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 Instruments English 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=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

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

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.

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

A foot is about the length of a floor tile.

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

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

Customary Capacity 1 gallon

Meet Mr. Gallon 4 quarts

Meet Mr. Gallon 8 pints

Meet Mr. Gallon 16 cups

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

Customary Weight A small car weighs about a ton.

A bag of coffee weighs about 1 pound.

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 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

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

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 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 ( km)

Metric Units – Length, Distance kmmmm 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 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

Metric Units – Weight/Mass kggmg 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 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

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

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

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.i 2.h 3.g 4.j 5.f 6.d 7.a 8.b 9.c 10.e

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___

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

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

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

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

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

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

Answer Key: II

Answer Key: III ,

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.

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

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 cm = 1 m 1 m 100 cm

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

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 dam to cm. The given unit, The desired unit, The conversion factor 1 dam = 1,000 cm Solution: dam x = 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. HTUthhthth ÷100 This is how we change 427cm into metres:-

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 ÷100 This is how we change 427cm into metres:-

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 ÷100 This is how we change 427cm into metres:-

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:-

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:-

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:-

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:-

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:-

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:-

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:-

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:-

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

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

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 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth 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:- HTUthth m = 351cm

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

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

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

KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit CENTI 0.01 Unit MILLI 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 How many jumps does it take? Starting Point Ending Point 4. 1 __. 2 3 = 4000 m

Try these conversions using the ladder method 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

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

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

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 # 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.

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 dm to km 2.12 dam to m 3.18 m to ft in. to hm 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 # 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

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 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 dm = km 2.12 dam = 1.2 m 3.18 m = ft in. = hm yrd = mi.

III. Problem Solving 1.Express 86 kilometers per hour in miles per hour. Ans: 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