Using English and Metric Measurements

Transcription

1 Lesson B3 1 Using English and Metric Measurements Unit B. Employability in Agricultural/Horticultural Industry Problem Area 3. Using Mathematics Skills Lesson 1. Using English and Metric Measurements New Mexico Content Standard: Pathway Strand: Agribusiness Systems Standard: IV: Employ AFNR industry concepts and practices to manage inventory. Benchmark: IV-A: Monitor inventory levels to accomplish practical inventory control. Performance Standard: 1. Maintain optimum inventory levels. 2. Apply just-in-time concept. 3. Calculate cost of carrying inventory. 4. Perform logistics management. Student Learning Objectives. Instruction in this lesson should result in students achieving the following objectives: 1. Explain English and metric linear measurement. 2. Explain English and metric area measurement. 3. Explain English and metric volume measurement. 4. Explain English and metric weight measurement. Unit B. Problem Area 3. Lesson 1. Page 1.

2 List of Resources. The following resources may be useful in teaching this lesson: Rogers, Betty C. Mathematics for Agriculture, Second Edition. Danville, Illinois: Interstate Publishers, Inc., VAS 30106, Surveying in Agriculture. Urbana, Illinois: Vocational Agricultural Service. VAS 6015, Mathematical Applications in Agriculture. Urbana, Illinois: Vocational Agricultural Service. VAS 3009A, Using the Square in Construction. Urbana, Illinois: Vocational Agriculture Service. List of Equipment, Tools, Supplies, and Facilities Writing surface Calculator Ruler Overhead projector Transparencies from attached masters Copies of Student Lab Sheets Terms. The following terms are presented in the lesson (shown in bold italics): Metric system Unit equation Interest Approach. Use an interest approach that will prepare the students for the lesson. Teachers often develop approaches for their unique class and student situations. Ask the students what type of occupations require being able to measure with a ruler. What are some common kinds of things that might require measurements with a ruler? When would you need to change English measurements to metric measurements? Unit B. Problem Area 3. Lesson 1. Page 2.

3 Summary of Content and Teaching Strategies Objective 1: Explain English and metric linear measurement. Anticipated Problem: What is the difference between English and metric linear measurement and how are they used? I. There are two customary systems of measurement used in our country the English system and the metric system. A. The metric system has the advantage of being a decimal system. B. The equivalents that are used to make conversions within each system are called unit equations. C. The method of using equations to make conversions involves arranging the unit equation as a fraction so that the given units will cancel and the desired units will remain. 1. Example: Change 28 miles/gallon to kilometers/liter a. 28 miles/gallon (1 gallon/3.785 liters) kilometers/1 mile b. By canceling out the gallons and miles the answer will be kilometers/liter. 28 ( kilometers/3.785 liters) = kilometers/liter. D. English linear units include: 12 inches (in.) = 1 foot (ft.) 3 ft. = 1 yard (yd.) 16.5 ft. = 1 rod (rd.) 5.5 yd. = 1 rd. 320 rd. = 1 mile (mi.) 5,280 ft. = 1 mi. 1,720 yd. = 1 mi. 1 furlong (fur.) = 1/8 mi. 1 fur. = 660 ft. E. Metric linear units include: 1 kilometer (km) = 1,000 meters (m) 1 hectometer (hm) = 100 m 1 decameter (dam) = 10 m 1 decimeter (dm) =.1 m 1 centimeter (cm) =.01 m 1 millimeter (mm) =.001 m 1m=10dm=100cm=1,000 mm F. English metric conversion units include: 1 in. = 25.4 mm 1 in. = 2.54 cm Unit B. Problem Area 3. Lesson 1. Page 3.

4 1 ft. = cm 1 ft. =.3048 mm 1 yd. =.9144 m 1 rd. = m 1 mi. = km 1 fur. = m 1 mm = in. 1 cm =.3937 in. 1 m = ft. 1 km =.6214 mi. Many techniques can be used to help students master this objective. Students need text materials to help them understand English and metric linear measurement. VAS Unit 6015 Mathematical Applications in Agriculture, VAS Unit 3009A Using the Square in Construction, and Mathematics for Agriculture are recommended. LS: B3 1A can be used to evaluate students understanding of English and metric linear measurement. Use TM: B3 1A, TM: B3 1B, and TM: B3 1C to discuss English and metric linear measurement. Objective 2: Explain English and metric area measurement. Anticipated Problem: How are English and metric area measurement used in calculating areas in agriculture? II. In agriculture applications, it is necessary to know how to convert English and metric measurements when figuring areas. A. English area units include: 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 sq. ft. = 1 square yard (sq. yd.) sq. yd. = 1 square rod (sq. rd.) 160 sq. rd. = 1 acre (A) 43,560 sq. ft. = 1 A 640 A = 1 square mile (sq. mi.) 36 sq. mi. = 1 township (twp.) B. Metric area units include: 1 square centimeter (cm 2 ) = 100 square millimeters (mm 2 ) 1 square decimeter (dm 2 ) = 100 cm 2 1 square meter (m 2 ) = 100 dm 2 10,000 m 2 = 1 hectare (ha) 1m 2 = 10,000 cm m 2 = 1 are (a) 100a=1ha Unit B. Problem Area 3. Lesson 1. Page 4.

5 C. English metric conversion units include: 1 sq. in. = cm 2 1 sq. ft. =.0929 cm 2 1 sq. yd. =.8361 m 2 1 sq. mi. = 259 ha 1 sq. mi. = square kilometers (km 2 ) 1 sq. rd. = m 2 1 A = a 1 A =.4047 ha 1cm 2 =.1549 sq. in. 1m 2 = 1549 sq. in. 1m 2 = sq. ft. 1m 2 = sq. yd. 1 ha = A 1 a = sq. yd. E. Refer to Lesson B3 2: Determining Area and Volume for information on area formulas used in agriculture. Use a variety of teaching techniques to help students master this objective. Providing text materials will enhance student learning. VAS Unit 6015 Mathematical Applications in Agriculture and Mathematics for Agriculture are suggested. Use LS: B3 1B to enhance student understanding of English and metric area measurement. TM: B3 1D, TM: B3 1E, and TM: B3 1F can be used to discuss English and metric area units. Objective 3: Explain English and metric volume measurement. Anticipated Problem: How do you calculate volume using English and metric measurement in agriculture? III. Several English and metric conversion measurements are needed to do metric calculations. A. English volume units include: Liquid measurements: 1 pint (pt.) = 16 ounces (oz.) 2 pt. = 1 quart (qt.) 4 qt. = 1 gallon (gal.) 31.5 gal. = 1 barrel (bbl.) 7.48 gal. = 1 cubic foot (cu. ft.) Dry measurements: 2 pt. = 1 qt. 8 qt. = 1 peck (pk.) Unit B. Problem Area 3. Lesson 1. Page 5.

6 4 pk. = 1 bushel (bu.) 1 bu. = 1.25 cu. ft. Household measurements: 1 teaspoon (tsp.) = 1/6 fluid ounce (fl. oz.) 3 tsp. = 1 tablespoon (tbs.) 1 tbs. = ½ fl. oz. 1 cup (c.) = 8 fl. oz. 2c.=1pt. B. Metric volume units include: Solid volume: 1 cubic centimeter (cm 3 ) = 1,000 cubic millimeter (mm 3 ) 1 cubic meter (m 3 ) = 1,000,000 cm 3 1,000 cm 3 = 1 cubic decimeter (dm 3 ) 1,000 cm 3 = 1 liter (L) 1cm 3 = 1 milliliter (ml) Liquid volume: 1 ml =.001 L 1 centiliter (cl) =.01 L 1 deciliter (dl) =.1 L 1 decaliter (dal) = 10 L 1 hectoliter (hl) = 100 L 1 kiloliter (kl) = 1,000 L C. English metric volume conversion units include: 1 pt. =.4732 L 1 qt. =.9463 L 1 L = qt. 1 gal. = L 1 L =.264 gal. 1 grain (gr.) =.0648 gram (g) 1 oz. = g 1 pound (lb.) = g 1 lb. =.4536 kilogram (kg) 1 g = gr. 1 g = oz. 1 kg = lb. I metric ton (MT) = ton (T) short ton Use a range of teaching strategies to illustrate English and metric volume measurement. Text materials will help students master this objective. VAS Unit 6015 Mathematical Applications in Agriculture and Unit B. Problem Area 3. Lesson 1. Page 6.

7 Mathematics for Agriculture are suggested. Use LS: B3 1C to help determine student understanding of volume measurement in agriculture applications. Use TM: B3 1G, TM: B3 1H, and TM: B3 1I to discuss English and metric volume measurement. Objective 4: Explain English and metric weight measurement. Anticipated Problem: How is weight calculated using English and metric measurement? IV. Several conversion factors are needed to understand English and metric weight measurement. A. English weight units include: gr. = 1 oz. 7,000 gr. = 1 lb. 16 oz. = 1 lb. 100 lb. = 1 hundredweight (cwt.) 2,000 lb. = 1 T 2,240 lb. = 1 long ton B. Metric weight units include: 1 milligram (mg) =.0001 g 1 centigram (cg) =.01 g 1 decigram (dg) =.1 g 1 decagram (dag) = 10 g 1 hectogram (hg) = 100 g 1 kg = 1,000 g 1 MT = 1,000 kg C. English metric weight conversion units include: 1 gr. =.0648 g 1 oz. = g 1 lb. = g 1 lb. =.4536 kg 1 T =.9072 MT Many teaching techniques can be used to assist students in understanding this objective. Text materials will enhance student learning. VAS Unit 6015 Mathematical Applications in Agriculture and Mathematics for Agriculture are suggested. Use LS: B3 1D to determine students ability in calculating weight measurements using the English and metric systems. Use TM: B3 1J, TM: B3 1K, and TM: B3 1L to discuss English and metric weight measurement. Review/Summary. Focus the review and summary of the lesson around the student learning objectives. Call on students to explain the content associated with each objective. Use Unit B. Problem Area 3. Lesson 1. Page 7.

8 their responses as the basis for determining any areas that need to be covered again. Questions at the ends of the chapters in the recommended textbooks may also be used in the review process. Use the lab activities in reviewing and reinforcing student learning. Application. Application can involve the following student activities: English and Metric Linear Measurement LS: B3 1A English and Metric Area Measurement LS: B3 1B English and Metric Volume Measurement LS: B3 1C English and Metric Weight Measurement LS: B3 1D Evaluation. Evaluation should focus on student achievement of the objectives for the lesson. Various techniques can be used, such as student performance on the application activities. A sample written test is attached. Answers to Sample Test: Part One: Matching 1=a, 2=e, 3=c, 4=d, 5=b, 6=g, 7=h, 8=f Part Two: Completion 1=160, 100 2=townships 3=4, 2 4=16 Part Three: Problem 1/3 bushels/acre loss Unit B. Problem Area 3. Lesson 1. Page 8.

9 Sample Test Name Part One: Matching Test Lesson B3 1: Using English and Metric Measurements Instructions. Match the term with the correct response. Write the letter of the term next to the definition. a. rod d. square foot g. square mile b. decameter e. mile h. pint c. kilometer f. acre feet 2. 5,280 feet 3. 1,000 meters square inches meters acres ounces 8. 43,560 square feet Part Two: Completion Instructions. Provide the word or words to complete the following statements. 1. One acre has square rods and square meters. 2. A is 36 square miles. 3. There are quarts in a gallon and pints in a quart. 4. One peck equals pints. Part Three: Problem If 21 bushels of corn fell on the ground in an area 30 inches by 30 inches and it represents a harvest loss of 1 bushel/acre, what is the loss if 21 bushels are found in an area 90 inches by 90 inches? Unit B. Problem Area 3. Lesson 1. Page 9.

10 TM: B3 1A English Linear Units 12 inches (in.) = 1 foot (ft.) 3 ft. = 1 yard (yd.) 16.5 ft. = 1 rod (rd.) 5.5 yd. = 1 rd. 320 rd. = 1 mile (mi.) 5280 ft. = 1mi yd. = 1mi. 1 furlong (fur.) = 1/8 mi. 1 fur. = 660 ft. Unit B. Problem Area 3. Lesson 1. Page 10.

11 TM: B3 1B Metric Linear Units 1 kilometer (km) = 1000 meters (m) 1 hectometer (hm) = 100 m 1 decameter (dam) = 10 m 1 decimeter (dm) =.1 m 1 centimeter (cm) =.01 m 1 millimeter (mm) =.001 m 1m = 10dm = 100cm = 1000 mm Unit B. Problem Area 3. Lesson 1. Page 11.

12 TM: B3 1C English Metric Conversion Units 1 in. = 25.4 mm 1 in. = 2.54 cm 1 ft. = cm 1 ft. =.3048 mm 1 yd. =.9144 m 1 rd. = m 1 mi. = km 1 fur. = m 1 mm = in. 1 cm =.3937 in. 1 m = ft. 1 km =.6214 mi. Unit B. Problem Area 3. Lesson 1. Page 12.

13 TM: B3 1D English Area Units 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 sq. ft. = 1 square yard (sq. yd.) sq. yd. = 1 square rod (sq. rd.) 160 sq. rd. = 1 acre (A) 43,560 sq. ft. = 1 A 640 A = 1 square mile (sq. mi.) 36 sq. mi. = 1 township (twp.) Unit B. Problem Area 3. Lesson 1. Page 13.

14 TM: B3 1E Metric Area Units 1 square centimeter (cm 2 )= 100 square millimeters (mm 2 ) 1 square decimeter (dm 2 ) = 100 cm 2 1 square meter (m 2 ) = 100 dm 2 10,000 m 2 = 1 hectare (ha) 1m 2 = 10,000 cm m 2 = 1 are (a) 100a=1ha Unit B. Problem Area 3. Lesson 1. Page 14.

15 TM: B3 1F English Metric Conversion Units 1 sq. in. = cm 2 1 sq. ft. =.0929 cm 2 1 sq. yd. =.8361 m 2 1 sq. mi. = 259 ha 1 sq. mi. = square kilometers (km 2 ) 1 sq. rd. = m 2 1 A = a 1 A =.4047 ha 1cm 2 =.1549 sq. in. 1m 2 = 1549 sq. in. 1m 2 = sq. ft. 1m 2 = sq. yd. 1 ha = A 1 a = sq. yd. Unit B. Problem Area 3. Lesson 1. Page 15.

16 TM: B3 1G English Volume Units Liquid measurements: 1 pint (pt.) = 16 ounces (oz.) 2 pt. = 1 quart (qt.) 4 qt. = 1 gallon (gal.) 31.5 gal. = 1 barrel (bbl.) 7.48 gal. = 1 cubic foot (cu. ft.) Dry measurements: 2 pt. = 1 qt. 8 qt. = 1 peck (pk.) 4 pk. = 1 bushel (bu.) 1 bu. = 1.25 cu. ft. Household measurements: 1 teaspoon (tsp.) = 1/6 fluid ounce (fl. oz.) 3 tsp. = 1 tablespoon (tbs.) 1 tbs. = ½ fl. oz. 1 cup (c.) = 8 fl. oz. 2c.=1pt. Unit B. Problem Area 3. Lesson 1. Page 16.

17 TM: B3 1H Metric Volume Units Solid volume: 1 cubic centimeter (cm 3 )= 1,000 cubic millimeter (mm 3 ) 1 cubic meter (m 3 ) = 1,000,000 cm 3 1,000 cm 3 = 1 cubic decimeter (dm 3 ) 1,000 cm 3 = 1 liter (L) 1cm 3 = 1 milliliter (ml) Liquid volume 1 ml =.001 L 1 centiliter (cl) =.01 L 1 deciliter (dl) =.1 L 1 decaliter (dal) = 10 L 1 hectoliter (hl) = 100 L 1 kiloliter (kl) = 1000 L Unit B. Problem Area 3. Lesson 1. Page 17.

18 TM: B3 1I English Metric Liquid Conversion Units 1 pt. =.4732 L 1 qt. =.9463 L 1 L = qt. 1 gal. = L 1 L =.264 gal. 1 grain (gr.) =.0648 gram (g) 1 oz. = g 1 pound (lb.) = g 1 lb. =.4536 kilogram (kg) 1 g = gr. 1 g = oz. 1 kg = lb. I metric ton (MT) = ton (T) Unit B. Problem Area 3. Lesson 1. Page 18.

19 TM: B3 1J English Weight Units gr. = 1oz. 7,000 gr. = 1lb. 16 oz. = 1 lb. 100 lb. = 1 hundredweight (cwt.) 2,000 lb. = 1T 2,240 lb. = 1 long ton Unit B. Problem Area 3. Lesson 1. Page 19.

20 TM: B3 1K Metric Weight Units 1 milligram (mg) =.0001 g 1 centigram (cg) =.01 g 1 decigram (dg) =.1 g 1 decagram (dag) = 10 g 1 hectogram (hg) = 100 g 1 kilogram (kg) = 1,000 g 1 MT = 1,000 kg Unit B. Problem Area 3. Lesson 1. Page 20.

21 TM: B3 1L English Metric Weight Conversion Units 1 gr. =.0648 g 1 oz. = g 1 lb. = g 1 lb. =.4536 kg 1 T =.9072 MT Unit B. Problem Area 3. Lesson 1. Page 21.

22 LS: B3 1A Name Lab Sheet English and Metric Linear Measurement The understanding of English and metric linear measurement is important in several agricultural applications. Purpose: Materials: Procedure: To enhance your skills in calculating English and metric linear measurements. Writing utensil Lab sheet Ruler Calculator Complete the following exercises on the lab sheet. Add and simplify: 1. 5 yd., 1 ft., and 11 in. + 3 yd., 2 ft., and 3 in. = Subtract: 2. 4 yd., 2 ft., and 6 in. + 7 yd., 1 ft., and 4 in. + 2 yd. and 6 in. = 3. 3 yd., 1 ft., and 8 in. 1 yd., 2 ft., and 10 in. = 4. 2 yd., 1 ft., and 11 in. 1 yd., 2 ft., and 7 in. = Using a ruler with both English and metric units, measure the lines in problems 5 and (to the nearest centimeter and 1/4 inch) cm in. 6. (to the nearest.1 centimeter and 1/8 inch) cm in. Unit B. Problem Area 3. Lesson 1. Page 22.

23 Make the following conversions: 7. 2 ft. 3 in. = yd cm = in ft. 8 in. = m 10. yd. = 156 m 11. 4,132 yd. = mi km = mi. 13. mi. = 690 ft. 14. rd. = 2.5 mi. Unit B. Problem Area 3. Lesson 1. Page 23.

24 LS: B3 1B Name Lab Sheet English and Metric Area Measurement English and metric measurement are used in calculating area in agriculture. Purpose: To improve your understanding of calculating area using metric and English units. Materials: Lab sheet Writing utensil Calculator Procedure: Complete the following exercises on the lab sheet. Add or subtract: 1. 1,420 sq. in sq. in. = sq. ft A 420 sq. rd. = sq. rd. Make the following conversions: A = m sq. in. = sq. ft sq. rd. = sq. ft A = ha 7. cm 2 = 67.0 sq. in m 2 = sq. yd m 2 = cm m 2 = a Unit B. Problem Area 3. Lesson 1. Page 24.

25 Complete the following problems, showing all your work: 11. A fertilizer needs to be applied at the rate of 300 pounds/acre. At this rate, how much fertilizer is needed for a garden having 5,600 square feet? 12. A farmer sold 8.5 acres to a realtor for $2,500/acre. If the realtor developed the area and sold 12,342 square foot lots for $4,500 a lot, how much profit did the realtor make? 13. A crop farmer hires custom combining for his corn. a. Which of the following proposals is better? 1. $1, for 95.4 acres 2. $1, for 40.0 acres b. What is the difference between the two offers? 14. A new subdivision project takes a strip of crop land 9 rods wide and 250 rods long from the side of your farm. How many acres did you lose from production? 15. A variety of fruit trees requires a growing area of 15 feet by 21 feet. How many trees can be planted in a 20-acre orchard? Unit B. Problem Area 3. Lesson 1. Page 25.

26 LS: B3 1C Name Lab Sheet English and Metric Volume Measurement English and metric measurements are commonly used in determining volume in agriculture. Purpose: Materials: Procedure: To develop your skills in using English and metric measurement units. Lab sheet Writing utensil Calculator Complete the following exercises on the lab sheet. Add or subtract: 1. 5 gal., 3 qt., and 2 pt. + 6 gal., 2 qt., and 1 pt. = 2. 8 gal. and 2 qt. 5 gal., 3 qt., and 1 pt. = Make the following conversions: 3. qt. = 48 fl. oz cm 3 = sq. in sq. ft. = sq. in L = qt pk. = bu gal. = pt. Unit B. Problem Area 3. Lesson 1. Page 26.

27 Complete the following problems, showing all work: 9. Gasoline is selling for $1.26/gallon. What would be the cost of 28 liters of gasoline? 10. How much wettable powder would be put into a 250-gallon tank if 12 gallons of water were applied per acre and 1.5 pounds of commercial product are applied per acre? 11. The owner of an orchard has 25 bushels of apples to sell. How many bags containing 1 peck and 1 quart of apples can be prepared for sale? 12. A landscaping plan includes the placement of 123 cubic feet of pine bark. What will be the total cost for the pine bark if it is sold in 3 cubic feet bags for $2.85 a bag? 13. If 1 cubic foot of storage space holds 0.75 bushels, what diameter would a 20-foot high round steel bin have to be to store 8,500 bushels of grain? Unit B. Problem Area 3. Lesson 1. Page 27.

28 LS: B3 1D Name Lab Sheet English and Metric Weight Measurement Determining weight calculations successfully depends upon your understanding of English and metric measurements. Purpose: Materials: Procedure: To learn how to use English and metric measurement in weight calculations. Lab sheet Writing utensil Calculator Complete the following exercises on the lab sheet. Add or subtract: 1. 8 lb. 2 oz. 4 lb. 7 oz lb. 9 oz. = lb. 4 oz. 6 lb. 8 oz. = Make the following conversions: oz. = g 4. 6 g = gr. 5. 2,860 lb. = MT kg = lb lb. = g t = lb. Unit B. Problem Area 3. Lesson 1. Page 28.

29 Complete the following problems, showing all work: 9. A grocery store add reads Tom Turkeys $.89/lb. What would it cost for a turkey weighing 24 pounds 8 ounces? 10. Your popcorn produced an average yield of 3,740 pounds/acre. Convert this yield to kilograms/hectare. 11. A truck gardener harvested 700 bushels of potatoes. One bushel of potatoes weighs 60 pounds and the potatoes are packed in 15-pound bags. How many bushels would remain to be processed after filling 1,500 bags? 12. A concrete culvert contains 26 cubic feet of concrete. How many tons does the culvert weigh? 13. A standing crop of alfalfa hay is being offered for sale. If baled hay is selling for $80 a ton and harvesting costs are considered to be 55 percent of the total value of baled hay, what should be charged per 75-pound bale harvested from the standing crop? Unit B. Problem Area 3. Lesson 1. Page 29.