The Essence of Mathematics Skills Textbook- Math Primary_2

101 Exercise 1 A. Write decimals which represent the shaded parts. (1) (2) (3) (4) B. Write the decimals in words. (1) 0.64 reads ____________________________________________________________________ (2) 0.80 reads ____________________________________________________________________ (3) 0.09 reads ____________________________________________________________________ (4) 0.82 reads ____________________________________________________________________ (5) 0.49 reads ____________________________________________________________________ C. Write the words in decimals. = ______________ (1) Zero point eight nine = ______________ (2) Zero point seven zero = ______________ (3) Zero point zero two = _____________ (4) Zero point four eight = ______________ (5) Zero point nine five = ____________ (6) Zero point eight eight

102 Topic 2: Place value and value of digit in each decimal place Study the following illustration. 0.40 The shaded part can be expressed as 0.46. 0.46 This is the first decimal place . So, the digit 0.06 equals or 0.4. Second decimal place. So, the digit equals or 0.06. 0.46 can be written as 0.46 = 0.40 + 0.06 or = 0.4 + 0.06 Exercise 2 (2) 0.75 =  + 0.05 A. Correctly fill in the blanks. (4) 0.66 = 0.6 +  (1) 0.53 = 0.5 +  (2) 0.84 = 0.8 +  (2) 0.3 + 0.01 =  (5) 0.67 =  + 0.07 (4) 0.2 + 0.09 =  B. Correctly fill in the blanks. (6) 0.4 + 0.08 =  (1) 0.8 + 0.04 =  (3) 0.6 + 0.05 =  (5) 0.1 + 0.02 = 

103 Topic 3: Writing decimals in an expanded form Writing decimals in an expanded form is a way to express the decimals as the sum of the value in each place. For example, the expanded form of 56.37 is: Tens Ones Tenths Hundredths 5637 So, 56.37 can be expressed as 50 + 6 + 0.3 + 0.07 Example: Write the decimals below in an expanded form. 1) 0.84 = ……………………… 2) 56.08 =……………………… 3) 5.32 =……………………… 4) 79.503 =……………………… Topic 4: Comparing and ordering decimals To compare decimals, start with comparing the numbers to the left of the decimal point. Then, compare the numbers to the right of the decimal point by starting with the tenths which is in the first decimal place. (1) Comparing the tenths 0.4 0.5 The above shaded bars represent 0.4 and 0.5. 0.4 means 4 tenths. 0.5 means 5 tenths. Hence, 0.4 < 0.5 or 0.5 > 0.4. 0.6 > 0.4

Exercise 3 (2) 104 Correctly fill < or > in the blanks. 0.5 (1) 0.3 0.4 0.9 0.3  0.4 0.5  0.9 (4) 0.8  0.9 (3) 0.4  0.3 (6) 0.6  0.3 (5) 0.3  0.7 (1) Comparing the hundredths 0.30 0.32 The above pictures illustrate 0.30 and 0.32. 0.30 means 30 hundredths. 0.32 means 32 hundredths. So, 0.30 < 0.32 and 0.32 > 0.30 0.74 0.84 0.74 < 0.84

105 Exercise 4 Correctly fill < or > in the blanks. (1) 0.90  0.50 (2) 0.51  0.48 (3) 0.75  0.60 (4) 0.28  0.18 (5) 0.50  0.55 (2) Comparing the tenths with the hundredths and others Take a paper of 5 cm X 5 cm. Picture 1 Draw lines to divide the paper into 10 equal parts as shown. Then, shade 5 parts out of 10 parts. The shaded section represents 0.5. Picture 2 Use the same paper, draw lines to horizontally divide the paper into 10 equal parts. Now, the paper has 100 equal parts. The shaded section now represents 50 hundredths and can be written as 0.50. Therefore, 0.5 = 0.50

106 Exercise 5 A. Change each decimal number into a one decimal digit. (1) 0.30 = (2) 0.70 = (3) 0.80 = (4) 0.40 = (5) 0.10 = (6) 0.20 = B. Change each decimal number into a two decimal digits and fill the answers in the blanks (2) 0.8 = (3) 0.5 = (1) 0.9 = (4) 0.7 = (5) 0.4 = (6) 0.3 = C. Arrange the following decimals according to a decreasing order. (1) 0.80 (2) 3.108 (3) 16.09 (4) 57.468 D. Arrange the following decimals according to an increasing order. (1) 6.024 (2) 26.44 (3) 108.009 (4) 0.04 Topic 5: Relationship between decimals and fractions You have learned that decimals are converted from fractions. We can change fractions into decimals and vice versa without changing their values. 5.1 Converting fractions into decimals. For example: 5 = 0.5 (5 represents the tenths and must be put in the first place to 10 the right of the decimal point) 6 = 0.06 (6 represents the hundredths and must be put in the second 100 place to the right of the decimal point) 8 = 0.008 (8 represents the thousands and must be put in the third 1000 place to the right of the decimal point) If the denominators are not the powers of ten (10, 100, 1000….), you can increase the denominators to the powers of ten. For example: 1 = 1 × 5 = 5 = 0.5 2 2 5 10 4  4  2 = 8 = 0.8 5 5 2 10 7  7  125 = 875 = 0.875 8 8 125 1000 Likewise, to convert decimals into fractions, you should expand the digit in each place according to its place value. For example: 8.6 = 8+ 6 = 8 6 = 8 3 (simplify 6 to the lowest terms) 10 10 5 10

107 16.15 = 16 + 15 = 16 15 = 16 3 (simplify 15 to the lowest terms) 100 100 20 100 Exercise 6 1. Convert the following fractions into decimals. 1) 4 = 2) 47 = 10 100 3) 106 = 4) 3 = 1000 1000 2. Convert the following decimals into fractions. 1) 0.3 = 2) 8.09 = 3) 10.82 = 4) 98.043 = Topic 6: Estimating decimal values Mathematically, estimation which is represented by “  ” sign is a way to identify the value which is nearest to the actual amount and can be applied. Below is the estimation guideline: 1) Rounding to the nearest whole number. For example: 63.785  64 78.05  78 2) Rounding to the nearest tenths. For example: 43.554  43.6 79.788  79.8 3) Rounding to the nearest hundredths. For example: 64.554  64.55 93.449  93.45 4) Rounding to the nearest thousandths. For example: 8.6873  8.687 108.4328  108.433 Observation 1) Rounding cannot be applied to non-quantifiable numbers such as telephone numbers, house numbers, ID numbers, etc. 2) We round only one digit in a number. For example, 25.449 can be rounded up to 25.45 and 25.45 can be rounded up to 25.5. Exercise 7 Round the numbers below. 1) Round to whole numbers. 8.8  43.4  2) Round to two decimal digits. 35.083  74.755 

108 3) Round to three decimal digits. 2  3 37 Topic 7: Adding and subtracting decimals and problem solving exercises Like whole numbers, decimals have place values and they must be lined up correctly according to their proper place-value position before addition or subtraction. Make sure that the decimal points are lined up in a column. Then, add or subtract down the columns. For example: Example: 32.35 + 45.73 – 27.8 =  Example: 96.28 – 28.95 + 12.22 =  Method: 96.28 - Method: 32.35 + 45.73 28.95 67.33 + 78.08 - 12.22 27.80 79.55 50.28 Answer: 79.55 Answer: 50.28 Exercise 8 Find the answers. (1) 45.75 + 10.05 – 15.5 =  (2) 108.15 + 197.83 – 201.35 =  (3) 163.62 + 101.23 – 87.98 =  (4) 267.77 + 101.01 – 183.3 =  (5) 389.19 + 38.05 – 111.5 =  Commutative property for decimal addition Example: Compare if 12.28 + 18.32 equals 18.32 + 12.28. Method: 12.28 + Method: 18.32 + 18.32 12.28 30.60 30.60 Associative property foTrhfrearecftoioren, 1a2d.2d8it+io18n.32 = 18.32 + 12.28 Analysis When 2 decimals are added, the sum is the same regardless of the orders of the addends. Therefore, it can be concluded that decimal addition has a commutative property.

109 Example: Compare if (25.75 + 18.13) + 12.25 equals (25.75 + 12.25) + 18.13 Method 1: (25.75 + 18.13) + 12.25 Method 2: (25.75 + 12.25) + 18.13 = 43.88 + 12.25 = 38.00 + 18.13 = 56.13 = 56.13 Therefore (25.75 + 18.13) + 12.25 = (25.75 + 12.25) + 18.13 Analysis Method 2 is simpler than method 1. This is because 25.75 + 12.25 = 38.00 ( .75 plus .25 is 1.00 and 1 must be carried forward to the next place) Decimal adTdhiteino,naadnddthseusbutmracatnidon18p.1r3otbolgeemthesor.lvTihnegteoxtaelrscuismesis equal to the total sum derived under method 1. Though we change the grouping of addends, the sum is the same. Therefore, we can conclude that decimal addition has an associative property. Example: Winai earned 235.75 baht from sales of goods and received 105.50 baht from a debt repayment. He paid 35 baht for goods delivered fees. How much money does he have left? 235.75 + baht Method: He gained from sales of goods 105.50 baht Debt repayment Subtotal 341.25 - baht He paid delivery fees of 35.00 baht He now has 306.25 baht Answer: 306.25 baht Exercise 9 Find the answers. (1) Suda bought a notebook for 12.75 baht and a book for 35.50 baht. She gave a banknote worth 50 baht to the seller. How much is the change? (2) 2 sacks of flour were bought. One sack weighed 3.5 kilograms and the other weighed 2.3 kilograms. After 1.5 kilogram of the flour is sold, how much is left? (3) There were 2 rice sacks. One weighed 100 kilograms and the other was 50 kilograms. After 16.5 kilograms of the rice were sold, how many kilograms of the rice are left? (4) Weera had to bike 3.7 kilometres from home to the market and 1.5 kilometres from the market to his school. After 4.5 kilometres of biking, his tires went flat. How much farther does he have to go to reach the school?

110 (5) There were 2 ropes. One was 10.5 metres and the other was 12.7 metres long. After they were knotted together, the rope‟s length was measured at 23.18 metres. How many metres of the rope were used for the knot? Topic 8: Multiplying and dividing decimals and problem solving exercises 8.1 Multiplying decimals and problem exercises Multiplication of decimals is similar to multiplication of positive integers. However, in decimal multiplication, the products will have as many decimal places as the sum of the decimal places in the multiplicand and the multiplier combined. Example: 6.25 × 2.3 =  Multiplicand has2 decimal places. Method: 6.2 5 Multiplier has 1 decimal place. 2. 3 × The sum of the decimal places in the 1875 multiplicand and the multiplier is 3. 1250 + 1 4.3 7 5 Observation Place the decimal in the answer by starting at the right and moving the point 3 places left. Commutative property for multiplication Example: Compare if 2.8 × 1.3 equals 1.3 × 2.8 Method: 2.8 Method: 1. 3 1.3 × 2. 8 × + 84 104 28 26 364 + 364 Therefore 2.8 × 1.3 = 1.3 × 2.8 Observation The products of 2.8 × 1.3 and 1.3 × 2.8 are the same. Thus, decimal multiplication has a commutative property. Example: If the gasoline is priced at 24.58 baht per litre and we put 15.5 litres of gasoline in a car, how much would it cost? Method: A litre of gasoline costs 24.58 baht

111 We put in the car 15.5 litres of gasoline It costs 24.58 x 15.5 = baht 24.58 15.5 x 12290 122900 + 245800 380.990 24.58 x 15.5 = 380.99 It costs 380.99 baht. Answer: 380.99 baht Exercise 10 1. Fill the answers in the blanks. 1) 59 x 0.5 = 2) 3.21 x 1.1 = 3) 5.66 x 1.07 = 4) 8.45 x 0.009 = 2. A shop sold 123 pairs of trousers. If a pair of trousers was sold at 87.50 baht, how much money did the shop earn from the sale? Answer _____________________________________________________________________ 3. A seller sold 403 kilograms of mangoes at 55.85 baht per kilogram. How much money did the seller get from the sale? Answer _____________________________________________________________________ 4. A rice farmer sold 25.25 tons of rice at 15.30 baht per ton. How much money did the farmer receive? Answer _____________________________________________________________________

112 8.2 Dividing decimals and problem exercises Dividing decimals by integers The simplest way to divide decimals by integers is to use the long division. Divide the dividend with the divisor like when you divide integers by integers. Then, add the decimal point to the quotient in the same spot as the dividend so that the quotient has the same number of decimal places as the dividend. Example 1: 3.36 ÷ 3 =  Method: 1. 1 2 3 ) 3. 3 6 3- 03 3- 06 6 00 - Answer: 1.12 Explanation: In this example, 3 which is the divisor is a single digit number. So, we divide each digit of the dividend from left to right by the divisor. Then, place the decimal point in the same spot as the dividend. You can see that the dividend and the quotient both have 2 decimal places. Example 1: 253.92 ÷ 12 =  Method: 2 1. 1 6 - - 12 )2 5 3. 9 2 - 24 13 12 19 12 72 7- 2 00 Answer: 21.16 Explanation: As 12 is a double digit number and cannot go into a single digit number, we have to divide it into 2 digit numbers in the divisor from left to right. Then, when you reach the ones place, put the decimal point up the divisor box in the same place as the dividend

113 and continue with the division as you normally would when dividing integers. The answers would have 2 decimal places like the dividend. Dividing decimals by decimals To divide decimals by decimals, multiply both the dividend and the divisor by the powers of ten (10, 100, 1,000, ...) in order to convert the divisor into an integer. Then, perform the division as you normally would when dividing integers as illustrated in the above 6.1. Example 1: 11.52 ÷ 0.8 =  Method: 11.52 = 11.52  10 0.8 0.8 10 = 115.2 8 14.4 8 115.2 38-5 3-2 32 3-2 00 Answer: 14.4 Explanation (1) 0.8 is a divisor with 1 decimal place. So, multiply 10 by both the dividend and the divisor. The dividend becomes 115.2 and the divisor is 8. (2) Divide 115.2 by 8 by using the long division. Put a decimal point after the ones place and continue with the division. The quotient is 14.4. Example 1: 342.4 ÷ 0.32 =  Method: 342.4 = 342.4  100 0.32 0.32 100 = 34240 32 1070 -- 32 )3 4 2 4 0 32 224 224 0000 Answer: 1,070

114 Dividing integers by decimals Dividing integers by decimals can be done in the same way we divide decimals by decimals. Start with multiplying both the dividend and the divisor by the powers of ten (10, 100, 1,000, ...) to change the divisor into an integer. Then, perform the division. Example: 765 ÷ 1.5 =  - - Method: 510 15 ) 7 6 5 0 75 15 15 00 Answer: 510 Explanation (1) 1.5 has one decimal place. So, we must multiply 10 by both the dividend and the divisor. The dividend becomes 7,650 and the divisor is 15. (2) Do the long division to divide 15 into 7,650. The quotient is 510 which is an integer. Dividing decimals with remainders Division may result in remainders. In such cases, the answer will be an estimate which is derived from rounding the quotient to the number of decimal places as required by the problem. Always divide to one more place than you are rounding to because the extra digit helps identify if you should round up or round down. If the digit is 5 or more, you must round up. If it is less than 5, you must round down. If the digit in the one‟s place is equal to or is more than 5, round up to the designated place. If the extra digit is less than 5, drop it. Example: 12.2 ÷ 3 =  (round the answer to 2 decimal places) Method: 4.066 3 12.200 12 020 18 20 18 2 Therefore 12.2 ÷ 3 = 4.07

115 Explanation (1) According to the problem, we have to round the answer to a 2 decimal place number but the dividend has only 1 decimal place. So, we must add 2 zeroes to it to change the dividend into a number with 3 decimal places. Adding zeroes to the left of the decimal point does not change the value of the decimals. (2) Divide 12.200 by 3. The quotient is 4.066 which is a 3 decimal digit. (3) The hundredths place of the quotient is 6 which is more than 5. So, we must round up by adding 1 to the digit in the tenths place. The digit in the tenths place then becomes 7. Decimal division problem solving exercises Decimal division problems are related to daily life like integer addition and subtraction problems. Example: The sugar was priced at 12.50 baht per kilogram. Usa paid a total of 106.25 baht for the sugar. How many kilograms of the sugar did she buy? Symbolic sentence 106.25 ÷ 12.50 =  Method: Usa paid for the sugar a total of 106.25 baht A kilogram of sugar cost 12.50 baht So, the sugar she bought is = 106.25  10 kilograms 12.5 10 = 1062.5 125 8.5 125 1062 .5 - 1000 625 - 625 000 Answer: 8.5 kilograms Explanation (1) Change the divisor into an integer by multiplying it by 10, 100, 1000, ...... (2) Divide 1,062.5 by 125 and the quotient is 8.5. Exercise 11: Show the method to solve the problems and find the answers. 1. 12.16 ÷ 4 =  2. 64.4 ÷ 7 =  3. 18.08 ÷ 16 = 

116 4. 6.05 ÷ 1.21 =  5. 18.54 ÷ 0.9 =  6. 437 ÷ 9.2 =  7. 8,379 ÷ 11.4 =  8. 653.73 ÷ 12 =  9. 729 ÷ 8.4 =  10. 323.55 ÷ 1.24 =  11. If a father bought 6 shirts for 213 baht. How much did each shirt cost? 12. A dump truck is loaded with 4.2 cubic metres of sand. If a wheelbarrow can carry 0.35 cubic metres of sand, how many trips are needed to move all the sand from the dump truck? 13. Suchada bought 11.55 metres of fabric and she could make 7 blouses out of it. How much fabric did she use to make a blouse? 14. A road is 10.64 kilometres long. If it takes a day to pave 0.64 kilometres with asphalt, how many days will it take to pave the entire road?

117 Lesson 4 Percentage Main content Meaning of percentage and the use of the percent symbol (%), relationship between fractions, decimals and percentages, problems exercises of multiplication, division (rule of three) and application. Expected learning outcome 1. Be able to write fractions with a denominator of 100 as a percentage and use the % symbol. 2. Be able to specify fractions and write percentages as a fraction 3. Be able to solve problem exercises of multiplication and division (rule of three) of percentages and apply the knowledge to everyday problems. Content scope Topic 1: Meaning of percentage Topic 2: Relationship between fractions and percentages Topic 3: Problem exercises of multiplication, division (rule of three) and applications

118 Topic 1: Definition of percentage Percentage means per hundred or out of a hundred. It is used to express a number as a fraction of 100, for example lemon costs Baht 200 per hundred meaning 100 lemons cost Baht 200. The term percentage comes from the Latin term „per centum‟ meaning per hundred and is expressed by the % symbol. For example, 3 percent can be written as 3%. However, we do not use percent and % at the same time. The rectangle on the left is divided into 100 equal squares. Seven squares are shaded while the remaining 93 are not. The shaded part is 7 out of 100 or 7 percent. The number can be written using the % symbol as 7% or as a fraction. The non-shaded part is 93 out of 100 or 93 percent or 93%. 93 out of a hundred can be written as 93 100 Therefore, a percentage is a fraction with a denominator of 100. 7 = 7 percent or 7% (read: seven percent) 100 93 = 93 percent or 93% (read: ninety-three percent) 100 Percentages can be applied in other matters such as: 1. 99% of primary students passed the exam. This means 99 out of 100 primary students passed the exam. 2. 5% of the country‟s population consists of farmers. This means if there are 100 people in the country, 5 of them are farmers. 3. Only 95% of all the piglets raised by Mr. Suk are still alive. This means if Mr. Suk had 100 piglets, only 95 piglets are still alive. Exercise 1 Explain the following statements: (1) Only 60% of the country‟s population pays an income tax. (2) 20% of newborn babies die. (3) 5% of tourists visiting our province are foreigners.

119 Example: Write numbers to represent the shaded and non-shaded part as a percentage and a fraction Shaded part Percentage: 40 percent or 40% Fraction: 40 100 Non-shaded part Percentage: 60 percent or 60% Fraction: 60 100 Exercise 2 a. Write the fraction as a percentage using the % symbol. Example 5 = 5% 100 (1) 12 = …………………………………………. 100 (2) 17 = …………………………………………. = …………………………………………. 100 = ………………………………………… (3) 20 = ………………………………………… 100 (4) 25 100 (5) 30 100 b. Write the percentages as a fraction. (1) 15 percent or ....................................................................... (2) 20 percent or .............................................................. ......... (3) 27 percent or ....................................................................... (4) 30 percent or ....................................................................... (5) 35 percent or ...................................................................... .

120 Topic 2: Relationship between fractions and percentages 2.1 Writing fractions as a percentage using the % symbol When the denominator is 100, simply write the numerator followed by the % symbol. For example, (1) 44 = 44 % 100 (2) 23 = 23% 100 When the denominator is any other number, convert it to 100 first. Then, write the numerator followed by the % symbol. For example, (1) 6 = 6 10 = 60 = 60 % 10 10 10 100 (2) 10 = 10 10 = 100 = 100 % 10 10 10 100 (3) 7 = 75 = 35 = 35 % 20 20  5 100 (4) 29 = 29 2 = 58 = 58 % 50 50 2 100 Exercise3 If an exam has a total score of 20, what is the percentage test score of each student? (1) Somchai got 15 marks or 15100 20 (2) Somsri got 18 marks or 18100 20 (3) Suchart got 17 marks or 17100 20 (4) Somsak got 20 marks or 20100 20 2.2 Writing percentages as a fraction To convert a percentage to a fraction, write it as a fraction with a denominator of 100 and reduce it to its lowest terms (if possible). For example: (1) 25 % 25 =1 = 4 100 (2) 45% 45 =9 = 20 100 (3) 30% 30 =3 = 10 100 (4) 60% 60 =3 = 5 100

121 Exercise 4 Write the following percentages as a fraction in its lowest terms (1) 5% = ___________________ (2) 25% = ___________________ (3) 22% = ___________________ (4) 98% = ___________________ (5) 45%= ___________________ (6) 87% = ___________________ Topic 3: Problem exercises for multiplication, division (rule of three) and applications Example: If there are 850 people in a village and 80% of the villagers are farmers. How many farmers are there in this village? Method 1: 80% of the villagers are farmers means 80 of 850 people are farmers. 100 This village has 80 × 850 = 680 farmers. 100 Method 2: 80% of the villagers are farmers means if the village has 100 people, there will be 80 farmers. If the village has 100 people, there are 80 farmers ” 1 person, ” 80 farmers 100 ” 850 persons, ” 80 × 850 = 680 100 Answer: There are a total of 680 farmers. Example: There are 10,500 people in Rai Som Sub-district accounting for 20% of the population of the province. How many people are there in this province? Method: The population of Rai Som Sub-district accounts for 20% of the province‟s population. That means if there are 20 people in Rai Som Sub-district, the province has 100 people. If Rai Som Sub-district has 20 people, the province has = 100 people ” 1 person, ” = 100 people ” 10,500 people, ” 20 = 100 10,500 20 = 52,500 people Answer: There are 52,500 people in the province.

122 Example: An English exam has a total of 200 marks. Orathai got 160 marks. What is the percentage of her test score? Method: From a total of 200 marks, Orathai got = 160 marks If the total would be 1 mark, ” = 160 200 ” 100 marks, ” = 160 100 % 200 = 80 % Therefore, Orathai got 80% for her English exam. Answer: 80% Example: There are 16,000 eligible voters in Kor Sub-district. If 12,000 people participate in the election, what is the percentage of the eligible voters‟ participation in the election? Method: There are 16,000 eligible voters, people participate in the election = 12,000 people 1 ”, ” = 12,000 people If there were 16,000 100 ” , ” If there were = 12,000  100 16,000 people 75% of eligible voters participate in the election. Answer: 75 % Example; A man has a net income of Baht 60,000. He has to pay income tax as follows: For the first Baht 50,000, he has to pay a tax rate of 5%. For the remaining amount, he has to pay a tax rate of 10%. Method: For a net income of Baht 60,000, the income tax is as follows: 1. For the first Baht 50,000, he has to pay tax at the rate of 5%. 2. For the remaining amount of Baht 10,000, he has to pay tax at the rate of 10%. Net income of Baht 100, income tax = 5 baht ” Baht 1, ” = 5 baht 100 ” Baht 50,000, ” = 5  50,000 baht 100 = 2,500 baht Net income of Baht 100, income tax = 10 baht ” Baht 1, ” = 10 baht 100 ” Baht 10,000, ” = 10 10,000 baht 100 = 1,000 baht He has to pay an income tax of 2,500 + 1,000 = 3,500 baht Answer: 3,500 baht

123 Exercise 5 Find the answers. (1) Winai has a net income of Baht 75,000. He has to pay an income tax as follows: a tax rate of 5% for the first Baht 50,000 and 10% for the remaining amount. How much income tax does he have to pay? (2) A refrigerator has a price tag of Baht 12,500. The seller gives a discount of 6% to customers who pay cash. If a customer pays cash for the refrigerator, how much money will the seller receive? (3) A company buys a spare part for Baht 50. It has to pay an import tax and municipal tax of 30% of the cost. If it sells the spare part for Baht 104, how much profit does the company make? (4) There are 800 students who can vote for the school captain. If 720 students participate in the election, what is the percentage of students participating in the election? (5) Orathai borrows Baht 30,000 from a bank. At the end of one year, she pays an interest of Baht 3,000. What is the percentage of the annual interest rate? (6) A company has 500 employees. 450 people are male and the remaining are female. What is the percentage of male employees? (7) A shop has 120 cassette tapes. It sells 90 of them. What is the percentage of tapes sold? (8) Suda wants to buy a house with land worth Baht 400,000. She has to place a deposit of Baht 152,000. What is the percentage of the requested deposit compared to the price? Application of percentages in trading In buying or selling things, trading businesses use several terms that we need to know: Cost price or purchase price or investment means the price you pay in order to get the item. Selling price is the price you sell the item for. This price may be higher, less or equal to the cost price. Loss is the difference between the selling price and the cost price when the selling price is less than the cost price. Profit is the difference between the selling price and the cost price when the selling price is higher than the cost price. Profit marginor loss margin is the amount of profit or loss compared to an investment of Baht 100. Cost price = Selling price - profit Selling price = Cost price + profit Profit = Selling price – cost price Loss = Cost price – Selling price Study the following statements: 1. A seller gets a profit of 5% from selling shirts. Meaning: If the seller buys the shirts for Baht 100, he gets a profit of Baht 5. Therefore, the seller sells shirts for 100 + 5 = 105 baht. 2. A seller suffers a loss of 8% from selling trousers.

124 Meaning: If the seller buys trousers for Baht 100, he suffers a loss of Baht 8. the seller sells trousers only for 100 – 8 = 92 baht. Therefore, 3. A seller gets a profit of 20% from selling oranges. Meaning: If the seller buys oranges for Baht 100, he gets a profit of Baht 20. Therefore, the seller sells oranges for 100 + 20 = 120 baht Exercise 6 Explain the following examples of profit margin and loss margin. (1) Suda gets a profit of 15% from selling a bag. What does this statement mean? .......................................................................... (2) Usa suffers a loss of 10% from selling a refrigerator. What does this statement mean? ................................................................................. (3) Udom gets a profit of 6% from selling a bicycle. What does this statement mean? ........................................................................ (4) Sakda suffers a loss of 5% from selling a car. What does this statement mean? ..................................................................... (5) Wirat gets a profit of 30% from selling pork. What does this statement mean? ........................................................................... Calculating profit margin and loss margin Calculating the profit margin or loss margin is calculating the amount of profit or loss calculated on an investment of Baht 100. The calculation is based on the cost price and the actual profit or loss on buying and selling things in our everyday life. The profit margin or loss margin must always be calculated based on the cost of Baht 100. Example: A seller buys a durian for Baht 80 and sells it for Baht 100. What is the profit margin? Method: Sell durian for 100 baht The cost price is 80 baht The profit is 100 – 80 = 20 baht Buying durian for Baht 80, the profit is 20 baht ” Baht 1, ” 20 baht 80 ” Baht 100, ” 20 100 baht = 25 baht 80 Therefore, the seller gets a profit of 25% from selling durian. Answer: 25 %

125 Exercise 7 Find the answers. (1) A dozen of pencils cost Baht 60. If the selling price is Baht 75, what is the profit or loss margin? (2) A pair of trousers costs Baht 200. If the selling price is Baht 250, what is the profit or loss margin? (3) A shirt costs Baht 150. If it can be sold for Baht 120, what is the profit or loss margin? (4) Kanda buys a bag for Baht 400 and sells it for Baht 460. What is the profit margin? (5) A plot of land costs Baht 400,000. If it is sold for Baht 350,000, what is the loss margin?

126 Lesson 5 Measurement Main content 1. Measurement of length, area, volume, capacity, weight and temperature requires attentiveness to various aspects or details such as objects to be measured and selection of the appropriate measuring tools and units of measurement. 2. Drawing or reading a map, a plan or a compass and the use of an appropriate scale will help readers to get clear and precise information. 3. A clock is an instrument used to express time in units of hours, minutes, seconds, etc. Time can be written in decimal form. The digits after the decimal mark indicate minutes with 60 minutes in each hour. 4. Money is a means of trade and exchange. Thai units of money are in Baht and Satang. A decimal mark is used to separate Baht from Satang. Expected learning outcome 1. Be able to measure length, height and distance using standard tools. 2. Be able to select the appropriate measuring tools and units to measure lengths, heights and distances of objects. 3. Be able to convert units of measurement of length, height and distance from larger units to smaller units and vice versa. 5. Be able to derive actual length, height or distance from a scaled down picture given a specific scale. 5. Be able to solve problems relating to the measurement of length, height and distance. 6. Be able to select the standard units of weights and measures that are suitable for the objects to be weighed or measured. 7. Be able to convert units of weights and measures. 8. Be able to calculate the area and perimeter of a geometric figure.

127 9. Be able to solve problems relating to finding the area of a geometric figure. 10. Be able to find the volume and capacity of a rectangle and solve problems. 11. Be able to tell the relationship between units of volume or units of capacity. 12. Be able to tell the name and the direction of each of the eight cardinal directions. 13. Be able to read and draw maps showing the locations of objects or travel plan information using scales. 14. Be able to write amounts of money in decimal form by using a decimal mark to separate the integer part from the fractional part. 15. Be able to compare amounts of money and exchange money. 16. Be able to solve problems relating to money. 17. Be able to read and record income and expense transactions. 18. Be able to measure temperature in Fahrenheit and Celsius. 19. Be able to convert units of temperature. 20. Be able to tell and write time from the clock dial and use a decimal mark to determine units of hours and minutes. 21. Be able to read timetables as well as record activities or events and specify the time when such activities or events occur. 22. Be able to convert units of time from larger units to smaller units and vice versa. 23. Be able to solve problems relating to time. 24. Be able to estimate length, area, volume, capacity, weight and time. Content scope Topic 1: Measurement of length and distance Topic 2: Weights and measures Topic 3: Measurement of area Topic 4: Measurement of volume

128 Topic 5: Direction and plan Topic 6: Money Topic 7: Temperature Topic 8: Time Topic 9: Estimation

129 Topic 1: Measurement of length and distance Measurement refers to the measuring of lengths, distances, and heights of objects using measuring tools and is based on standard units of measurement in various systems. 1. Units of length 1) Units of length in the metric system are standard units of length recognized worldwide: 10 millimetres (mm) = 1 centimetre (cm) 100 centimetres = 1 metre (m) 1,000 metres = 1 kilometre (km) Remark: The words in the brackets above are the abbreviations for those units. 2) Thai standard units of length are used only in Thailand: 12 Niew = 1 Khuep 2 Khuep = 1 Sok 4 Sok = 1 Wah 20 Wah = 1 Sen 3) Standard units of length in the British system 12 inches = 1 foot = 3 feet 1 yard 1,760 yards = 1 mile Comparison of units of length in various systems 1) The Thai system versus the metric system 25 Sen = 1 kilometre 1 Wah = 2 metres 2) The British system versus the metric system 5 miles = 8 kilometres 40 inches = 1 metre 12 inches = 1 foot = 30 centimetres

130 Length measuring tools Standard tools are metre sticks, rulers, measuring tapes, etc. Learners shall practice measuring the objects stated below by using the appropriate measuring tools. No. Objects Estimated Measured Error (cm) 10 1 The width of the front gate of a house length length (cm) The width of a window The height of a wardrobe (cm) 80 The length of a math textbook 70 2 3 4 The length of a shoe The length of a belt 5 The length of the palm 6 The length between the wrist and the 7 elbow 8 2. Selection of the appropriate tools and units to measure lengths, heights or distances In selecting the appropriate standard tools and units to measure the length, height and distance of an object, learners must know the purpose of the measurement and the size of the object to be measured. Lengths and heights are typically measured by a metre stick, a ruler, a measuring tape or a protractor, depending upon the details of the object to be measured. For example, in measuring objects with a very long distance such as a plot of land, the measuring tape is commonly used. Learners shall practice selecting the proper measuring tool to determine the distance, length or height of an object in the table below. The object to be The Length Height Distance measured measuring Unit of Unit of The measured measurement measurement 1. Football field tool Tape measure value - - …………metre(s) 2. The height of a table 3. 4. 5. 3. Conversion of units of measurement Converting between units of length, height or distance can be done in the following two ways: 3.1 Converting from larger units to smaller units such as converting the width of a classroom from 8 meters to 800 centimetres or the length of a book from 1 foot to 12 inches. 3.2 Converting from smaller units to larger units such as converting the length of a road from 6,000 metres to 6 kilometres.

131 Fill in the correct number showing the conversion between units of measurement in the table below. Inch Foot …………….. 24 …………….. 5 …………….. 72 ……………. 120 ……………. 10 Centimetre Metre Kilometre 100 …………….. 400 …………….. …………….. …………….. …………….. 20 900 6 32 …………….. ……………. 1,000 15 …………….. Yard …………….. Sen 3 50 6 125 ……………. ……………. ……………. ……………. Foot 6 …………….. ……………. 24 48 Exercise 1: Fill in the answer. 1) A piece of cloth is 6 metres and 15 centimetres long or….……………….…….centimetres long. 2) The length of a stick is 8 and a half metres which equals ……….……………........centimetres. 3) The length of a rope is 5 Wa (fathom) which can be converted to………….…..……..Sok . 4) The thickness of a book is 3 centimetres and 2 millimetres or …………….…………millimetres. 5) A road is 3 kilometres and 10 Sen (rope) long which is equivalent to ……….…Sen long.

132 6) A road‟s length of 16 kilometres is equivalent to …………….…………….……………..miles. 4. Scale In drawing pictures, shapes, heights, lengths, etc., learners may scale down such drawings by using scales. For example: The pine tree in the picture is 8.5 centimetres high. 8.5 ซc.ม. The height of the pine tree pictured is 8.5 cm m high. This means that the real pine tree is 170 cm high or 1 m 70 cm high. Scale: 1 cm: 20 cm Learners can find not only the height but also the width of an object using scales. Example: Find the length, width and height of the box below. 2 Scale: 1 cm : 2 m cm 3.5 cm 10 cm From the picture, the box is 10 cm long, 3.5 cm high and 2 cm wide. Therefore, the real size of the box is as follows: The length in the picture is 10 cm; the actual length is 10  2 m = 20 m The width in the picture is 2 cm; the actual width is 2  2 m = 4 m The height in the picture is 3.5 cm; the actual height is 3.5  2 m = 7 m

133 Exercise 2 1. Find the length, height and width of the house in the picture by using a ruler. Scale: 1 cm: 5 m 1. Measure the size of your classroom and draw a map of it below. 2. In the picture below, how far does A have to walk from his house to school? 12 cm Scale: 1 cm: 2 km 5. Problems relating to the measurement of lengths, heights and distances Sometimes in solving problems regarding the measurement of lengths, heights and distances, scale information may be given with or without a supporting picture. For example: A line is drawn between the house of Mr. Kanit and the hospital and it is 9 inches long. Given the scale of 1 inch: 5 miles, what is the distance between Mr. Kanit‟s house and the hospital? Distance: 9  5 miles = 45 miles Therefore, the distance between Mr. Kanit‟s house and the hospital is 45 miles. Answer: 45 miles.

134 Exercise 3 1. If a 2 cm line is drawn to represent a wooden stick which is 6 m long, what is the scale used? 2. A classroom is 9 m wide and 15 m long. If the picture of such a classroom is 3 cm wide and 5 cm long, what is the scale used? 3. A line is drawn between the police station and the school and its length is 18 cm. Given the scale of 1 cm: 3 km, what is the real distance between the police station and the school? Topic 2: Weights and measures 2.1 Weights Weights refer to the measurement of the mass of human beings, animals and objects by using different types of weighing scales that are suitable for objects to be weighed. 2.1.1 Weighing scales can be divided into five types as follows: 1) Spring scale that is commonly known as “Kilo Scale” and used by vendors in the market. 1.1 Numbers around the dial indicate units of measurement in kilograms. The numbers 1-15 mean that the scale can weigh up to 15 kilograms. There are 10 small marks (“Kheet” in Thai) in each interval of 1 kilogram. The interval between each small mark represents 100 grams. 1.2 The weighing pan on the scale is used to support an object to be weighed. When the object is put on the pan, the pan will be pressed down and the pointer will point to the number indicating the weight of the object. 2) Large-size scale This type of scale is commonly used in wholesale stores, train stations or rice mills and there are different types of such scales. One of the most common types is “platform scale or balance scale” as shown in the picture. This type of scale is used to weigh very heavy objects such as sacks of rice or large baskets of goods.

135 3) Bathroom scale A bathroom scale is another type of spring scale used to measure the body weight of human beings. It has a dial on top of the scale and a platform for a person to step on and read the weight information from the dial. Normally, when the scale is not used, the hand will reset to “0”. To use the scale, a person must take off one‟s shoes before stepping on the platform and must stand straight without holding on to anything and read the number which the hand points to. 4) Equal-arm beam scale with two weighing pans Type A Type B This beam scale applies the concept of the balance of two arms of the lever with a pivot in the middle. The Type A scale is commonly used in pharmacy practice or used for weighing chemical substances. To weigh an object, place the object to be weighed in one of the weighing pans. People commonly place the object to be weighed on the left pan and a counterweight on the other pan. When the lever is balanced, the hand will point to the line in the center of the dial. Then, the weight of the object will be determined from the number of the counterweights used. The Type B scale is commonly used in gold, pink gold, silver or high value item shops. This scale is highly sensitive as it must be very precise and accurate. Thus, it is usually placed in a glass cabinet to be protected from wind.

136 5) Unequal arm scale This scale applies the concept of the balance of the lever that sticks out. To weigh an object, place the object to be weighed on the weighing pan on the right. Then, move the bracket that is tied to the lever to the left until the balance of the lever is achieved or the lever remains flat in the horizontal position. If, after being moved to the end of the lever arm balance is still not achieved, attach an additional counterweight (which comes in different sizes) to the pendulum that hangs to the left. This scale is a medium-size scale and can measure up to around 100 kilograms. 2.1.2 How to read a weighing scale Weight The weight indicated Read as by the pointer 2 kg and 2 marks 2 kilograms and 200 (Kheet) grams 3 kg and 5 marks 3 kilograms and a half (Kheet) or 3 kilograms and 500 grams

137 In reading a weighing scale, the previous section mentions that the number in the dial indicates the number of kilograms. The marks (Kheet) in each interval of 1 kilogram indicate units of grams. As there are10 marks (Kheet) in each interval of 1 kilogram, each mark (Kheet) represents 100 grams. When placing an object on the weighing pan, the weight of the object will be determined from the number which the hand points to. For example, in weighing a chicken, if the hand points to the 2nd mark (Kheet) after number 2, the weight can be read as 2 kilograms and 200 grams. Exercise 4 a. Read the weight shown on the weighing scale and fill in the answer in the table below. Weight The weight indicated by Read as the pointer (1) ............................................ .......................................... (2) ............................................ ............................................ (3) .................................................... .............................................. (4) ..................................................... .............................................. (5) ...................................................... ................................................

138 b. Select the appropriate weighing scale for each item specified below. Picture 1 Picture 2 Picture 3 Picture 4 (1) Comparison of the body weight of boxers (2) Bear‟s gall-bladder (3) 5 sacks of soybeans (4) 1 letter (5) 1 basket of kales (6) 20 oranges (7) 1 bracelet made of pink gold (8) 1 bucket of washing powder (10) The youngest (9) 30 crates of fish cans daughter 2.1.3 The standard units of measurement of weight in the metric system are as follows: 1. The official units of measurement used by government authorities: 1,000 grams equals 1 kilogram (kg) 1,000 kilograms equals 1 metric ton 2. The commercial units of measurement used generally by the market: 1 kilogram equals 1,000 grams 1 kilogram equals 10 Kheet (hectogram) 1 Kheet equals 100 grams (g) 3. Units of weight of valuable metal such as gold, pink gold and silver: 1 baht equals 15 grams The abbreviations for kilogram and gram are “kg” and “g” respectively. The local word “Kheet” is widely used in the local market while “gram” is the official term used by government authorities. We can compare units of weight by using the data mentioned above. Problem exercises Problems related to weight, price and comparison of weights of objects can be solved through a combination of calculation methods, i.e. addition, subtraction, multiplication and division. Examples are as follows:

139 Example: Yodrak and Yodchai weigh 65 kilograms and 58 kilograms respectively. Who is heavier and by how much? 65 - kilograms Method: Yodrak weighs 58 kilograms Yodchai weighs Therefore, Yodrak is heavier by 7 kilograms Answer 7 kilograms Example: Mr. Chumpol sold 2 metric tons 480 kilograms and 500 grams of soybeans. He subsequently sold 3 metric tons 930 kilograms and 750 grams of soybeans. Please determine the total weight of soybeans sold by Mr. Chumpol. Method: metric ton kilogram gram First sale of soybeans 2 480 500 Second sale of soybeans 3 930 750 5 1,410 1,250 Or = 6 411 250 Answer: 6 metric tons 411 kilograms and 250 grams Analysis To convert smaller to larger units: 1. Add the number of weight units in grams together as follows: 500 + 750 =1,250. Then, convert grams to kilograms as follows: 1 kilogram and 250 grams. 2. Add the number of weight units in kilograms as follows: 480 + 930 = 1,410. Then, add 1 kilogram to 1,410 kilograms which equals to 1,411 kilograms. Convert kilograms to metric tons as follows: 1 metric ton and 411 kilograms. 3. Add the number of weight units in metric tons as follows: 2 + 3 + 1 (converted from kilograms = 6 metric tons. 2.2 Measures Measures refer to the measurement of the quantities or capacity of objects using measuring tools that are suitable for the objects of which the quantities are to be measured. 2.2.1 Types of measuring tools Measuring tools are divided into two categories: 1) Non-standard measuring tools: Any objects which are customized for use by people according to their functional requirements such as buckets, dippers, glasses, spoons, etc. Use of non-standard measuring tools may cause misunderstanding. Thus, they are not commonly used for measuring things. Pictures of non-standard measuring tools

140 2) Standard measuring tools: Tools recognized by government authorities as they each have equal measures such as beakers, litre containers, measuring cups and measuring spoons. Pictures of standard measuring tools 2.2.2 There are several methods for measuring quantities, depending upon the characteristics of the objects to be measured. 1) Method for measuring quantities of liquid such as water and oil: Fill the measuring container to the brim without spilling the content or leaving the container partly empty. Tools for measuring quantities of liquid objects 2) Method for measuring quantities of small, fine objects such as grains of rice, powder, sugar and salt: Fill the measuring container to the brim.

141 Tools for measuring quantities of dry, fine objects Fill the container until the object is higher than the brim  Use a stick to scrape off the excessive amount until the content is full to the brim  Get the measuring details as required 3) Method for measuring quantities of coarse objects such as coal, truffle and water chestnut: Fill the measuring container until the object is higher than the brim to compensate for empty spaces left in the container. Tools for measuring quantities of dry objects: 2.2.3 Units of measures categories: Standard units of measures can be divided into the following 2 1) Units under the international standard systems: There are several systems of measures such as the British system (ounce and gallon), the Thai system (Kwian, Thang, litre) and the metric system (litre, millilitre or cubic centimetre). The Metric system is the most widely used system in the world and is recognized by government authorities as the standard system. A “litre” is the standard unit for liquids. 2) Units commonly used by Thai people in daily life: Millimetre, litre, Thang, Kwian, measuring cup, table spoon and tea spoon. Comparison of different units is as follows: 1 litre (l) 1,000 millilitres (ml) = 20 litres = 1 Thang 100 Thang = 1 Kwian 1 measuring cup = 8 ounces or 16 table spoons 1 tablespoon = 3 teaspoons 1 millilitre = 1 cubic centimetre (cc)

142 Remark: The words in the brackets above are the abbreviations for those units. We can compare units of measure by using the data mentioned above as follows: Example: 3 teaspoons = 1 tablespoon 6 teaspoons = 16 tablespoons = 2 tablespoons 1,000 millilitres = 1 measuring cup 4,000 millilitres = 1 litre 7,500 millilitres = 4 litres 7 and a half litres or 20 litres = 7 litres 500 millilitres 50 litres = 1 Thang 75 litres = 2 and a half Thang or 2 Thang and 10 litres Problem exercise 200 Thang = 3 Thang and 15 litres 650 Thang = 2 Kwian 3,000 cubic centimetres = 6 and a half Kwian or 6 Kwian and 50 Thang = 3 litres 600 cubic centimetres = 600 millilitres Example: Mr. Somchok sold 11 Kwian and 80 Thang of rice. Mr. Somchai sold 16 Kwian and 15 Thang of rice. How many units of rice did Mr. Somchok sell less than Mr. Somchai? Method: Kwian Thang Kwian Thang Rice quantity sold by Mr. Somchai 16 15 15 115 Rice quantity sold by Mr. Somchok 11 80 11 80 - Therefore, Mr. Somchok sold less rice than Mr. Somchai by 4 35 Answer: 4 Kwian and 35 Thang Example: To fill 100-milliltre bottles with 30 litres of fish sauce, how many bottles are needed? 1 litre = 1,000 millilitres Method: 30 litres = 1,000 × 30 millilitres Therefore, 30 litres of fish sauce = 30,000 millilitres Each bottle has a capacity = 100 millilitres The number of bottles needed= 30,000 ÷ 100 = 30,000 ÷ (10 × 10) = (30,000 ÷ 10) ÷ 10 = 3,000 ÷ 10 = 300 bottles Answer: 300 bottles

143 Measures 1. Measures refer to the determination of quantities or capacity of objects by using measuring tools. Standard measuring tools are litre containers, beakers, measuring cups and measuring spoons. The standard unit of measure is a litre. Units of measures widely used in our country are millilitre, Thang, Kwian, tablespoon, teaspoon and cup. 2. Measuring methods: In case of liquid objects, fill the measuring container to the brim. As for small, fine objects, fill the measuring container to the level above the brim and scrape off the excessive amount. As regards, coarse objects, fill the measuring container to the level above the brim. Remark: The divisor is 100 which can be rewritten as 10 × 10. Then, divide the dividend by each of the two tens. As the dividend has a trailing zero and the divisor is 10, we can remove the zero from both the dividend and the divisor to yield a quotient. In this case, as the divisor is 100 and the dividend has several trailing zeroes, we can remove two trailing zeroes from the dividend to yield a division result. Exercise 5 a. Fill in the proper symbol (>, < or =) in the . (1) 20 litres of rice  1 Thang of rice (2) 1 litre of water  1 glass of water (3) 1 cup of sugar  1 litre of sugar (4) Half Thang of rice  15 litres of rice (5) 4 Thang of beans  40 litres of beans (6) 4,000 millilitres of water  4 litres of milk (7) 3 Kwian (cart) of green beans  250 Thang of peanuts (8) 1,800 millilitres of corns  2 Thang of corns b. Estimate the amount of the following objects with your eyes and use the standard measuring tools to measure the amount thereof as well as record the data in the table below. No. Name of object Estimated Actual Error 1 1 can of water amount amount 1 litre 1 dipper of rice 1 can of gravel 5 litres 6 litres 1 glass of water 2 3 4 1 bucket of rice 1 bag of sand 5 1 bowl of chaff 6 1 milk can of saw dust 7 8

144 Remark: Dippers, cans, glasses, buckets, bags, large bowls and jugs may come in different sizes. Apart from litres, other standard measuring tools may also be used. c. Answer the following questions without demonstrating the calculation. (1) To fill 2 litres of vegetable oil in 500-millilitre bottles, how many bottles are needed? (2) To pack one Thang (tank) of salt in 2-litre bags, how many bags are needed? (3) Auntie Si has been prescribed a liquid medicine to relieve her stomach ache (stomachic mixture). She has to take 1 tablespoon of medicine 3 times a day. How many tablespoons would she take over a period of 5 days? (4) 4 litres of green beans are worth 20 baht. How much will one Thang (tank) of green beans cost? (5) 3 Thang (tank) of green beans are bought, each of which costs 60 baht. If we boil these beans for sale at 4 baht per litre, how much profit or loss will we make on the beans? (6) 8 litres of oil are bought at 32 baht total. How much does 1 litre of oil cost? (7) A 1-litre bottle is filled up with soft drink. After filling up 3 glasses (each of which has equal capacity), 100 millilitres of soft drink is still left in the bottle. What is the capacity of each glass? d. Please show the calculation for the following cases: (1) If one bag of sugar has a capacity of 2 litres and 200 millilitres, please determine the total capacity of 5 bags of sugar, each of which has the same capacity. (2) If we need to pour a 15-litre bucket of water into a jar 20 times in order to fill it up, how many litres of water does this jar hold? (3) If each bottle of liquid medicine contains 400 millilitres of medicine, please determine the total amount of the medicine in 9 bottles. (4) If we need to use 6 Thang (tank) of rice and we already have 3 Thang and 7 litres of rice in stock, how many more units of rice do we need? (5) Given that each Thang (tank) of rice costs 70 baht and each litre of rice costs 4 baht, if we want to buy 1 Thang of rice, should we buy it in litre or in Thang to get the cheapest price? How much cheaper is one than the other? (6) Given that 1 Kwian (cart) of paddy rice can yield 55 Thang (tanks) of milled rice, if a farmer wants to mill 8 Kwian of paddy rice, how many Thang of milled rice will he get? Topic 3: Measurement of area 3.1 Measurement of the area and perimeter of a two-dimensional geometric shape 1) We can measure an area by counting the number of squares or the number of units therein. If each side of the square is 1 unit long, the square area size is 1 square unit.

145 A 1 unit B 1 cm 1 unit 1 cm Each side of Square A is 1 unit long. Thus, the area size of Square A is 1 square unit. Each side of Square B is 1 cm long. Thus, the area size of Square B is 1x1 = 1 square centimetre. Example: What is the size of the shaded area? Answer: The number of squares in the shaded area is 16. So the area size is 16 square units. Example: Find the area size of Triangle ABE and Rectangle ABCD by counting the number of rectangle units. D EC 3 2 units 44 2 31 4 A 4 units B

146 Answer: The area size of Rectangle ABCD = 8 square units. The area size of Triangle ABE = 4 square units. Note that Rectangle ABCD has a base length of 4 units and a height or width of 2 units. Thus, the area size equals 4 units 2 units = 8 square units. Formula: The area of a rectangle = Length  Width b. Find the area size of the following rectangles by using the formula: (1) 2 metres (2) 2 metres 1.5 metres 2 metres 3.2 Problem exercises relating to measurement of the area of a geometrical shape The formulas commonly used for solving problems relating to measurement of the area of a geometrical shape are as follows: Area of a square = side x side Area of a rectangle = width x length Area of parallelogram = base x height Area of a trapezoid = 1 x height x sum of lengths of 2 parallel sides Area of a triangle = 1 x base x height 2 Example: A plot of land has the shape of a rectangle with a width of 6 metres and a length of 12 metres. What is the area size of this piece of land? Method: The formula for finding the area of a rectangle = width x length = 6 m x 12 m = 72 square metres Therefore, the size of the land is 72 square metres. Answer: 72 square metres Remark: A square metre can also be expressed in the form of m 2 . Exercise 6 1. Find the area size of the following four-sided shapes: 1.1 A square with each side 7 cm long 1.2 A rectangle with a length of 5 cm and a width of 3 cm 1.3 A parallelogram with a base length of 10 metres and a height of 5 metres

147 2. Find the area size of the following triangles: 2.1 A triangle with a base length of 10 metres and a height of 5 metres 2.2 A triangle with a base length of 6 cm and a height of 5 cm 2.3 A triangle with a base length of 10 cm and a height of 8 cm 3. Given a piece of paper in the shape of a square with each side 10 inches long, if we cut the paper into small rectangular pieces of equal sizes, each of which has a base length of 5 inches and a height of 8 inches, how many rectangles do we get? 4. A classroom is 5 metres wide and 12.5 metres long. If we have a carpet with a width of 2.5 metres, determine the length of the carpet to make it fit the classroom. 5. Mr. Kanit wants to make a plot of vegetable plants in the shape of a rectangle with a length of 10 yards and a width of 2 yards and 2 feet. How many square feet is the plot? Topic 4: Volume and capacity 4.1 Measurement of the volume and capacity of a cuboid and problem solving 1.1 Volume is the capacity of a three-dimensional shape. To measure the volume of a three-dimensional shape, we use the unit of measurement called cubic unit. 1.2 Capacity is the volume of a particular container. 1 unit A cuboid with the width, length and height of an 1 unit equal size of 1 unit has the volume of 1 cubic unit. 1 unit The formula for finding the volume is as follows: Formula: The volume of a cuboid = width × length × height Or = Base area × height The volume of cube above = 1×1× 1 = 1 cubic unit (If the unit of length is metre, the unit of volume will be cubic metre.) Example (1) Find the volume of a cuboid with a width of 3 metres, a length of 4 metres and a height of 2 metres. Method: Volume = width × length × height = 3×4×2 = 24 cubic metres (2) Find the volume of a milk box with a width of 3 inches, a length of 5 inches and a height of 6 inches. = width × length × height Method: Volume = 3×5×6 = 90 cubic inches

148 Exercise 7 Answer the following questions and show the calculation method: 1. Determine the capacity of a swimming pool with the shape of a cuboid with a width of 10 metres, a length of 15 metres and a depth of 1.5 metres. 2. Cut wood into small cubes with each side 10 cm long. Determine the volume of each cube. 3. A round steel bar has the volume of 500 cubic centimetres. If it is cut into small 5 pieces of equal size, determine the volume of each piece. 4. Determine the capacity of a warehouse with a length of 7 metres, a width of 5 metres and a height of 4 metres. 5. Determine the volume of a 3 metre pole in the shape of a square with each side 20 centimetres wide. 4.2 Relationship between units of volume or units of capacity Capacity is the volume of a container. We measure the volume of a container by filling up the container with the object. If we know the volume of the object, we will be able to determine the capacity of that particular container by using the following ratios for comparison: 1 litre = 1000 millilitres 1 millilitre = 1 cubic centimetre 1,000,000 cubic centimetres = 1 cubic metre 1 cup = 240 millilitres 1 tablespoon = 15 millilitres 1 Thang = 20 litres 1 Thang = 15 kilograms 1 Kwian = 100 Thang 1 Kwian = 200 litres Example: A tank having the shape of a cube is filled up with water to the brim. The tank is 40 cm long, 20 cm wide and 30 cm tall. Determine the capacity of the tank in litres. Method: The volume of a cube = width x length x height = 20 x 40 x 30 = 24000 cc 1 cc of water = 1 millilitre 24000 cc of water = 24000 millilitres 1000 millilitre of water = 1 litre Therefore, the volume of the tank = 24000 = 24 litres Answer: 24 litres 1000 Exercise 8 1. Determine how many measuring cups are needed for 2000 millilitres of sugar given that each cup has a capacity of 500 millilitres. 2. A jug can contain up to 3 litres of water. Determine the capacity of the jug in millilitres. 3. A can is filled up with water and the volume of the water is 10 litres. Determine the volume of this can in cubic metres.

149 4. A bucket can carry up to 5 Thang of rice. Determine the volume of this bucket in cubic centimetres. Topic 5: Direction and plan 5.1 Name and direction of the eight cardinal directions There are four key cardinal directions, i.e. north, south, east, and west. The sunrise direction is called east and the sunset direction is called west. If we stand facing east, our left will be north and our right will be south. North West East South In addition to the four key cardinal directions, there are four other non key cardinal directions with specific names, i.e. northeast, southeast, northwest and southwest. These are the eight cardinal directions as shown in a figure below. North (Udon) Northwest Northeast (Phayub) (Issan) West East (Prajim) (Burapa) Southwest Southeast (Horradi) (Arkaney) South (Taksin) 5.2 Reading and drawing a plan A plan involves a scaled down or scaled up picture that shows the size and direction of the place or object it represents. The scale will be marked and an arrow pointing to the north will be marked with “N”.

150 Example: Mr. Wichit‟s travel plan from home to school 7 School N centimeters 5 centimeters 2 Wichit‟s centimete Kaewta‟s scale 1 cm. : 100 house rs house meters From the plan, we know a lot of information such as: 1. Wichit‟s house is located to the west of Kaewta‟s house. 2. Kaewta‟s house is located to the south of the school and it is at the corner of the road. 3. The school is located to the northeast of Wichit‟s house. 4. Wichit‟s house is located 7 centimetres away from the school on the plan, which is 700 metres in actual distance (scale 1 cm. : 100 metres)ใ 5. Kaewta‟s house is located 2 centimetres away from Wichit‟s house on the plan, which is 200 metres in actual distance. 6. Kaewta‟s house is located 5 centimetres away from the school on the plan, which is 500 metres in actual distance. When drawing a plan, the actual size of the object must be known and the size of the plan must be known so as to be able to determine the suitable scale to be used. Thereafter, it will be easy to make calculations for a precise drawing of the plan. Example: Draw a plan for an office which is 8 meters long and 6 meters wide. Given that the desired scale is 1 centimetre is equal to 1 metre, place a table which is 1 metre wide and 1 metre long in the middle of the room. 8 cm 1 cm 6 cm scale 1 cm : 1 m