MeasurementMeasuring 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 • A mile is about half the length of Talladega Super Speedway. • Talladega is 2.9 miles long. This represents about 1 mile. 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
Metric Units – Length, Distance 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 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 We use millimetres (mm) for very small things: • The thickness of a coin • The diameter of a screw
Metric Units – Weight/Mass 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 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 We use milligrams (mg) for very small things: • The amount of paracetamol in a tablet
Metric Units – Capacity/Volume 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 • 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 • A teaspoon is about 5 ml • A can of coke is bout 330 ml
Metric Units – Capacity/Volume • 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 • 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. • 10 • 0.1 • 100 • 1000 • 10 • 10
Answer Key: III. 13. 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.
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 m x = Note that we can cancel units when multiplying fractions since they behave like numbers. 4 m x = 400cm
Rules in Changing Units • To change from a larger unit to a smaller unit, multiply. • To change from a smaller unit to a larger unit, divide.
Examples: • 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