The Essence of Mathematics Skills Textbook- Math Primary_2

201 4) How much was the overall value of goods, in million baht, exported by the company between January and August? 1.3 Reading a pie chart Reading a pie chart is similar to reading other types of charts. A pie chart is one way of data presentation by using the area in a circle to represent the total numbers or quantities of all data and divide the circle from the center into segments according to the number of data. Each segment of the circle area represents the number or quantity of 1 represented data. The pie chart represents the stamps of various countries that Thidarat collects. Number of Stamps from Various Countries owned by Thidarat Thidarat has stamps from 5 countries, thus the circle area is split into 5 segments, one segment for each country. The area of each segment will be larger or smaller depending on the number of stamps from that country. The larger the number of stamps, the larger the segment will be. Hence, the pie chart example can be interpreted as follows: 1. Most of Thidarat’s stamps are from Thailand. 2. Thidarat has few stamps from China. 3. Thidarat has fewer stamps from Japan than from Thailand and the United States of America.

202 Exercise 3 Use the given pie chart to answer the following questions: Number of Teachers and Students in Lertwittaya School Male Student 50% Teacher 5% Female Student 1) If there are a total of 1,200 teachers and students in this school, how many female students are there? 2) If there are a total of 1,200 teachers and students in this school, how many male students are there? 3) If there are 80 male students more than female students, how many teachers and students are there altogether? 4) If there are 100 male students, how many teachers are there? 5) If there are 30 teachers, how many students are there?

203 Exercise 4 1. Draw a bar chart to represent the number of honey suckle oranges collected from an orange orchard during January – May as follows: January 7,000 kg February 6,000 kg March 6,500 kg April 6,500 kg May 5,000 kg June 5,500 kg (Let 1 unit of orange represent 1,000 kg) 2. Draw a bar chart to represent a family’s household spending in January using the following data obtained during a survey: Food 6,000 Baht Clothes 2,500 Baht 2 Children’ expenses 5,000 Baht Appliance/Equipment 3,000 Baht Social affairs 2,000 Baht Miscellaneous expenses 4,500 Baht Topic 2: Introduction to probability Consider the following situations and discuss with classmates. A box contains 2 white table tennis balls and 1 yellow table tennis ball. Somchit wants to pick up a table tennis ball without looking or to make a random selection. The probabilities of the events occurring from the random selection of the table tennis balls are as follows:

204 1. Pick up 1 table tennis ball, and as a result 1) get a table tennis ball. This event may certainly occur. 2) get a white table tennis ball. This event may or may not occur. 3) get a yellow ball. This event may or may not occur. 4) get a red ball. This event may certainly not occur. 2. Pick up 2 table tennis balls simultaneously, and as a result 1) get two yellow table tennis balls. This event may certainly not occur. 2) get two white table tennis balls. This event may or may not occur. 3) get at least one white table tennis ball. This event may certainly occur. The elementary probability is the likelihood of an event occurring according to one of these scenarios, i.e. the event may certainly occur, may or may not occur, or may certainly not occur. Exercise 5 Answer the questions from the given scenarios. 1. A bag contains one yellow tangerine and three green tangerines. If one tangerine is randomly picked up from the bag, (1) Is it certain that a tangerine may be picked up? Why? (2) Is it certain that a green tangerine may be picked up? Why? (3) Is it certain that a yellow tangerine may be picked up? Why? (4) Which color of tangerines is more likely to be picked up? Why? (5) Is there any chance of picking up other types of fruit? Why? 2. Three red and three blue abacus balls are put into a paper box. If one abacus ball is randomly picked up, (1) which color ball may probably be picked up? Why? (2) which color ball is more likely to be picked up? Why? (3) is there any chance to pick up a green ball? Why? 3. A box contains one A-letter card, five B-letter cards, and two C-letter cards. If one letter card is randomly picked up,

205 (1) which letter card may probably be picked up? Why? (2) which letter card has the most likelihood to be picked up? (3) which letter card has the least likelihood to be picked up? (4) is there any chance to pick up an E-letter card? Why? 2.1 Definition of Probability Probability is a measurement or estimation representing the likelihood of occurrence of an event based on the consideration of the possible events which may occur as per the following example: Event Likelihood of occurrence 1. Tossing a 10-baht coin once There are 2 possible events i.e. head or tail 2. Roll a dice once There are 6 possible events i.e. face of 1, 2, 3, 4, 5, 3. Tossing two one-baht coins or 6 simultaneously There are 4 possible events: 1) heads and tails 2) heads and heads 3) tails and heads 4) tails and tails 2.2 Likelihood of events Example 1: A box contains 4 white balls and 2 yellow balls. What is the probability to pick up a ball with the following color? 1. white 2. yellow 3. red Analysis 1. The probability or the likelihood to get a white ball is high since there are 4 white balls. 2. The probability or the likelihood to get a yellow ball is low since there are only 2 yellow balls. 3. The probability or the likelihood to get a red ball is zero since there is no red ball in the box. Example 2: Find the likelihood or probability of each of the following outcomes when tossing a one-baht coin and rolling a dice simultaneously. 1. How many possible occurrences where the coin may turn up heads (H)? 2. How many possible occurrences where the coin may turn up tails (T)? 3. How many possible occurrences where the coin may turn up heads and tails

206 Analysis: (H and T)? 4. How many possible occurrences where the dice may turn up 5 or more? 1. The number of occurrences of the coin turning up heads (H) when tossing a one-baht coin and a dice simultaneously is (H, 1) , (H, 2), (H, 3), (H, 4), (H, 5), (H, 6) = 6 events 2. The number of occurrences of the coin turning up tails (T) when tossing a one- baht coin and a dice simultaneously is (T, 1) , (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) = 6 events. 3. The occurrence that a coin turns up heads and tails never occurs since a coin cannot turn up both heads and tails simultaneously. 4. There are only 2 occurrences where the dice turns up 5 or more i.e. (H, 6) , (T, 6) Exercise 6 Fill in the answer a. A bag contains 4 blue table tennis balls and 1 yellow table tennis ball. Consider if the likelihood of occurrence is high, low, or nil when a ball is randomly picked up in the following scenarios: (1) A blue ball is picked up The probability of occurrence is ______________ (high, low, or nil) (2) A yellow ball is picked up The probability of occurrence is ______________ (high, low, or nil) (3) A white ball is picked up The probability of occurrence is ______________ (high, low, or nil) b. Consider whether the probability of occurrence is high, low, or nil when one item at a time is picked up in the following scenarios: (1) A shirt is picked up The probability of occurrence is ______________ (high, low, or nil) (2) A short pants is picked up The probability of occurrence is ______________ (high, low, or nil)

207 (3) A long pants is picked up The probability of occurrence is ______________ (high, low, or nil) c. How often can the following events occur when rolling two dices simultaneously? How many possible occurrences are there so that (1) the overall score is less than 5? ____________________ occurrences (2) the overall score is more than 10?____________________ occurrences (3) the overall score is more than 12?____________________ occurrences

208 Exercise Answer Key Lesson 1: Number and Operation Exercise 1 (a) 1. 5 and ๕ 2. 7 and ๗ 3. 9 and ๙ 4. 4 and ๔ 5. 8 and ๘ Exercise 1 (b) 1234567890 ๑ ๒๓๔๕๖ ๗๘๙ ๐ Exercise 2 (a) 1. 19 and ๑๙ 2. 22 and ๒๒ 3. 37 and ๓๗ 4. 45 and ๔๕ 5. 68 and ๖๘ Exercise 2 (b) ๒๘ ๓๗ ๔๖ ๕๐ ๑๑ ๑๙ 28 34 46 50 11 19 Exercise 2 (c) ๑๐ ๑๑ ๑๒ ๑๓ ๑๔ ๑๕ ๑๖ ๑๗ ๑๘ ๑๙ ๒๐ ๒๑ ๒๒ ๒๓ ๒๔ ๒๕ ๒๖ ๒๗ ๒๘ ๒๙ ๓๐ 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

209 Exercise 2 (d) 1. 38 2. 65 3. 77 4. 81 5. 96 6. 99 Exercise 2 (e) 1. Thirty five 2. Fifty three 3. Sixty eight 4. Eighty six 5. Seventy nine 6. Ninety seven Exercise 3 1. Three hundred and forty-five 2. Eight thousand and seven 3. Twenty thousand eight hundred and ninety-seven 4. Three hundred two thousand four hundred and sixty six 5. One million three hundred sixty-seven thousand five hundred and eighty nine 6. Seven hundred three million nine hundred and seventy thousand five hundred. Exercise 4 1. 1 in the ten thousands place has the value of ten thousand. 2. 5 in the thousands place has the value of five thousand. 3. 9 in the millions place has the value of nine million. 4. 1 in the ten millions place has the value of ten million 5. 4 in the hundred millions place has the value of four hundred million Exercise 5 1. 500,000 + 4,000 + 100 + 20 2. 400,000 + 60,000 + 8,000 + 700 + 90 + 3 3. 10,000,000 + 9,000,000 + 700,000 + 50,000 + 4,000 + 800 + 30 4. 500,000,000 + 60,000,000 + 2,000,000 + 800,000 + 40,000 + 9,000 + 300 + 20 + 1 Exercise 6 69,945 659,024 956,420 965,204 1. 69,594 10,500 111,100 110,001 1,001,001 2. 10,050 769,386 893,013 972,142 1,001,900 3. 100,119 2,403,107 2,460,710 2,471,613 2,498,789 4. 999,991

210 Exercise 7 2.  1.  4.  3.  6.  5.  8.  7. = 10.  9. = 6. 720 Exercise 8 (a) 7. 900 1. 50 8. 920 2. 130 9. 1,050 3. 380 10. 2,660 4. 560 5. 680 6. 1,000 7. 2,500 Exercise 8 (b) 8. 5,000 1. 100 9. 14,300 2. 200 10. 203,100 3. 300 4. 600 2. 55,200,000 5. 600 4. 1,004,000,000 Exercise 8 (c) 2. = 1. 118,500,000 4.  3. 688,600,000 5. 279,900,000,000 2. 77 4. 626 Exercise 9 (a) 1.  3.  Exercise 9 (b) 1. 68 3. 3,337 5. 5,859

211 Exercise 10 (a) Answer 263 1. 100 +40 + 0 100 + 20 + 3 200 + 60 + 3 2. 200 + 10 + 0 Answer 577 300 + 0 + 4 60 + 3 500 + 70 + 7 3. 10,000 + 1,000 + 200 + 0 + 0 Answer 37,887 3,000 + 500 + 0 + 4 20,000 + 3,000 + 100 + 80 + 3 30,000 + 7,000 + 800 + 80 + 7 4. 200,000 + 10,000 + 0 + 200 + 50 + 0 Answer 697,495 400,000 + 50,000 + 4,000 + 100 + 0 + 4 30,000 + 3,000 + 100 + 40 + 1 600,000 + 90,000 + 7,000 + 400 + 90 + 5 Exercise 10 (b) 121 1. 100 + 20 + 1 47 40 + 7 168 100 + 60 + 8 Answer 168 2. 100 + 30 + 2 132 300 + 20 + 5 325 400 + 50 + 7 457 Answer 457

212 3. 10,000 + 2,000 + 100 12,100 400,000 + 50,000 + 4,000 + 100 + 0 + 4 454,104 30,000 + 3,000 + 100 + 40 + 1 33,141 599,345 400,000 + 90,000 + 9,000 + 300 + 40 + 5 Answer 599,345 4. 1,000,000 + 100,000 + 50,000 + 2,000 + 100 + 10 + 3 1,152,113 2,000,000 + 100,000 + 10,000 + 2,000 + 400 + 20 + 1 2,112,421 1,000,000 + 300,000 + 20,000 + 0 + 200 + 60 + 0 1,320,260 3,000,000 + 500,000 + 80,000 + 4,000 + 700 + 90 + 4 3,584,794 Answer 3,584,794 Exercise 11 (a) 1. 50,000 + 4,000 + 600 + 20 + 3 + 90,000 + 3,000 + 500 + 40 + 5 = 100,000 +40,000 + 8,000 + 100 + 60 + 8 = 148,168 2. (800,000 + 70,000 + 1,000 + 400 + 90 + 6 ) + ( 200,000 + 40,000 + 7,000 + 300 + 8) = 1,000,000 + 100,000 + 10,000 + 8,000 + 800 + 4 = 1,118,804 Exercise 11 (b) 3,486,801 1. 3,000,000 + 400,000 + 80,000 + 6,000 + 800 + 0 +1 1,670,528 1,000,000 + 600,000 + 70,000 + 0 + 500 + 20 + 8 5,157,329 5,000,000 + 100,000 + 50,000 + 7,000 + 300 + 20 + 9 Answer 5,157,329 2. 500,000 +80,000 + 4,000 + 100 +60 + 9 584,169 900,000+50,000 + 8,000 + 700 + 80 + 2 958,782 300,000+20,000 + 1,000 + 400 + 50 + 6 321,456 1,864,407 1,000,000 + 800,000 + 60,000 + 4,000 + 400 + 0 + 7

213 Answer 1,864,407 Exercise 12 1. 15,348 2. 47,847 3. 482,496 4. 6,500 Exercise 13 2. 161 1. 500 4. 38 3. 5,010 6. 17,842 5. 6,207 8. 31,230 7. 2,113 Exercise 14 X 1 2 3 4 5 6 7 8 9 10 11 12 4 4 8 12 16 20 24 28 32 36 40 44 48 X3 4 5 6 7 13 4 5 6 7 2 6 8 10 12 14 3 3 12 15 18 21 4 12 16 20 24 28 5 15 20 25 30 35 X 9 10 11 12 6 54 60 66 72 7 63 70 77 84 8 72 80 88 96

214 9 81 90 99 108 10 90 100 110 120 Exercise 15 (a) 2. 3 3. 40 + 7 4. 100 , 3 1. 7 5. 40 , 9 Exercise 15 (b) 2. 312 3. 448 4. 720 1. 84 5. 2,624 2. 990 4. 2,370 Exercise 16 (a) 1. 612 3. 2,200 5. 2,583 Exercise 16 (b) 2. 1,323 3. 3,696 4. 18,656 1. 1,080 2. 7,056 3. 46,200 4. 79,920 Exercise 16 (c) 1. 4,680 Exercise 17 (a) 2. 45,375 3. 93,132 4. 375,124 1. 15,096 Exercise 17 (b) 2. 74,880 3. 210,960 4. 293,440 1. 49,400 Exercise 18 150 baht 1. 72 persons 2. 334 plants 3. 195 persons 4. 193,500 baht 5.

215 Exercise 19 2. 4 1. 0 4. 0 3. 1 6. 0 5. 8 8. 50 7. 210 10. 69 9. 7 11. 5,040 Exercise 20 (a) 1. 20 16 12 8 4 0 2. 24 18 16 6 0 3. 35 28 21 14 7 0 4. 3 baskets 5. 9 pieces

216 Exercise 20 (b) 3. 6 4. 7 1. 3 2. 3 7. 8 8. 49 5. 5 6. 9 9. 80 3. 200 4. 1,150 Exercise 20 (c) 3. 121 4. 121 1. 21 2. 112 5. 30,796 2. 5 with a remainder of 0 4. 11 with a remainder of 1 Exercise 20 (d) 6. 70 ducks with 5 ducks left 1. 16 2. 11 5. 8 2. 8 with a remainder of 3 4. 12 with a remainder of 6 Exercise 21 (a) 6. 193 with a remainder of 38 1. 4 with a remainder of 1 3. 10 with a remainder of 7 5. 2 kilograms Exercise 21 (b) 1. 6 with a remainder of 2 3. 41 5. 20 with a remainder of 11 Exercise 22 1. 64,802 baht 2. 45 baht 3. 24,434,000 baht 4. 90,500 baht 5. 84 baht Exercise 23 1. Yes, since 4 exactly divides 20. 2. Yes, since 4 exactly divides 18. 3. No, since 7 does not exactly divide 37. 4. Yes, since 9 exactly divides 45. 5. 2, 8, 12, 14 6. 3, 6, 15, 24 7. 25, 30, 35

217 8. 18, 24, 30, 36 Exercise 24 1. 1, 2, 3, 4, 6, 12 2. 1, 2, 3, 4, 6, 12 3. 1, 2, 3, 6, 9, 18 4. 1, 2, 3, 6, 9, 18 Exercise 25 1. Yes, since no other numbers can exactly divide 13 except 1 and 13. 2. No, since 15 can be exactly divided by 3. 3. 23, 29 4. 51, 53, 57, 59 5. 91, 93, 97 Exercise 26 1. 1, 3, 9 Prime factor is 3 x 3 2. 1, 2, 11, 22 Prime factor is 2 x 11 3. 1, 2, 3, 4, 6, 9, 12, 18, 36 Prime factor is 3 x 3 x 2 x 2 4. 1, 2, 5, 10 ,25 , 50 Prime factor is 2 x 5 x 5 5. 37 Exercise 27 (a) 1. 7 x 3 2. 6 x 4 3. 2 x 14 4. 6 x 6 8. 9 x 9 5. 7 x 7 6. 17 x 3 7. 9 x 7 9. 9 x 8 10. 9 x 10 Exercise 27 (b) Answer: No, since the given numbers are prime numbers. No other numbers can exactly divide a prime number except 1 and itself

218 Exercise 28 1. 2 x 3 2. 2 x 7 3. 2 x 14 4. 7 x 5 5. 6 x 6 6. 26 x 2 7. 9 x 5 8. 10 x 6 9. 9 x 8 10. 10 x 10 Exercise 29 1. 3 x 3 2. 3 x 13 3. 2 x 3 x 7 4. 2 x 2 x 2 x 7 5. 2 x 2 x 7 6. 6 x 4 x 4 7. 5 x 5 x 10 8. 2 x 2 x 2 x 27

Exercise 30 2. 4,416 219 1. 1,656 5. 2,950 4. 6,104 3. 5,670 2. 8 6. 8,192 Exercise 31 5. 2 1. 6 3. 9 4. 1 2. 3 6. 10 5. 4 Exercise 32 8. 10 3. 14 1. 2 6. 6 4. 1 2. 5 9. 9 7. 2 5. 7 8. 15 3. 2 Exercise 33 6. 2 1. 4 2. 4 9. 9 4. 1 5. 2 7. 7 3. 3 2. 4 6. 5 Exercise 34 5. 24 1. 1 3. 18 4. 5 2. 150 6. 40 5. 60 Exercise 35 8. 240 3. 90 1. 30 6. 45 4. 30 2. 45 5. 140 3. 72 Exercise 36 8. 396 6. 240 1. 30 4. 60 7. 112 Exercise 37 1. 48 4. 96 7. 196

220 Exercise 1 Answer Keys (5) 2 A. Lesson 2: Fraction 3 (1) 1 (2) 2 (3) 4 (4) 4 2 486 B. 2. Four-eighths 3. Seven-ninths 1. Five-sixths 5. Six-sevenths 4. One-seventh C. 2. 2 3. 7 4. 6 5. 3 1. 5 39 75 8 2.  3.  4.  Exercise 2 6.  7.  8.  1.  10.  11.  12.  5.  14.  15.  16.  9.  18.  19.  20.  13.  17.  2. 9 3. 7 4. 5 Exercise 3 5 87 1. 5 6. 1 7. 7 8. 0 7 9 9 5. 1 10. 0 11. 1 12. 0 10 2. 10 3. 23 4. 16 9. 3 12 40 21 7 6. 47 Exercise 4 1. 9 156 10 5. 13 20

221 Exercise 5 2. 19 3. 2 4. 25 1. 5 27 5 29 9 6. 19 3. 2 4. 3 5. 11 87 94 23 Exercise 6 2. 3 1. 2 7 5 Exercise 7 1. 8 of a bag 9 2. 5 litre 7 3. 5 of a cup 6 4. 4 of the plot 5 5. 4 of the pot 5 Exercise 8 1. 6 of the bag 13 2. Suda grew more by 3 of the land 11 3. 6 of the box 12 4. 1 kilometre 15 5. 2 kilometre 7 Exercise 9 2. 16 3. 9 11 4. 7 5 6. 815 1. 11 4 12 14 18 15 5. 78 7 10

Exercise 10 2. 6 3. 14 222 4. 11 1. 16 5 45 30 21 3. 2 4 4. 5 5 5. 5 7 6 9 7. 4 1 8. 412 Exercise 11 3 17 1. 5 1 2. 4 1 4 11 5. 3 9 6. 2 1 13 5 Exercise 12 1. 250 square wah 2. 900 students 3. 40 metres 4. 10 chickens 5. 25 trees Exercise 13 Part 1 1. 16 7. 18 25 2. 7 8. 8 3. 1 9. 14  2 4 55 9 10. 9 4. 2 62 15 11. 45 58 5. 1 12. 72 6. 1 1 Part 2 55 1. 18 11 2. 6 3 days 4 3. 1 of the well 6 4. 3 cans

223 Exercise 14 Part 1 1. 39 64 2. 7 4 3. 5 49 4. 1 11 7 5. 14 3 11 6. 12 35 7. 126 45 8. 5 28 24 Part 2 1. 1 kilograms 3 12 2. 381 metres 3 3. 4 hours 4. 40 plots 5. 30 kilometres 6. 3,000 baht

224 Exercise 1 Answer Key 4. 0.4 A. Lesson 3: Decimals 1. 0.2 2. 0.5 3. 0.3 B. 2. Zero point eight zero 1. Zero point six four 4. Zero point eight two 3. Zero point zero nine 5. Zero point four nine 2. 0.70 3. 0.02 5. 0.95 6. 0.88 C. 1. 0.89 4. 0.48 Exercise 2 2. 0.7 3. 0.04 A. 5. 0.6 3. 0.65 1. 0.03 2. 0.31 6. 0.48 4. 0.06 5. 0.12 B. 1. 0.84 4. 0.29 Exercise 3 1.  2.  3.  4.  5.  6.  Exercise 4 1. > 2. > 3. > 4.> 5. <

225 Exercise 5 2. 0.7 3. 0.8 A. 5. 0.1 6. 0.2 1. 0.3 2. 0.80 3.. 0.50 4. 0.4 5. 0.40 6. 0.30 B. 1. 0.90 16.09 3.108 0.80 4. 0.70 6.024 108.009 C. 26.44 57.468 ง. 0.04 Exercise 6 2) 0.47 1. 4) 0.003 1) 0.40 2) 809 3) 0.106 2. 100 1) 3 4) 98043 10 1000 3) 1082 100 Exercise 7 1. 9 and 43 2. 35.08 and 74.76 3. 0.667 and 0.429 Exercise 8 1) 40.30 2) 104.63 3) 176.87 4) 185.48 5) 315.74

226 Exercise 9 1. 1.75 baht 2. 4.3 kilograms 3. 133.5 kilograms 4. 700 metres or 0.7 kilometre 5. 0.02 metre Exercise 10 2) 3.531 3) 6.0562 4) 0.07605 1. 1) 29.5 2. 10,762.5 baht 3. 22,507.55 baht 4. 38,632.5 baht Exercise 11 1. 3.04 2. 9.2 3. 1.13 4. 5 5. 20.6 6. 47.5 7. 735 8. 54.4775 9. 86.786 10. 260.927 11. 35.5 12. 12 trips 13. 1.65 metres 14. 14 days

227 Answer Key Lesson 4: Percentage Exercise 1 1. Only 60 out of 100 people pay income tax. 2. Two out of 100 newborn babies will die. 3. Five out of 100 tourists visiting our province are foreigners. Exercise 2 2. 17 % a. 4. 25 % 1. 12 % 2. 20 3. 20 % 5. 30 % 100 b. 4. 30 1. 15 100 100 3. 27 100 5. 35 100 Exercise 3 1. 75% 2. 90% 3. 85% 4. 100% Exercise 4 2. 1 1. 1 4 20 4. 49 3. 11 50 50 6. 87 5. 9 100 20

228 Exercise 5 1. Baht 5,000 2. Baht 11,750 3. The profit is Baht 39. 4. 90 % 5. 10 % per year 6. 90 % 7. 75 % 8. 38 % Exercise 6 1. If the bag costs 100, Suda sells it for Baht 115. 2. If the refrigerator costs Baht 100, Usa suffers a loss of Baht 10. 3. If the bicycle costs Baht 100, Udom sells it for Baht 106. 4. If the car costs Baht 100, Sakda got only Baht 95 from selling it. 5. If pork costs Baht 100 per kilogram, Wirat sells it for Baht 130. Exercise 7 1. Profit margin of 25% 2. Profit margin of 25% 3. Profit margin of 20% 4. Profit margin of 15% 5. Loss margin of 12.5%

229 Answer Key Lesson 5: Measurement Exercise 1 1. 615 centimetres 2. 850 centimetres 3. 20 Sok 4. 32 millimetres 5. 85 Sen 6. 10 miles Exercise 2 1. Answer: At the discretion of the teacher 2. Answer: At the discretion of the teacher 3. 24 kilometres Exercise 3 1. 1 Centimetre : 3 Metres 2. Scale of width and length equal to 1 Centimetre : 3 Metres 3. 54 Kilometres Exercise 4 (a) 1. 0.5 Read as half a Kilogram 2. 1.5 Read as one and a half Kilograms 3. 4 Read as four Kilograms 4. 1.1 Read as one Kilogram and one hundred grams 5. 2.8 Read as two Kilograms and eight hundred grams Exercise 4 (b) 1. Figure 4 2. Figure 3 3. Figure 1 4. Figure 3 5. Figure 2 6. Figure 2 7. Figure 3 8. Figure 1 9. Figure 1 10. Figure 4

Exercise 5 (a) 3.  230 7.  1. = 2.  4.  8.  5.  6. = Exercise 5 (b) Answer: At the discretion of the teacher Exercise 5 (c) 1. 4 Bottles 2. 10 Bags 3. 15 Table Spoons 4. 100 Baht 5. Gain 60 Baht profit 6. 4 Baht 7. 300 Milliliters Exercise 5 (d) 1. 11 Liters or 11,000 Milliliters 2. 300 Liters 3. 3 Liters 600 Milliliters 4. 2 Tank 13 Liters 5. Buying a whole Tank is 10 Baht cheaper 6. 440 Tank Exercise 6 1. 1.1 49 Square Centimetres 1.2 15 Square Centimetres 1.3 25 Square Centimetres 2. 2.1 25 Square Metres 2.2 15 Square Centimetres 2.3 40 Square Centimetres 3. 2 Figures 4. 25 Metres 5. 240 Square Feet

231 Exercise 7 1. 225 Cubic Metres 2. 1,000 Cubic Centimetres 3. 100 Cubic Centimetres 4. 140 Cubic Metres 5. 120,000 Cubic Centimetres Exercise 8 1. 4 Cups 2. 3,000 Milliliters 3. 10,000 Cubic Centimetres 4. 20,000 Cubic Centimetres Exercise 9 (a) 1. Rectangle 2. North and 3 Metres 3. 9 Metres 4. Flower 5. 4 Metres Exercise 9 (b) 1. 2 Kilometres to the South 2. 5 Kilometres Exercise 9 (c) 1. Northeast and East with a distance of 3,500 Metres 2. 100 Metres to the South 3. West, 1,500 Metres nearer than walking to the coffee shop Exercise 9 (d) Answer: At the discretion of the teacher Exercise 10 1. 62.50 baht 2. 249 baht 3. 250 baht 4. 274 baht 5. 120 baht

232

233 Satang

234 Exercise 12 Answer: (1) At the discretion of the teacher (2) At the discretion of the teacher Exercise 13 (1) 06.00 hrs. (2) 23.15 hrs. (3) 01.30 hrs. (4) 24.00 hrs. (5) 14.45 hrs. (6) 11.30 hrs. (7) 10.40 hrs. (8) 04.12 hrs. Exercise 14 Answer: (1) At the discretion of the teacher (2) At the discretion of the teacher

235 Exercise 15 1. 4 months which are April, June, September, November 2. 7 months which are January, March, May, July, August, October, December 3. 4 weeks 4. The 29th 5. The 7th 6. The 8th 7. The 31th which is a Tuesday 8. 6, 13, 20, 27 9. 365 days 10. Thursday, 5 th May 2011

236 Answer Key Lesson 6: Geometry 1. ว ย 1.1  ง ส ข 1.2 Straight line segment DE Straight line segment DE a. b. Straight line segment FG Straight line segment FG c. Straight line segment HI Straight line segment HI 2. a. Angle ABC is an acute angle of 60 degrees. b. Angle EFG is an obtuse angle with 120 degrees. 3. 1. Both right angles of 90 degrees. 2. Both right angles of 90 degrees. 3. Both right angles of 90 degrees. 4. Table, blackboard, paper, floor, wall. 5. Fold one of the angles of each one of the above items 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 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 on a thin piece of paper. 7. Angle AB is a straight angle of 180 degrees. Angle CD is a straight angle of 180 degrees. Angle EF is a straight angle of 180 degrees. Exercise 2 3. Write the symbol indicating that the straight line segments are parallel.

237 AB D EF CH G 1.AB // EF 2. BC // FG 3. CD // GH Exercise 3. 1. Draw a straight line passing point A which is parallel to BP. „A P B 2. Draw a straight line passing 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. DE A C FB DE is parallel to AB.

238 Exercise4 (2) Fill in the answers. F (1) C A B D E AB = 3 cm. DE = 5 cm. AC = 3 cm. DF = 3 cm. BC = 3 cm. EF = 4 cm. ABC is an equilateral triangle. DEF is a right triangle. (3) I (4) C 2 cm. 2 cm. G 3 cm. H AB GI = 3 cm. A = 45 degrees B = 90 degrees IH = 2 cm. C = 45 degrees GH = 2 cm. ABC is a right triangle. GHI is an isosceles triangle. A + B + C = 45 + 90 + 45 = 180 degrees (5) (6) H L 1 IG J 50° 70° K I = 40 degrees G = 80 degrees L = 60 degrees H = 60 degrees IGH is a scalene triangle J = 50 degrees I + G + H = 180 degrees K = 70 degrees JKL is a scalene triangle L + J + K =180 degrees

239 (7) C AD B For  ABC: If AB is the base, CB is the altitude. If AD is the altitude, DC is the base. If AC is the base, - is the altitude AB = 6 cm. CF = 4 cm. Exercise 5 (1) Give the type of the following quadrilateral shapes: 1. Rectangle 2. Square 3. Rhombus 4. Parallelogram 5. Trapezoid 6. Kite 7. Trapezium (2) Mark in front of true answers and  in front of false answers. . a. The two diagonals of a kite shape are of the same length.  b. The two diagonals of a rhombus intersect by forming right angles.  c. A diagonal of a triangle divides the triangle into two triangles of the 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) Ping-pong ball, football, rattan ball. (2) In this illustration, how many circles are there? 6 circles. (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.

240 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 BC = 3 cm. (4) Draw a circle with a radius of 3 cm. (5) Create an illustration with triangles, quadrilaterals and circles.

241 Exercise 8 Specify the type and number of 2D shapes contained in the 3D shapes below: 5. 4 triangles 1 quadrilateral 6. 6 triangles 1 trapezoid 7. 5 quadrilaterals 2 pentagons 8. 3 quadrilaterals 2 triangles

242 Answer Key Lesson 7: Introduction to Statistics and Probability Exercise 1 1. sweetened condensed milk, 8.1 grams 2. fresh milk, 3.5 grams 3. sweetened condensed milk has more protein, 1.1 grams 4. skim milk, 0.4 grams 5. skim milk has less fat, 3.1 grams Exercise 2 1. Aug, 9 million baht 2. Apr and Jul, 8 million baht 3. Jan, 5 million baht 4. 57.5 million baht Exercise 3 1. 540 persons 2. 600 persons 3. 1,600 persons 4. 10 persons 5. 570 persons

Exercise 4 243 1. Food Clothes เดอืMนonth Children’s Jมaกnuรaาrคyม Appliance/Equipment Fกeุมbภruาaพryันธ์ Social affairs Mมนีarาcคhม Miscellaneous expenses Aเมpษriาlยน Mพaฤyษภาคม Jมuถิneนุ ายน 2. A Chart representing household expenses in January:

244 Exercise 5 1. 1.1 Yes, it may certainly occur because there are only tangerines in the bag. 1.2 No, because there is a yellow tangerine in the bag. 1.3 No, because there are some green tangerines in the bag. 1.4 Green tangerine, since there are more green tangerines than yellow ones. 1.5 No, because there are only tangerines. 2. 2.1 Red and blue colors since there are only two colors of abacus balls in the box. 2.2 Each color is equally likely to be picked up since the number of abacus balls for both colors are equal. 2.3 No, because no green abacus ball is put into the box. 3. 3.1 A, B, and C, since there are cards of only these letters in the box. 3.2 B-letter card since it has the highest number of cards which is 5. 3.3 A-letter card since it has the least number of cards which is 1. 3.4 No, because no E-letter card is put into the box. Exercise 6 a. (1) high (2) low (3) nil b. (1) high (2) low (3) nil c. (1) 3 (2) 1 (3) 0

245 Working Group Advisors 1. Mr. Prasert Boonrueng ONIE Secretary General ONIE Vice Secretary 2. Dr. Chaiyos Aim-Suwan ONIE Vice Secretary ONIE Curriculum Consultant 3. Mr. Watcharin Jumpee Director of ONIE Development Division 4. Dr. Thongyou Kaewsaiha Retired Official Retired Official 5. Mrs. Rakhana Tanthawutto Retired Official Writers Retired Official ONIE, Samut Sakhon Province 1. Mr. Chaiyo Muangboonmee ONIE, Samut Sakhon Province Retired Official 2. Miss Karuna Tatiyarattanaporn ONIE Development Division Editors and Developers ONIE Development Division ONIE Development Division 1. Mr. Chumphol Noosong ONIE Development Division ONIE Development Division 2. Mr. Chaiyo Muangboonmee ONIE Development Division 3. Miss Sirindhorn Nakkhum ONIE Development Division 4. Miss Pipiara Samut ONIE Development Division 5. Mrs. Pornthip Klarop 6. Mr. Surapong Manmano Working Group 1. Mr. Surapong Manmano 2. Mr. Supachoke Srirattasil 3. Miss Wannaporn Pattamanond 4. Miss Sarinya Kulapradit 5. Miss Phetcharin Luengchitwattana Typist of the Original Version Miss Phetcharin Leungchitwattana Textbook Cover Design Mr. Supachoke Srirattanasil