- - AGRICULTURE CORE CURRICULUM - - (CLF2000) Advanced Core Cluster: AGRICULTURAL MECHANICS (CLF2150) Unit Title: MEASUREMENTS ___________________________________________________________________________ (CLF2151) Topic: MEASUREMENT SYSTEMS Time Year(s) 2 hours 1 / 2 / 3 / 4 ___________________________________________________________________________ Topic Objectives: Upon completion of this lesson, the students will be able to: Learning Outcome #: (C-4) - Differentiate between U.S. Customary and metric measurement units (in linear, area, and volumetric measurements). Special Material and Equipment: References: Cooper, E. L. (1987). AGRICULTURAL MECHANICS: FUNDAMENTALS AND APPLICATIONS. Albany, NY: Delmar Publishers. Hokanson, C. M. (1984). APPLIED PROBLEMS IN MATHEMATICS FOR AGRICULTURE. Danville, IL: Interstate Printers & Publishers. Evaluation: Quiz by instructor. TOPIC PRESENTATION: MEASUREMENT SYSTEMS A. Introduction to Measurement Systems in the U.S. 1. There are two basic systems of measurement in use in the United States: a. U.S. Customary System (based on, but not identical with, the English System) b. International Metric System 2. The United States Congress has passed legislation calling for a voluntary changeover to the metric system. a. Despite the fact that the metric system is more logical and used by most countries, the changeover in the United States has met with much resistance. c. The adoption of the metric system in America has been slow because it is harder to visualize than the English system which is based to a large extent on body parts, the foot for example. b. Due to the slow adoption of the metric system and increased imports of foreign-made tractors and farm machinery, those working in agricultural mechanics need to be functional with both systems. 3. Changing English Measurement Unit Sizes a. To change a larger unit of measure to a smaller unit, such as feet to inches, one multiplies. b. To change a smaller unit of measure to a larger unit, such as feet to yards, one divides. B. The English System (from which the U.S. Customary System is in large part derived) 1. The Basis of the English System a. Most non-metric measures are based on body measurements, dating from the days when manufactured measuring tools were not in common use. 1) The "hand" is still used to measure horse height. (Approx. 4") 2) The "cubit," the length of the forearm from elbow to the tip of the middle finger, is mentioned in Biblical descriptions of Noah's Ark. b. The English System, inherited from the British during the colonial period, uses units of various size which are based on similarity to certain familiar objects or part of the human body. 1) The English System does not seem very logical; for example, a) There are twelve inches in a foot. b) There are three feet in a yard. c) There are 5,280 feet in a mile. 2) In early times, people could function satisfactorily with approximate measures. 3) However, as the technological age evolved, measurements had to be standardized. 4) Today, the foot and most other English units of measuremet are very percise. a) The foot should be the same length on all measuring tools. b) Variations may occur, however, on poor-quality tools and tools that measure long distances, such as tapes. 2. English Units of Measure a. Linear Units (Length) - 1) 12 inches (in. or ") = 1 foot (ft or ') 2) 3 feet = 1 yard (yd) 3) 16 1/2 feet = 1 rod (rd) 4) 5 1/2 yards = 1 rod 5) 320 rods = 1 mile (mi) 6) 5,280 feet = 1 mile 7) 1,760 yards = 1 mile 8) 1 furlong (fur) = 1/8 mile or 660 feet b. Square Units (Area) - 1) 144 square inches 2 2 (sq in. or in. ) = 1 square foot (sq ft or ft ) 2 2) 9 square feet = 1 square yard (sq yd or yd ) 2 3) 30 1/4 square yards = 1 square rod (sq rd or rd ) 4) 160 square rods = 1 acre (A) 5) 43,560 square feet = 1 acre 2 6) 640 acres = 1 square mile (sq mi or mi ) c. Cubic Units (Volume) - 1) 1,728 cubic inches 3 3 (cu in. or in. ) = 1 cubic foot (cu ft or ft ) 3 2) 27 cubic feet = 1 cubic yard (cu yd or yd ) 3) 128 cubic feet = 1 cord (cd) - measure of wood C. International Metric System 1. Advantages of the Metric System a. The metric system has the advantage of being a completely decimal system. b. The units of measure in the metric system relate to one another by multiples of ten. c. This makes the metric system mathematically logical and easy to use. d. Instead of working with complicated division and multiplication to change from one measurement unit to another, the decimal point is merely moved. 1) To change sizes of metric units, multiply or divide by 10, 100, 1,000 or 1,000,000, which is as simple as moving a decimal point. 2) For example, to change 357 centimeters to meters, divide by 100. The answer is obvious without figuring--3.57 meters. 2. Below is a table of metric prefixes whose meaning indicates whether to multiply or divide when changing measurement: a. Mega- = 1,000,000 times the basic unit (meter, liter, grams). b. Kilo- = 1,000 times the basic unit. c. Hecto- = 100 times the basic unit. d. Deca- = 10 times the basic unit. e. Deci- = 1/10 times the basic unit. f. Centi- = 1/100 times the basic unit. g. Milli- = 1/1000 times the basic unit. h. Micro- = 1/1,000,000 times the basic unit. 3. Metric Units of Measure a. Linear Units (Length) 1) 1 kilometer (km) = 1,000 meters 2) 1 hectometer (hm) = 100 meters 3) 1 decameter (dkm) = 10 meters 4) 1 meter (m) 5) 1 decimeter (dm) = 0.1 m 1 m = 10 dm 6) 1 centimeter (cm) = 0.01 m 1 m = 100 cm 7) 1 millimeter (mm) = 0.001 m 1 m = 1,000 mm b. Square Units (Area) 2 2 1) 1 square centimeter (cm ) = 100 square millimeters (mm ) 2 2) 1 square decimeter (dm ) = 100 square centimeters 2 3) 1 square meter (m ) = 100 square decimeters 4) 100 square meters = 1 are (a) 5) 100 ares = 1 hectare (ha) 6) 10,000 square meters = 1 hectare c. Cubic Units (Volume) 3 3 1) 1 cubic centimeter (cm ) = 1,000 cubic millimeters (mm ) 3 2) 1 cubic meter (m ) = 1,000,000 cubic centimeters 3 3) 1,000 cubic centimeters = 1 cubic decimeter (dm ) 4) 1,000 cubic centimeters = 1 liter (L) 5) 1 cubic centimeter (cc) = 1 milliliter (ml) D. English to Metric Conversions 1. Linear Measurement Units a. 1 in = 25.4 mm or 1 mm = 0.03937 in b. 1 in = 2.54 cm or 1 cm = 0.3937 in c. 1 ft = 30.48 cm or 1 m = 39.37 in d. 1 ft = 0.3048 m or 1 m = 3.281 ft e. 1 yd = 0.9144 m or 1 m = 1.0936 yd f. 1 mi = 1.6093 km or 1 km = 0.6214 mi 2. Square Measurement Units 2 2 2 2 a. 1 in = 6.452 cm or 1 cm = 0.1549 in 2 2 2 2 b. 1 ft = 0.0929 m or 1 m = 10.76 ft 2 2 2 2 c. 1 yd = 0.8361 m or 1 m = 1.196 yd 2 d. 1 mi = 259 ha 2 2 e. 1 mi = 2.589 km f. 1 a = 0.4047 ha 1 ha = 2.471 a 3. Cubic Measurement Units 3 3 3 3 a. 1 in = 16.387 cm or 1 cm = 0.06102 in 3 3 3 3 b. 1 ft = 0.0283 m or 1 m = 35.32 ft 3 3 3 3 c. 1 yd = 0.7646 m or 1 m = 1.208 yd _________________________________________________________ ACTIVITY: 1. Add and subtract both English and metric units of measure; then discuss the use of common fractions in English unit manipulation and the use of decimals in metric unit manipulation. 2. Perform English-to-metric and metric-to-English conversions. 3. Compare U.S. standard measure and metric measure tools and identify engines and machinery which require metric measure tools. _________________________________________________________ 6/27/91 OLR/tf #%&C