 115 baht; and cook‟s salary is 800 baht. On 2 May 2010 Food sale is 4,115 baht; fresh food purchase is 1,500 baht; rice purchase is 200 baht; electricity expense is 318 baht; and transportation of goods is 130 baht. On 3 May 2010 Catering service fee is 4,200 baht and transportation of goods is 200 baht. c. Prepare the cash account of Panya Stationery Shop based on the following transactions: Balance brought forward 2,500 baht Goods purchase 3,400 baht On 6 April 2010 Textbooks sale 3,000 baht Stationery sale 4,000 baht On 7 April 2010 Textbooks sale 5,200 baht Scout uniforms sale 2,100 baht Student shoes sale 1,500 baht Water utility 165 baht

159 Electricity utility 135 baht On 8 April 2010 Goods transportation 215 baht Textbook sale 2,420 baht Cash received from customer1,200 baht Summary: Recording of income - expense - Recording of daily income - expense in the cash account - Transactions in the cash account can be recorded on either left or right side. Transactions on the left side are income or accounts receivable and transactions on the right side are expense or accounts payable. - When closing a cash account, calculate the total amount of income and expense: total income – total expense = balance carried forward (in the expense column) - The balance carried forward will be recognized as income on the following day. total expense – balance carried forward = total income Topic 7: Temperature Temperature means the amount of heat or coldness of something that is measured in a degree unit. 7.1 Unit of temperature measurements symbol: K 1) Universal system (SI) symbol: °C The unit in Kelvin symbol: °F 2) Other accepted systems: Symbol: °R The unit in degree Celsius The unit in degree Fahrenheit The unit in degree Réaumur Temperature measurement devices Note: The normal temperature of the human body is approximately 37 °C or 98.6 F 7.2 Unit conversions of temperature measurements

160 We can convert units of temperature from one to another as follows: Boiling point Celsius Fahrenheit Kelvin Freezing point 212 F 371 K 100 °C 32 F 273 K Body temperature (normal) 98.6 F 101 K 0 °C 77 F 68.2 K Room temperature 37 °C 25 °C It can be seen that there are one hundred degrees between the freezing and the boiling points in Celsius and 180 degrees in Fahrenheit (212 – 32 = 180). Therefore, 1 degree Celsius equals to 1.8 degrees Fahrenheit. Example: If the room temperature is measured 30 degree Celsius (30°C), what is the temperature in Fahrenheit? = 1.8 degree Fahrenheit = 1.8  30 degrees Fahrenheit Method: 1 degree Celsius 30 degrees Celsius = 54 Thus the temperature in Fahrenheit is 32 + 54 = 86 °F (Because the Fahrenheit unit has a freezing point at 32 °F which is equal to 0 °C in Celsius unit) Exercise 12 1. Put a thermometer under your tongue for 3 minutes then read the temperature of the thermometer in Celsius and Fahrenheit. 2. Analyze the temperature reading results and tell if the body temperature is normal or not? Topic 8: Time 5.1 Telling and writing the time from the clock dial 1) Components of the clock Components of the clock are: 1.1 The dial - The dial has a circular scale which is numbered 1 through 12 indicating the hours in a 12 hour cycle for the short hand and minutes in an hour for the longer hand. Depending on the size of the clock, the space between the numbers may be further marked with 5 or more small ticks representing minutes. 1.2 The clock – The short “hour” hand indicates the hour and the long “minute” hand indicates the minute. The long hand takes 60 minutes to makes a complete rotation from “12 to 12”. For every rotation of the long hand, the short hand will move from one hour mark to the next. Therefore, an hour is equal to 60 minutes. 2) Telling the time or reading a clock dial

161 In Thai, there is an official terminology and a spoken terminology for reading time as per the following example: Time before noon Time after noon Time Official Spoken Official Spoken terminology terminology terminology terminology 7 o‟clock 7 mohng 19 hours 1 thum chao 0 hour Thiang 12 o‟clock Thiang 25 minutes 25 minutes kheun 25 minutes 25 minutes 10 o‟clock 10 mohng 22 hours 4 thum 45 minutes 45 minutes chao 45 minutes 45 minutes 12 o‟clock Thiang 24 hours Thiang kheun 3) Writing and telling time in numerals

162 In order to tell the time in numerals, a decimal point is used similarly to that used for money. The difference is that the decimal point of money refers to 100 satang but the time decimal point refers to 60 minutes. The number to the left of the decimal point represents the hours. The number to the right of the decimal point represents the minutes which cannot be greater than 60 for any number greater than 60 will be counted as 1 hour. The telling of time written in numerals will be read in the same fashion as shown in 2. Examples are as follows: Time Written as Official Spoken terminology terminology 09.30 hrs. 05.00 hrs. 9 o‟clock 30 Gao mong kreung 01.45 hrs. 13.00 hrs. minutes Dtee haa 07.05 hrs. 16.25 hrs. 5 o‟clock Dtee neung see sip haa 24.00 hrs. 23.14 hrs. 1 o‟clock 45 Bai mong 18.00 hrs. Jet mong haa na tee minutes baai see mong yee sip 13 o‟clock haa na tee 7 o‟clock 5 minutes Tiang keun 16 o‟clock 25 Haa tum sip see na tee minutes Hok mong yen 24 o‟clock 23 o‟clock 14 minutes 18 o‟clock Note: “hrs.” is the abbreviation for hours. Exercise 13 Write the following times in the decimal form: (1) 6 mhong chao (2) 23 hours 15 minutes (3) Dtee neung kreung (4) Tiang keun 5 na tee (5) Bai 2 mong 45 na tee (6) 11 hours 30 minutes (7) 10 hours 40 minutes (8) 4 hours 12 minutes

163 8.2 Reading the timetable and recording events or activities Read the timetable and answer questions below: Timetable for Bangkok to Ubon Ratchathani train Station Express High- Ordinary train speed train 1 train 63 39 Bangkok Departure 21.00 18.45 15.25 Saraburi Arrival 23.00 20.48 17.47 23.01 20.49 17.48 Departure Nakorn Ratchasima Arrival Departure 01.46 23.28 21.01 Ubon Ratchathani Arrival 01.51 23.33 21.08 06.30 04.40 03.35 (1) What time does the high-speed train depart Bangkok? (2) What time does the express train arrive at Ubon Ratchathani? (3) How many minutes does the express train rest at Nakorn Ratchasima station? (4) How long does the high-speed train take to travel from Saraburi to Ubon Ratchathani? (5) How much faster is the express train from Bangkok to Ubon Ratchathani compared to the ordinary train? (6) Which train is the last train arriving in Nakorn Ratchasima? (7) How much faster or slower does the high-speed train travel from Saraburi to Nakorn Ratchasima compared to the express train? Exercise 14 1. Learners shall practice reading the train timetable in their province. 2. Learners shall practice recording their class attendance time for a period of one month. 8.3 Relationship between units of time The relationship between units of time or so called “time scale” are as follows: 60 seconds is equal to 1 minute 60 minutes is equal to 1 hour 24 hoursis equal to 1 day 7 days is equal to 1 week 30 days is equal to 1 month 12 months is equal to 1 year

164 52 weeks is equal to 1 year We can distribute or change the time scale simply in the same manner as for measuring units as follows: Example: Convert 9 days 4 hours 25 minutes to minutes Method: 9 × days 24 hours 1 day is 9 days is 216 + hours and 4 hours total 220 hours 1 hour equal to × 60 minutes 220 hours equal to 13,200 + minutes and 25 minutes total 13,225 minutes Answer: 13,225 minutes Example: 2,349 minutes is equivalent to how many days, hours and minutes? Method: 60 minutes is 1 hour. 2,349 minutes converted to hours 2,349 ÷ 60 hours 39 hours 60 ) 2349 - 180 549 540 - 9 Equal to 39 hours 9 minutes But 24 hours is 1 day 39 hours converted to days 39 ÷ 24 days 1 24 ) 39 24 - 15 Equals to 1 day 15 hours Therefore, 2,349 minutes is 1 day 15 hours 9 minutes Answer: 1 day 15 hours 9 minutes 8.4 Solving problems relating to time

165 Example 1: I exercised from 19.30 hrs. to 21.40 hrs. How much time did I spend on exercise? hrs minutes Method: I finished my exercise at 21 40 - Started at 19 30 2 10 Answer: 2 hours 10 minutes Exercise 2 The express train departed from Chiang Mai at 16.50 hrs. and arrived in Bangkok at 06.25 hrs. What is the total travel time of this train? Method: Chiang Mai 7.10 hours 6.25 hours Bangkok 16.50 hrs. 24.00 hrs. 06.25 hrs. from 16.50 hrs. to 24.00 hrs. equals = 24.00 – 16.50 hours = 7.10 hours from 24.00 hrs. to 06.25 hrs. equals = 6.25 hours Therefore travel from Chiang Mai to Bangkok takes = 7.10 + 6.25 hours = 13.35 hours Answer: 13 hours 35 minutes Summary Time 1. Time is used to measure how long something takes or the age of something. Long period time scales are year, month, week and day. Short period time scales are hour, minute and second. 2. The standard time measuring device is the clock. The dial has only 12 hours. The short hand indicates the hour and the long hand indicates the minute. 3. Time writing can be done in full and decimal formats. Time reading can be done in official and spoken terminologies. Exercise 15 a. Answer the following questions: (1) How many months have 30 days and what are the names of those months? (2) How many months have 31 days and what are the names of those months? (3) Normally how many weeks are there in a month? (4) How many days are there in 2011? (5) On which date and day does the Coronation Day fall upon in 2011?

166 b. Use this May 2011 calendar to answer the following questions: May 2011 Sun Mon Tue Wed Thu Fri Sat 12 34567 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 (1) From the calendar, what are the dates in the last week of May 2011? (2) What is the date of the first Saturday in May 2011? (3) If the first day of the month is Monday, what is the date of the next Monday? (4) What is the date of the last day of May 2011 and what day does it fall upon? (5) In May 2011, which are the dates that fall on Friday? Topic 9: Estimation 1. Estimation of length, area, volume, capacity, weight and time. Master Kanit uses the width of his palm and his footstep to estimate objects as illustrated in the figure below. Kanit 9 cm 50 cm Kanit can estimate distances by using his footsteps. For example, given that Kanit walks 20 steps for an entire length of a field. Therefore, the field is approximately 1000 cm or 10m long. In the same way, he can use his palm to estimate

167 the height of a cabinet. Also, if the estimated length is given, Kanit can also estimate the area of the field by using the estimated length x width. Try estimating length, width, area, volume, capacity, weight and time by practicing estimation of real objects. Lesson 6

168 Geometry Main points 1. A shape with a contour line starting from a point which does not reconnect to the starting point again is called an open shape and a shape with a contour line starting from a point which is then reconnected to the starting point is called a closed shape. 2. A triangle is a closed shape with 3 straight sides and 3 angles. Each angle is called an internal angle of a triangle. 3. A quadrilateral is a closed shape with 4 straight sides and 4 angles. Each angle is called an internal angle of a quadrilateral. 4. A plane shape where all points are equidistant from a fixed point is called a circle. The contour line of a circle is called the circumference and the fixed point is called the centre. The distance between the centre and the circumference is called the radius. Expected learning outcome 1. Be able to distinguish one-, two- and three-dimensional geometric shapes. 2. Understand the properties of a cube and be able to apply the understanding. 3. Be able to draw one-dimensional, two-dimensional and three-dimensional geometric shapes and to construct three-dimensional shapes. Content scope Topic 1: One-dimensional (1D) geometric shape Topic 2: Two-dimensional (2D) geometric shape Topic 3: Three-dimensional (3D) geometric shape Topic 4: Cubic shape Topic 5: Construction of geometric shapes Topic 6: Construction of three-dimensional (3D) geometric shapes Topic 1: One-dimensional (1D) geometric shapes

169 One-dimensional (1D) geometric shapes are for example points, straight lines, rays and angles. 1. Point: Serves to ensure a common understanding to indicate a position. It is a normal practice to use it together with either Thai or English capital letters, for example: . ก .A .P .ข .M 2. Straight line By linking two or more points one creates a straight line or a curved line. It is normal practice to call a straight line according to the two letters which are the names of the two points figuring on the straight line. MN The straight line MN is represented with the symbol MN 3. Straight line segment A straight line segment is a segment of the straight line with a specific length located between two points which are the endpoints of the straight line segment. The straight line segment B C is represented with the symbol BC and is called the straight line segment BC. In this case, the straight line segment is the only part we are focusing on. 4. Ray Beams of light come out from a flashlight as shown above. It can be seen that light is projected out in a one-way direction from the light bulb which is the starting point and that it does not go back in the direction of the starting point. Also, the length of light can not be specified. This form of light is called a ray. A ray is a straight line segment with just one endpoint. A ray AB starts from point A as in A B and its written symbol is AB. 5. Angle An angle as in the illustration is created by two rays which have the same end point. B A C พ The rays AB and AC have the same endpoint or have a starting point at point A which lead to the creation of an angle.

170 The common endpoint is called the vertex of the angle which in this case is point A. Each ray or each straight line segment is called a side of the angle. The sides of the angle with A as the vertex are therefore the rays AB and AC. 6. Name of an angle The name of an angle consists of the following three letters: A A: the name of a point on one side of the angle B: the name of the vertex B C: the name of a point on the other side of the angle C Its written symbol is  and the angle is called angle ABC. ABC Or it can be replaced by CAB and be called angle CAB. Sometimes, angles can be called just by the name of the vertex such as B and is then called angle B. The written symbols of angles are either  or .   For example, angle ABC can be symbolically written ABC or ABC. 7. Type of angle Angles are classified into types according to their size as follows: A 7.1 Right angle: a 90 degree angle angle. The symbol can be written as the B right angle. ABC is a 90 degree C ABC is thus a right angle. C 7.2 Acute angle: an angle smaller than a right angle  or 90 degrees. The angle CAB has 80 degrees CAB is thus an acute angle .A . B 7.3 Obtuse angle: an angle bigger than aright angle but A sm aller than two right angles. ABC has 120 degrees. ABC is thus an obtuse angle. B C AB C 7.4 Straight angle: an angle the size of 2 right angles or กฉ ฉ 180 degrees. Angle ABC is equal to 2 จ right angles. ABC is thus a straight Dจ Fข angle. ด ถกจ จ Eจตขก ข 7.5 Reflex angle: an angle bigger than 2 right anglesbut ข ก smaller than 4 right angles. Angle DEF has 210 degrees. DEF is thus a reflex angle. Exกercise No. 1 ข ก

171 1. 1.1 Write 5 points together with the name of the points. 1.2 Write the name and symbol of the following straight line segments, straight lines and rays. D E (a) D E G (b) F F G I (c) H HI 2. Measure the size of this angle and give the type of angle. (a) A BC Name of angle: ................................................. Type of angle: ............................... Size of angle: .................................................. degrees (b) Name of angle: ................................................ Type of angle:............................... Size of angle: .................................................. degrees E FG 3. What type are these angles? Are they equal? (1) The upper and lower angles of this textbook. (2) The angles on both sides of a ruler. (3) The upper and lower angles of a door. 4. Name 5 items which form part of a plane. 5. Fold one of the angles of the each one of the above item with a piece of paper or copy the angle on a piece of paper and compare it to the angle on the other side. For each item, see which two angles are equal. 6. Create an angle of the size of the angle in #5 by folding a piece of paper or by copying it with a thin piece of paper. 7. Write the symbol indicating the straight line segments which are parallel to each other. AB

172 CD EF Name of angle:.................................................. Type of angle:............................... Size of angle: .................................................. degrees Exercise No. 2 Write the symbol indicating the straight line segments which are parallel to each other. AB C D EF G H Exercise No. 3 1. Draw a straight line passing point A which is parallel to BP „A  P B 2. Draw a line passing through point C which is parallel to MN M „C N 3. Draw EF which is perpendicular to AB with EF // CD and which is of the same length as CD. Draw DE. D „E A C FB Is DE parallel to AB? Topic 2: Two-dimensional (2D) geometric shapes A 2D geometric shape is a closed shape on the same plane, such as

173 Triangle Square Polygons Oval Circle 1. Property and type of a triangle A triangle is a closed shape consisting of 3 sides and 3 angles and the sum of the three angles shall always be equal to 180 degrees as in this illustration: C The 3 sides are AB,AC and BC.  The 3 angles are CAB, ACB and ABC.   CAB + ACB + ABC = 180 ° The written symbol representing the triangle ABC is  ABC. A B 1.1 Triangles are classified into 3 types according to the properties of their angles as follows: C (1) Right triangle: a triangle where one of the angles is a right angle (or 90 degrees). In this illustration:  ABC is a right triangle becauseABC is a right B angle. A (2) Oblique triangle: a triangle where all the angles are acute angles (angles smaller than 90 degrees). F In this illustration beEcaFuGseisEaGnFoibsliaqnueacturitaenagnlegle E GFE is an acute angle G FEG is an acute angle (3) Obtuse triangle: a triangle where one C of the angles is an obtuse angle (angle bigger than 90 degrees). In this illustration: becauAsBe CCAisBanisoabntuosbetutrsieanagnlgele. A B Example1. What type are the triangles below and why? C

174 1.  ABC is an obtuse triangle because BAC = 120° (bigger than a right angle) 12 B F 0A 2.  DEF is a right triangle because DEF =90° (a right angle) DE 3.  GHI is an oblique triangle because G GHI = 60° which is smaller than 90° 70 HIG = 70° which is smaller than 90° IGH = 50° which is smaller than 90° 60 50 H I 1.2 Triangles can also be classified into 3 types according to their sides as follows: B (1) Equilateral triangle: a triangle where the 3 sides are equal in length and each angle is equal to 60 degrees. In this illustration,  ABC is an equilateral triangle A C becauseAB= BC = AC E A=B=C N (2) Isosceles triangle: a triangle where บ 2 of the sides are equal in length F M because DF = EF As the isosceles triangle has 2 sides which are equal in length, the angles opposite these 2 sides are also equal. aInndthaenigllluesEtraistioonp,poonsietecatonDseFe. that angle D is opposite to EF D Therefore, D = E An isosceles triangle has 2 sides and 2 angles which are equal. (3) Scalene triangle: a triangle in which all the 3 sides are unequal. P In this illustration,  PNM is a scalene triangle because PM, MN and NP are unequal. Example 2: ABC where AB = 3 cm., AC = 4 cm. and BC = 3 cm. What type of triangle is ABC B

175 3 cm. 3 cm. As AB = BC = 3 cm. AC Therefore,  ABC is an isosceles triangle. 4 cm. Example 3: Calculate the internal angle of the triangles according to details in the table below: Angle 1 Angle 2 Angle 3 Triangle  ABC 50 50 ABC: 3 =80°  DEF 60 60 DEF: 2 = 60°  GHI 30 80 GHI: 3 =70° 1.3 Altitude and base of a triangle: The perpendicular line drawn from the corner of a triangle to the opposite side is called altitude and the opposite side is called base. B M As can be seen from this illustration of  ABP: บ N If AP is the base, BC is the altitude A If BP is the base, AN is the altitude. If AB is the base, MP is the altitude. P ป C Example 4. Find the altitude of the right triangle ABC in this illustration. C 4.5 cm. Alternative 1: If AB is considered as the base, 3 cm. the altitude is AC = 3 cm. Alternative 2: If AC is considered as the base, the altitude is AB = 3.5 cm. A 3.5 cm. Example 5. Find the altitude of DEF in the following illustration.

176 F Method: From the illustration, 5 cm. G 5 cm. as FG is perpendicular to DE at point G D 8 cm. E FG is the altitude of  DEF and FG = 3 cm. Example 6. In this illustration, which is the altitude of the scalene triangle HKJ which has KJ as its base? Method: As H is the top corner of  HKJ and is H perpendicular to the extension of KJ which I K is the base, HI is the altitude of  HKJ. J Example 7. In this illustration, the isosceles triangle ABC has sides AB = AC = 4 cm. and AD is perpendicuDlar to CB. Measure at point D the lengths of CD and DB. A Method: By measuring, the results are as follows: CD = 2.5 cm. 4 cm. 4 cm. DB = 2.5 cm. C 5 cm. B Therefore, CD = DB = 2.5 cm. This shows that the altitude of an isosceles triangle is perpendicular to the base and that it bisects the base. 2. Property and type of a quadrilateral A quadrilateral is a closed shape with 4 sides and 4 angles. The sum of all the 4 internal angles is equal to 360 degrees and the written symbol of a quadrilateral is  DC AB

177 In the illustration, the 4 sides are AB, BC, CD and DA and the 4 angles are DAB, ABC, BCD and CDA. DAB + ABC + BCD + CDA = 360 ° The written symbol of the quadrilateral ABCD is  ABCD. 2.1 Rectangle: a quadrilateral where all the angles are right angles and the opposite sides are equal is called a rectangle. In the illustration of  ABCD D C  ABC = BCD =CDA= DAB = 90 ° AB and CD are opposite sides and AB= CD AD and BC are opposite sides and AD = BC A B Therefore, the  ABCD is a rectangle. 2.2 Square: A quadrilateral where all the angles are right angles and all 4 sides are equal is called a square. In the illustration of  EFGH HG   E = F = G = H = 90 ° EF = FG = GH = HE = 3.5 cm. Therefore, EFGH is a square. E 2.3 ParallelogramF : A quadrilateral where the opposite sides are parallel and equal is called a parallelogram. O In the illustration, the sides of  MNOP P MN // OP and are equal MP // NO and are equal Therefore,  MNOP is a parallelogram MN 2.4 Rhombus: A quadrilateral where all four sides are equal and none of the angles are right angles is called a rhombus. N M In the illustration, the sides of  KLMN KL = LM = MN = NK ธ     K, L, N are not right angles M, Therefore,  KLMN is a rhombus. KL

178 2.5 Trapezoid: A quadrilateral where two of the sides are parallel is called a trapezoid. C In the illustration,  ABCD has 2 sides D AB // DC Therefore,  ABCD is a trapezoid. AB ข 2.6 Kite: a quadrilateral where the two sides of two of the opposite angles are equal and the diagonals are unequal in length but intersect each other by forming a right angle is called a kite. A In the illustration of ABCD  BD Sides AB = AD and sides BC = CD Therefore,  ABCD is a kite shape. C 2.7 Trapezium: a quadrilateral where all the four sides are unequal is called a trapezium. In the illustration of  ABCD, D C all the four sides are unequal in length. AB งง 3. Diagonal and intersection of diagonals D C All quadrilaterals have 2 pairs of opposite angles.  The first pair of opposite angles is A and C.  The second pair of opposite angles is D and B. A B H  G The first pair of opposite angles is H and F. 

179 BD. The second pair of opposite angles is E and G. O  ABCD has 2 diagonals which are AC and The straight line segment linking the oppositecorners of a quadrilateral is called a diagonal. EF  EFGH is a rectangle. In the illustration of  EFGH, EG and HF are diagonals which intersect at point O. EO and OH are equal in length. Diagonals of a rectangle are equal in length and bisect each other. 3. Circle A circle is a closed shape as can be seen in the illustration and the point in the circle which is equidistant from all the points of the circle‟s circumference is called the centre.  In the illustration, A is the centre of the circle and the distance between the centre and any point of the circumference is called the radius. It is possible to draw several radiuses. AB is a radius of the circle in which A is the centre. A B C The straight line segment between 2 points of the circumference which passes through the centre is called a diameter. In this illustration, point A is the centre. AB and AC are the radiuses. BC is the diameter.

180 Topic 3: Three- dimensional (3-D) geometric shapes A 3-D geometric shape is a geometric shape with a width, length and height. Examples of 3D geometric shapes are spheres, cubes, pyramids, prisms, cylinders and cones. 1. Property and type of 3D geometric shapes This is the quadrilateral shape one gets when tracing the bottom of a box on a piece of paper with a pencil: Which shape do we get by tracing the bottom of a round glass? Illustration 1 Illustration 2 Learners will discover that Illustration 2 represents the trace of a glass bottom. Paper boxes, dices, glasses, cans, pots, balls, etc. all have a height rising from the plane. We call these forms 3D geometrical shapes. Geometrical shapes There are several kinds of 3D geometrical shapes such as the following: Cube: A rectangular shape where each face is a square such as a dice. A cube has a total of 6 faces which are squares.

181 Prism: a 3D shape consisting of rectangles on the sides while the two cross- section faces can be any polygon shape such as a triangle, rectangle, pentagon, etc. of the same size on parallel planes. Pyramid: a 3D shape with an apex and faces consisting of triangles. The base of a pyramid can be any polygon shape. Square pyramid Pentagonal pyramid Cylinder: a 3D shape with a round flat top and bottom which are of the same size and a curved side surface. By opening up the curved side surface, it becomes a rectangle. Cone: a 3D shape with an apex, a round base and a curved side surface such as banana leaf cones and cake cones, etc. Sphere: a 3D geometric shape with a curved surface where all the points of the surface are at the same distance from the centre such as ping-pong and other kinds of balls and marbles. Activity: Observe tools, equipments and appliances which have a 3D shape and record details in the table below. 3D shapes Tools, equipments and appliances

182 Sphere ....................................................................................................................... Cube ....................................................................................................................... Prism ...................................................................................................................... . Pyramid .................................................. ..................................................................... Cylinder ....................................................................................................................... Cone .................................................................. .................................................... . Topic 4: Cube A cube is a 3D geometrical square shape. Each face of the cube is a square which means that its width, length and height are equal in length. A cube with a width, length and height equal to one unit has a volume of 1 cubic unit. \\1 1 1 unit A 1 of cซc1มmm. .. cm 1 m. 1mมm. .. 1 unit volucซmมm.e. 1ซcมu. bic A volume of 1 cubic m. 1 (cubic cm. or cm3) (cubic m. or m3) u n To find the volume of a cuboid: i 1. By folding cubes: 30 cubes can be folded with each c3u0bceวtยuhbaicvicnegnatimvoeltuemrseoor f301 centimeter. Therefore, the cuboid has a volume of cubic cubic cm. or 30 cm3 2 cm. 5 cm. ซม. 3 cm. 2. By way of a calculation: The above cuboid has a width of 3 cm., a length of 5 cm. and a height of 2 cm. Therefore, the volume of the cuboid = 3 5  2 cubic cm. Exercise: Find the volume of the following cuboids: 1. Volume Cubic units 2.

Volume 183 Cubic units Topic 5: Construction of a geometrical shape 5.1 Construction of a straight line of the same length as the one shown. PQ is the straight line given. Construct MN which shall be equal in length to PQ PQ Construction method: 1. Draw line SO which should be longer than PQ S O 2. Extend the compass to a radius equal to PQ 3. Use S as the centre of the radius PQ. Draw the curve of the circle to intersect SO at point Q. 4. SQ is constructed with PQ = SQ as instructed. 5.2 Construction of an angle Angle MNR is as given.  Based on MNR, create CAB of the same size as MNR. M N R Construction method: 1. Draw a sufficiently long straight line AB AB

184 2. Use N as a centre. Extend the compass ensuring a sufficiently long radius. Draw the curve intersecting NR and NM at point X and point Y respectively. M X N R Y 3. Use A as a centre. Extend the same radius for the compass. Draw the curve intersecting AB at point D (as in the illustration). A B D 4. Use D as a centre and a compass radius equal to XY. Draw a curve intersecting the previous curve at point E (as in the illustration). E A B D 5. Draw line AC passing through point E to obtain CAˆ B where M ( CAˆ B ) = M ( MNˆR ) as instructed as in the illustration below: C E A B D C 5.3 Construction of a square D AB Use the same method as to construct a rectangle but the length and the width must be as instructed.

185 5.4 Construction of a circle To construct a circle with the desired radius, a compass shall be used as follows: Construction method: 1. Extend the compass to 2 cm. on a ruler. 2. Fix a centre. Then press the sharp compass point onto the centre point and draw a circle around the centre by rotating the compass pencil. X Activity: Create a pattern with what you have learned about ,  and . Topic 6: Construction of a 3D geometric shape A 3D geometric shape is a shape where all the 3 dimensions are visible and the real shape consisting of the width, length and height can be viewed. If the 3D shape is opened, one gets a flat 2D shape as shown: Prism Cube

186 Cuboid Exercise 4 (2) F Fill in the answers: (1) C AB DE AB = …………………………. cm. DE = …………………………. cm. AC = …………………………. cm. DF = …………………………. cm. BC = …………………………. cm. EF = …………………………. cm.

ABC is a …………………..triangle 187 DEF is a ..............................triamgle I (3) (4) C GH AB GI = …………………………. cm. A = …………………………. degrees IH = …………………………. cm. B = …………………………. degrees GH = …………………………cm. C = …………………………. degrees GHI is a ………………….triangle ABC is a ............................triangle A + B +C = .............................degrees (5) (6) I L 1 GH G = …………………………. degrees J 50° 70° K H = …………………………. degrees I = …………………………. degrees L = …………………………. degrees GHE is a …………………triangle J = 50 degrees G +H +I = .............................degrees K = 70 degrees (7) LJK is a …………………triangle L + J + K= ............................degrees C EF A DB For  ABC: If AB is the base, ................................................. will be is the altitude If AF is the altitude,............................................... will be the base If AC is the base, ...................................................will be the altitude

188 Exercise 5 (1) Give the type of the following quadrilateral shapes:

189 (2) Mark in front of true answers and  in front of false answers ................... a. The 2 diagonals of a kite shape are of the same length. .................. b. The 2 diagonals of a rhombus intersect by forming a right angle. .................. c. One of the diagonals of a rectangle divides the rectangle into 2 triangles of same size. ................. d. The diagonals of a trapezium bisect each other. ................. e. A rectangle and a parallelogram have diagonals with the same properties. Exercise 6 (1) Name 3 things which have a circle shape. (2) In this illustration, how many circles are there?

190 (3) Mark in front of true answers and  in front of false answers. ................... (1) There is only one centre in each circle. .................. (2) Only one diameter can be drawn per circle. .................. (3) All radiuses of a circle are equal in length. ................. (4) A diameter of a circle is twice as long as the radius of the same circle. ................. (5) The endpoints of a diameter are on the circle. Exercise 7 (1) Draw a triangle ABC with AB = 4 cm., AC = 5 cm. and BC = 6 cm. (2) Draw a square ABCD with sides which are 4 cm. long. (3) Draw a rectangle ABCD with AB = 4 cm. and CD = 3 cm. (4) Draw a circle with a radius of 3 cm. (5) Create an illustration with triangles, quadrilaterals and circles. Exercise 8 Specify the type and number of 2D shapes contained in the 3D shapes below: 1. Triangle:............................... Quadrilateral:.......................

191 2. Quadrilateral: ........................ Trapezium: ............................ 3. Quadrilateral: ......................... Pentagon: ............................... 4. Quadrilateral: ............................. Triangle: ..................................... Lesson 7 Introduction to Statistics and Probability Main point 1. Data are facts, numbers or statements, used as a basis for comparative calculation or forecast. 2. Data collection methods include observation, questioning, interviewing, testing, or gathering from registers.

192 3. Data presentation can be in the form of tables, pictograms, bar charts, pie charts, and line charts. 4. Data comparison of two identical matters with the same characteristics or more can be depicted by bar charts. 5. Line chart is a way to present data by using points connected by straight line segments. Each data point represents the number or the quantity of such data compared to a second set of data. A line chart is often used to show continuous changes in data in chronological order. 6. Relationship of data can be illustrated by line charts. 7. Pie chart is a way to present data by using the area in a circle to represent the number or the quantity of such data compared to the total of all data. 8. Probability is the likelihood of occurrence of an event that can fall into one of these scenarios, i.e. chance that it may occur, chance that it may or may not occur, and chance that it may not occur. Expected Learning Outcome 1. Be able to collect data relevant to the issues. 2. Be able to read and discuss issues from bar charts. 3. Be able to construct a bar chart from a given data set. 4. Be able to read and discuss issues from line charts. 5. Be able to construct a line chart from a given data set. 6. Be able to read and discuss issues from pie charts. 7. Be able to discuss suggested events and to be familiar with the phrases with similar meanings to “Chance that it may occur”, “Chance that it may or may not occur” and “Chance that it may not happen”, and be able to apply these phrases. Content Scope Topic 1: Introduction to Statistics Topic 2: Introduction to Probability

193 Topic 1: Introduction to Statistics Data are facts or details of things of interest which may be numbers for calculating comparisons or estimations regarding the truth and can be used as part of decision making or problem solving. Data of things which are of interest to us can be collected from observations, interviews, tests, questions, or gathered from various registers. 1.1 Reading, drawing and comparing a bar chart and a pictogram Drawing a bar chart Drawing a bar chart is to present the collected data in the form of bar charts. A bar chart is composed of the following elements: 1. A bar chart is a type of data presentation using rectangles to represent numbers or quantities of two data sets or more for comparison. 2. A title is placed at the top of the chart to indicate the overall data description. 3. A bar chart is typically drawn by two perpendicular lines with one line forming the vertical axis and the other the horizontal axis. The line indicating the data in numbers or quantities shall have an arrow at one end. 4. Each rectangle which is used to represent the numbers or quantities of data must have the same width and start from the same level. To draw a vertical bar chart, start from the bottom upwards and start from left to right in the case of a horizontal bar chart. 5. Use the height or length of the rectangle to represent the numbers or quantities of each listed data. 6. Color the rectangles or use symbols to distinguish each data set. The same color or symbol shall be applied for the same data set. Pictures or descriptions might also be added. 7. In case there are large amounts of data or the values of data are very close to each other, the quantity axis shall be retracted. 8. In order to correctly interpret data, a number should be written at the top end of each rectangle. 9. If the data are factual and the sources are known, the data sources should be indicated at the bottom of the chart.

194 Example of Bar Charts Air Temperature during 13.00 – 18.00 hrs Temperature (degree Celsius) Time A bar chart representing air temperature during 13.00 – 18.00 hrs. Reading and comparing bar charts Data of two or more identical items may be compared by using bar charts as shown in the following chart, a comparison of fatalities from road accidents during Songkran festival from 11 – 17 April in 2002 and in 2003. Number of fatalities from road accidents during Songkran festival During 11 – 17 April 2002 and 2003 Number of Fatalities 2002 2003

195 The above bar chart used for comparison makes it convenient to compare identical data. As a bar chart is used to compare two or more sets of identical data, it should therefore have a chart legend to identify the data sets. Reading the above bar chart, we can interpret the data as follows. 1. This bar chart represents the number of fatalities from road accidents during Songkran festival for the periods of 11 – 17 April in 2002 and 2003. 2. In 2002, the date with the highest number of fatalities was 13 April 2002. 3. In 2002 and 2003, the number of fatalities was equal on 15 April. 4. 13 April 2003 had the highest number of fatalities. 5. 17 April 2003 had the least fatalities.

196 Exercise Amount of protein and fat in various types of milk per 100 grams of milk Amount (grams) Protein Fat mFrielksh Scwonemdeeitlenknseedd Ucnosnmwdeielekntseended mSkilikm Type of milk 1) What kind of milk has the highest protein amount and how many grams is the said amount? 2) What kind of milk has an equal amount of protein and fat and how many grams is the sad amount? 3) Between sweetened and unsweetened condensed milk, which one has more protein and how many grams of protein does it have more than the other? 4) What kind of milk has the least amount of fat and how many grams of fat does it have?

197 5) Between fresh milk and skim milk, which one has less fat and how many grams less? 1.2 Reading a line chart A line chart can be read by looking at the location of a data point on the chart to see its value both on the vertical and the horizontal axis. For instance, the first data point shows that at the time of 13.00 hrs, the air temperature was 32 degrees Celsius. Look at the line chart and answer the following questions: 1. What data does the line chart represent? 2. What period of time of the day does the line chart represent? 3. What is the maximum temperature? 4. What is the minimum temperature? 5. What is the starting time when the data was recorded? 6. How much is the difference between the highest and the lowest recorded temperature levels? Air Temperature during 13.00 – 18.00 hrs Temperature (Celsius degree) Time A chart representing the air temperature during 13.00 – 18.00 hrs. In summary, a line chart is a way to present data using points connected by straight line segments. Each data point represents the number or the quantity of the

198 respective data. The line chart is often used to show continuous changes in data according to a chronological order. Drawing a line chart A line chart is composed of the following elements. 1. A title on the top of the line chart. 2. Two perpendicular lines are drawn as left and bottom borders. The vertical line represents the numbers or quantities of the respective data. The horizontal line represents the independent list data, e.g. periods of time in a day, periods of time in a week, etc. 3. To draw a line chart, start by plotting the data points that represent the numbers or quantities of the respective data. Then connect all the points by straight line segments starting from the first data point to the following points until the last point is connected. Example: Steps for drawing a line chart are as follows:. Suthee’s weight from May to October Month Weight (kg) May June July August September October Step 1. Write the name of the line chart. Step 2: Draw two lines perpendicular to each other, the horizontal line representing the month and the vertical line representing the weight.

199 1. In case all data have large amounts or all of the data values are close to each other, the number axis (y-axis) shall be retracted as follows: Suthee’s weight from May to October Weight (kg) May Jun Jul Aug Sep Mont Step 3: Plot a point to represeOnctt the weight during each mh onth. This point is at the intersection of an imaginary vertical line representing the month and an imaginary horizontal line representing the weight. Suthee’s weight from May to October Weight (kg) May Jun Jul Aug Sep Mont Oct h Step 4: Draw a line segment connecting the first data point to the following points until the last point is connected.

200 Exercise 2 Answer the following questions. Suthee’s weight from May to October Weight (kg) Mont May Jun Jul Aug Sep Oct h The values of export goods of a company from January to August Amount (Million Baht) Jan Feb Mar Apr May Jun Jul Mont Aug h 1) In which month did the company’s export reach the highest value and how much was it? 2) In which months were the values of the company’s export equal and how much was it? 3) In which month did the company’s export reach the lowest value and how much was it?