Measurement Measuring Length Capacity Weight Conversion of Units

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

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.

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.

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

• 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?

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.

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.

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

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.

• 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

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

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

Customary Length • A mile is about half the length of Talladega Super Speedway. This represents about 1 mile. • Talladega is 2. 9 miles long. Talladega Super Speedway

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

Customary Length • A foot is about the length of a floor tile.

Customary Length • An inch is about the length of a drink bottle top.

Customary Capacity 1 gallon

Meet Mr. Gallon 4 quarts

Meet Mr. Gallon 8 pints

Meet Mr. Gallon 16 cups

Customary Weight • A small car weighs about a ton.

Customary Weight • A bag of coffee weighs about 1 pound.

Customary Weight • An ounce weighs the same as 8 nickels.

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”.

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

The following table shows some examples of these units 1000 10 1 0. 01 0. 001 Prefixes Kilo(k) Hecto(h) Deca(da) Basic Unit Deci(d) Centi(c) Milli(m) Length km hm dam Metre (m) dm cm mm Mass kg hg dag Gram (g) dg cg mg Capacity kl hl dal Litre (l) dl cl ml Prefixes Symbol Name Equivalence Kilo k thousand 1, 000 Hecto h hundred 100 Deca da ten 10 Deci d One-tenth 0. 1 Centi c One-hundredth 0. 01 Milli m One-thousandtth 0. 001 29

SI Prefixes Symbol Name Power of Ten yotta Y Septillion 1024 deci d tenth 10 -1 zetta Z Sextillion 1021 centi c hundredth 10 -2 exa E Quintillion 1018 milli m Thousandth 10 -3 peta P Quadrillio n 1015 micro μ Millionth 10 -6 tera T Trillion 1012 nano n Billionth 10 -9 giga G Billion 109 pico p Trilllionth 10 -12 mega M Million 106 femto f Quadrilliont h 10 -15 kilo K Thousand 103 atto a Quintillionth 10 -18 hecto H Hundred 102 zepto z Sextillionth 10 -21 deca da Ten 101 yocto y Septillionth 10 -24 One 100

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

Metric Units – Length, Distance km m 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)

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

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)

Metric Units – Weight/Mass kg g 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

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

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

Metric Units – Capacity/Volume kl l • 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

Metric Units – Capacity/Volume kl l • A teaspoon is about 5 ml • A can of coke is bout 330 ml ml

Metric Units – Capacity/Volume kl l cl • A bottle of wine is 75 cl • A drinking cup (paper) is about 20 cl ml

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

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

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

Practice and Application I. 1. 2. 3. 4. 5. 6. Complete each of the following. 1 kiloliter = ___ liter 1 dekaliter = ___ liter 1 hectometer = ___ meter 1 centiliter = ___ liter 1 milliliter = ___ liter 1 decimeter = ___ meter

Answer Key: II. 7. 10 8. 0. 1 9. 100 10. 1000 11. 10 12. 10

Answer Key: III. 13. 14. 15. 16. 17. 18. 0. 33 3, 300 0. 0033 0. 033 330 33

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 Item 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 Span Ruler (cm) Meterstick (m)

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

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

4 mx = Note that we cancel units when multiplying fractions since they behave like numbers. 4 mx = 400 cm

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.

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

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

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

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. This is how we change 427 cm into metres: H T U th hth th ÷ 100 4 2 7 0 0 0

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. This is how we change 427 cm into metres: H T U th hth th ÷ 100 4 2 7 0 0 0

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. This is how we change 427 cm into metres: H T 4 2 U th hth th ÷ 100 7 0 0

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. This is how we change 427 cm into metres: H T 4 2 U th hth th ÷ 100 7 0

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. This is how we change 427 cm into metres: H T 4 2 U th hth th ÷ 100 7 0

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. This is how we change 427 cm into metres: H 4 T U 2 th hth th ÷ 100 7 0

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. This is how we change 427 cm into metres: H 4 T U th hth th ÷ 100 2 7 0

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. This is how we change 427 cm into metres: H 4 T U th hth th ÷ 100 2 7 0

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. This is how we change 427 cm into metres: H T 4 U th hth th ÷ 100 2 7 0

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. This is how we change 427 cm into metres: H T U th hth th ÷ 100 4 2 7 0

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. This is how we change 427 cm into metres: H T U th hth th ÷ 100 4 2 7 0

Therefore: - 427 cm = 4. 27 m cm H m T U t h th 3 2 6 H T U t h th 4 7 6 H T U t 1 6 5 3 h th ÷ 100 H T U t h th 3 2 6 H T U t h th 0 4 7 6 H T U t h th 1 6 5 3

Convert from centimetres to metres 354 cm 3. 54 m 15. 4 cm 0. 154 m 779 cm 7. 79 m 52. 4 cm ÷ 100 0. 524 m 939 cm 9. 39 m 395 cm 3. 95 m 25. 8 cm 0. 258 m

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: - 3. 51 m = H T U t h 3 5 1 th

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: - 3. 51 m = H T U t h 3 5 1 th

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: - 3. 51 m = H T 3 U t h 5 1 th

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: - 3. 51 m = H 3 T U t h 5 1 th

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: - 3. 51 m = H 3 T U t h 5 1 th

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: - 3. 51 m = H 3 T U 5 t h 1 th

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: - 3. 51 m = H T 3 5 U t h 1 th

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: - 3. 51 m = H T 3 5 U t h 1 th

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: - 3. 51 m = H T 3 5 U t 1 h th

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: - 3. 51 m = H T U 3 5 1 t h th

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: - 3. 51 m = 351 cm H T U 3 5 1 t h th

Try changing these measurements in metres into centimetres 5. 4 m 540 cm 6. 2 m 620 cm 12. 7 m 1270 cm 3 m x 100 300 cm 7. 6 m 760 cm 0. 54 m 54 cm 0. 3 m 30 cm

Approximate English and Metric Equivalents 1 inch (in. ) 1 foot (ft. ) 1 yard (yd. ) 1 mile (mi. ) = = = 2. 54 centimeters (cm) = 30. 48 centimeters(cm) 0. 9 meter (m) 1. 6 kilometers (km) Convert the following: a. 15 inches to centimeters b. 138 miles to kilometers c. 35, 400 millimeters to inches

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

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

Quiz # 1 July 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.

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?

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.

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?

Quiz # 1 Answer 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

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

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

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

II. Computation • Convert the given measurement to the unit indicated. 1. 2. 3. 4. 5. 48 dm = 0. 0048 km 12 dam = 1. 2 m 18 m = 59. 06 ft. 160 in. = 0. 04064 hm 3. 54 yrd = 0. 002 mi.

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

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