1. Measurement Measuring Length, Capacity, Weight Conversion of Units Involving length By Mr. Gerzon B. Mascariñas

2. Math Prayer Dear Lord, May we add purity to the world. Subtract evil from our lives. Multiply good works for your son, Jesus. Divide our gifts and share them with others. Amen.

3. Objectives: Trace the history and development of measurement. Name instrument used in measuring length. Distinguish the appropriate units used in measuring. Convert one unit of measurement to another using dimensional analysis. Solve real-life problems involving measurement.

4. Concept Map Mathematics Quantitive (in nature) Measurement Dev’t Units Instruments English Metric (SI) Nature Standard

5. Have you ever imagined yourself living in a world where there is no common understanding of how long a certain is? Or how heavy a certain object is? Or maybe how brief a certain instance is? What do you think would life be without standard measurement?

6. History of Measurement Early human beings – made use of the parts of the human body for measuring. 1. Span It is the distance from the tip of the little finger to the tip of the thumb of an outstretched hand. 2. Palm It is the distance across the base of the four fingers that form the palm.

7. 3. Digit It is the thickness or width of the index finger. 4. Foot It is the length of a foot. 5. Cubit It is the distance from the tip of the middle finger of the outstretched hand to the front of the elbow. 6. Pace It is the distance of one full step.

8. The body measures depend upon the person who is performing the measuring. Hence, different persons have different lengths of arms and hands.

9. The English System of Measurement Different systems for the same purpose developed and became established in different parts of the world. Through royal decrees, England was able to standardized its system of units of measurement.

10. King Henry I – decreed that a yard was a distance from his nose to the end of his thumb on his outstretched hand. Queen Elizabeth I – changed the measure of the mile from 5,000 feet to 5, 280 feet

11. Familiar Units in the English System Length 12 inches = 1 foot 3 feet = 1 yard 5 feet= 1 pace 5, 280 feet = 1 mile 220 yards= 1 furlong 8 furlongs= 1 mile 125 paces = 1 furlong

12. Weight 16 ounces=1 pound 2, 000 pounds=1 ton Capacity 3 teaspoons=1 tablespoon 16 tablespoon=1 cup 8 ounces=1 cup 2 cups=1 pint 2 pints=1 quart

13. Customary Length 12 inches (in) = 1 foot (ft) 36 inches = 3 feet or 1 yard (yd) 5,280 feet = 1 mile (mi) To change from a larger unit of measure to a smaller unit, MULTIPLY. To change from a smaller unit of measure to a larger unit, DIVIDE. Copy this in your booklet page 12

14. Customary Length A mile is about half the length of Talladega Super Speedway. Talladega is 2.9 miles long. Talladega Super Speedway This represents about 1 mile.

15. Customary Length A yard is about the length of a walking stick.

16. A foot is about the length of a floor tile.

17. An inch is about the length of a drink bottle top.

18. Customary Capacity 4 quarts = 1 gallon (gal) 2 pints = 1 quart (qt) 2 cups = 1 pint (pt) 8 fluid ounces (fl oz) = 1 cup (c) To change from a larger unit of measure to a smaller unit, MULTIPLY. To change from a smaller unit of measure to a larger unit, DIVIDE. Copy this in your booklet page 12

19. Customary Capacity 1 gallon

20. Meet Mr. Gallon 4 quarts

21. Meet Mr. Gallon 8 pints

22. Meet Mr. Gallon 16 cups

23. Customary Weight 16 ounces (oz) = 1 pound (lb) 2,000 pounds = 1 ton (T) To change from a larger unit of measure to a smaller unit, MULTIPLY. To change from a smaller unit of measure to a larger unit, DIVIDE. Copy this in your booklet page 12

24. Customary Weight A small car weighs about a ton.

25. A bag of coffee weighs about 1 pound.

26. An ounce weighs the same as 8 nickels.

27. The Metric System of Measurement During the French revolution, a group of French scientists thought of creating a more simplified system of measurement that would provide convenience converting from smaller or larger version of the unit. The International Metric System was developed and introduced in Europe in the times of Napoleon Metric system is a “base-10” or “decimal system”.

28. The Metric System of Measurement Metric system uses prefixes to indicate units larger or smaller than a given base unit. Each prefix is a multiple of 10. Prefix is a word or letter written in front of a basic metric unit to specify the fraction or multiple of the unit

29. The following table shows some examples of these units 10001001010.10.010.001 PrefixesKilo(k)Hecto(h)Deca(da)Basic UnitDeci(d)Centi(c)Milli(m) LengthkmhmdamMetre (m)dmcmmm MasskghgdagGram (g)dgcgmg CapacityklhldalLitre (l)dlclml 29 PrefixesSymbol NameEquivalence Kilok thousand 1, 000 Hectoh hundred 100 Decada ten 10 Decid One-tenth 0.1 Centic One-hundredth 0.01 Millim One-thousandtth 0.001

30. SI Prefixes PrefixesSymbol NamePower of Ten PrefixesSymbol NamePower of Ten yottaY Septillion 10 24 decidtenth10 -1 zettaZ Sextillion 10 21 centic hundredth 10 -2 exaE Quintillion 10 18 millim Thousandth 10 -3 petaP Quadrillio n 10 15 micro μ Millionth 10 -6 teraT Trillion 10 12 nanon Billionth 10 -9 gigaG Billion 10 9 picop Trilllionth 10 -12 megaM Million 10 6 femtof Quadrilliont h 10 -15 kiloK Thousand 10 3 attoa Quintillionth 10 -18 hectoH Hundred 10 2 zeptoz Sextillionth 10 -21 decadaTen10 1 yoctoy Septillionth 10 -24 One10 0 One10 0

31. Metric Units – Length, Distance m The base unit for measuring distance is the metre (m) We use metres to measure: The height of a door The length of a corridor The length and width of a room

32. Metric Units – Length, Distance kmm We use kilometres (km) for longer distances, such as: The distance between cities (for example, between Madrid and Barcelona, or Manchester and Leeds) The distance to the next services on the motorway The distance from the Earth to the moon (400 000 km)

33. Metric Units – Length, Distance kmmmm We use millimetres (mm) for very small things: The thickness of a coin The diameter of a screw

34. Metric Units – Weight/Mass g The base unit for measuring weight is the gram (g) A sugar cube weighs a few grams We use grams to weigh sliced ham (200 g)

35. Metric Units – Weight/Mass kgg A more familiar unit for weight is the kilogram (kg): A bag of sugar weighs 1 kg A normal wash-load is 1.5 kg My weight is about 81 kg

36. Metric Units – Weight/Mass kggmg We use milligrams (mg) for very small things: The amount of paracetamol in a tablet

37. Metric Units – Capacity/Volume l The base unit for measuring distance is the litre (l) A large bottle of Coke contains 2 l: The petrol tank of an average car holds 40 l

38. Metric Units – Capacity/Volume kll Kilolitres (kl) are rarely used in everyday life The capacity of a swimming pool could be measured in kl but is more commonly measured in thousands of litres instead

39. Metric Units – Capacity/Volume kllml A teaspoon is about 5 ml A can of coke is bout 330 ml

40. Metric Units – Capacity/Volume kllclml A bottle of wine is 75 cl A drinking cup (paper) is about 20 cl

41. The International System of Measurement The International Bureau of Weights and Measures in France works in the development and improvement of the metric system. In 1960, the General Conference on Weights and Measures adopted the modernized metric system and called it Le Systeme International d’Unites (International System of Units) or SI

42. Book Exercises Answer Vocabulary and Concepts, Practice and Application I, II AND III on pages 23 – 24.

43. Answer Key: Vocabulary and Concepts: 1.i 2.h 3.g 4.j 5.f 6.d 7.a 8.b 9.c 10.e

44. Practice and Application I.Complete each of the following. 1.1 kiloliter =___ liter___ 2.1 dekaliter=___ liter___ 3.1 hectometer =___ meter___ 4.1 centiliter=___ liter___ 5.1 milliliter=___ liter___ 6.1 decimeter=___ meter___

45. The prefix kilo indicates 1,000.prefix 1 kiloliter = 1 x 1,000 liters = 1,000 liters

46. The prefix deka indicates 10.prefix 1 dekaliter = 1 x 10 liters = 10 liters

47. The prefix hecto indicates 100.prefix 1 hectometer = 1 x 100 meters = 100 meters

48. The prefix centi indicates 0.01.prefix 1 centiliter = 1 x 0.01 liter = 0.01 liter

49. The prefix milli indicates 0.001prefix 1 milliliter = 1 x 0.001 liters = 0.001 liters

50. The prefix deci indicates 0.1.prefix 1 decimeter = 1 x 0.1 meter= 0.1 meter

51. Answer Key: II. 7.10 8.0.1 9.100 10. 1000 11. 10 12. 10

52. Answer Key: III. 13. 0.33 14. 3,300 15. 0.0033 16. 0.033 17. 330 18. 33

53. Essay Writing 1.In the metric system, a prefix is used to relate each unit to a basic unit. Discuss how the decimal place-value positions are related to metric prefixes. 2.Describe advantages of the Metric system over the English system.

54. Class Activity Find the measure of each item in the leftmost column using the indicated units of measurement and measuring instrument and record the results. Units of Measurement/ Measuring Instrument ItemSpanRuler (cm)Meterstick (m) 1. Width of the teacher’s table 2. Height of the student’s chair 3. Width of the door 4. Height of blackboard 5. Length of the classroom

55. Converting Measurements Dimensional analysis – a method of calculating that uses numbers in the form of fractions, which enables us to convert from one type of unit to another. It consists of three components: The given unit, The desired unit, The conversion factor

56. Example: Suppose the black board is 4 meters long. You want to find its length in centimetres. The given unit - meter The desired unit - centimeter The conversion factor - 100 cm = 1 m 1 m 100 cm

57. 4 m x = Note that we can cancel units when multiplying fractions since they behave like numbers. 4 m x = 400cm

58. Rules in Changing Units 1.To change from a larger unit to a smaller unit, multiply. 2.To change from a smaller unit to a larger unit, divide.

59. Examples: 1.Convert 5.237 dam to cm. The given unit, The desired unit, The conversion factor 1 dam = 1,000 cm Solution: 5.237 dam x = 5.237 x 1,000 cm = 5, 237 cm

60. Examples: 2. Convert 750 mm to m. The given unit, The desired unit, The conversion factor 1 m = 1,000 mm Solution: 750 mm x = 750 m 1,000 = 0.75 m

61. We are going to use our knowledge about multiplying and dividing by 100 to convert centimetres to metres and to convert metres to centimetres.

62. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 427000 ÷100 This is how we change 427cm into metres:-

63. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 427000 ÷100 This is how we change 427cm into metres:-

64. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 42700 ÷100 This is how we change 427cm into metres:-

65. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

66. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

67. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

68. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

69. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

70. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

71. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

72. There are 100 centimetres in 1 metre When we change from cm to m we divide by:- Remember! When we divide by 100 the units move two places to the right. HTUthhthth 4270 ÷100 This is how we change 427cm into metres:-

73. Therefore:- 427cm = 4.27m HTUthth 326 HTUth 326 HTUth 476 HTUth 1653 HTUth 0476 HTUth 1653 ÷100 ÷100 ÷100 cm m

74. 354cm15.4cm779cm52.4cm939cm395cm25.8cm 3.54m 0.154m 7.79m 0.524m 9.39m 3.95m 0.258m ÷100 Convert from centimetres to metres

75. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

76. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

77. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

78. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

79. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

80. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

81. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

82. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

83. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

84. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m =

85. To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- HTUthth 351 3.51m = 351cm

86. 5.4m6.2m12.7m3m7.6m0.54m0.3m 540cm620cm1270cm300cm760cm54cm30cm x100 Try changing these measurements in metres into centimetres

87. Approximate English and Metric Equivalents 1 inch (in.)= 2.54 centimeters (cm) 1 foot (ft.)=30.48 centimeters(cm) 1 yard (yd.)=0.9 meter (m) 1 mile (mi.)=1.6 kilometers (km) Convert the following: a.15 inches to centimeters b.138 miles to kilometers c.35,400 millimeters to inches

88. English System 12 inches (in.)= 1 foot (ft.) 3 feet (ft.)=1 yard (yd) 36 inches (in.)=1 yard (yd) 5, 280 feet (ft.)=1 mile (mi.) 1,760 yards (yd.)=1 mile (mi.) Convert the following: a.45 inches to feet b.15,400 feet to miles c.16 inches to yards

89. KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit CENTI 0.01 Unit MILLI 0.001 Unit Meters Liters Grams Ladder Method How do you use the “ladder” method? 1 st – Determine your starting point. 2 nd – Count the “jumps” to your ending point. 3 rd – Move the decimal the same number of jumps in the same direction. 4 km = _________ m 1 2 3 How many jumps does it take? Starting Point Ending Point 4. 1 __. 2 3 = 4000 m

90. Try these conversions using the ladder method. 1000 mg = _______ g 1 L = _______ mL160 cm = _______ mm 14 km = _______ m109 g = _______ kg 250 m = _______ km Conversion Practice Compare using, or =. 56 cm 6 m 7 g 698 mg

91. Write the correct abbreviation for each metric unit. 1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____ 2) Meter _____ 5) Millimeter _____ 8) Centimeter _____ 3) Gram _____ 6) Liter _____ 9) Milligram _____ Try these conversions, using the ladder method. 10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm 11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km 12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg 13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm 14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g Metric Conversion Challenge

92. Compare using, or =. 25) 63 cm 6 m 27) 5 g 508 mg 29) 1,500 mL 1.5 L 26) 536 cm 53.6 dm 28) 43 mg 5 g 30) 3.6 m 36 cm

93. Problem Solving 1.My grandparents walk 1.5 kilometers every morning. What is the total distance that they walk in meters? 2. The speed limit in many subdivisions is 30 kph. How many miles per hour is this? 1 mile = 1.6 km

95. Quiz # 1July 2, 2012 I.Identification 1.What did the early civilizations use in measuring? 2.It is the distance across the hand from the tip of the thumb to the tip of the little finger of an outstretched hand. 3.What is the metric system’s basic unit of length? 4.Who was the king of England decreed that a yard was the distance from the tip of his nose to the end of his thumb on his outstretched hand.

96. 5. It is a word or letter written in front of a basic metric unit to specify the fraction or multiple of the unit. 6. How many meters in 1 micrometer. 7. What is the value of hecto? 8. Which metric unit of measure is most appropriate to use in measuring the length of a chalk? (e.g. 12 ___long) 9. What is the basic unit of weight? 10. What is the basic unit of capacity/volume?

97. II. Computation Convert the given measurement to the unit indicated. 1.48 dm to km 2.12 dam to m 3.18 m to ft. 4.160 in. to hm 5.3.54 yrd to mi.

98. III. Problem Solving 1.Express 86 kilometers per hour in miles per hour. 2. A notebook is 0.37 decimeters thick. How thick is the notebooks in millimeters?

99. Quiz # 1Answer Key I.Identification 1.What did the early civilizations use in measuring? Ans: Natural measures or body parts 2.It is the distance across the hand from the tip of the thumb to the tip of the little finger of an outstretched hand. Ans: span or dangkal

100. 3.What is he metric system’s basic unit of length? Ans: meter 4.Who was the king of England decreed that a yard was the distance from the tip of his nose to the end of his thumb on his outstretched hand. Ans: King Henry I

101. 5. It is a word or letter written in front of a basic metric unit to specify the fraction or multiple of the unit. Ans: Prefix 6. How many meters in 1 micrometer. Ans: one-millionth meter or 0.000001 meter 7. What is the value of hecto? Ans: 100

102. 8. Which metric unit of measure is most appropriate to use in measuring the length of a chalk? (e.g. 12 ___long) Ans: cm or centimeter 9. What is the basic unit of weight? Ans: gram 10. What is the basic unit of capacity/volume? Ans: liter

103. II. Computation Convert the given measurement to the unit indicated. 1.48 dm = 0.0048 km 2.12 dam = 1.2 m 3.18 m = 59.06 ft. 4.160 in. = 0.04064 hm 5.3.54 yrd = 0.002 mi.

104. III. Problem Solving 1.Express 86 kilometers per hour in miles per hour. Ans: 53.75 mi/hr 2. A notebook is 0.37 decimeters thick. How thick is the notebooks in millimeters? Ans: 37 mm

105. Assignment Answer Practice and Application I, II and III on page 33