Name Period Date GEO5 STUDENT PAGES GEOMETRY AND MEASUREMENT Student Pages for Packet 5: GEO5.1 Conversions Compare measurements within and between measurement systems. Convert measurements within and between measurement systems. Use measurements expressed as rates to solve problems. GEO5.2 Scale Drawings Construct and read drawings made to scale. GEO5.3 Vocabulary, Skill Builders, and Review 19 1 13 GEO5 SP
WORD BANK (GEO5) Word Definition Example or Picture conversion rate conversion statement rate ratio scale drawing unit price unit rate GEO5 SP0
5.1 Conversions CONVERSIONS Ready (Summary) Set (Goals) We will compare and convert units of measure, both within and between measurement systems. We will solve problems using rates and explore the meaning of different measurements. Go (Warmup) 1. Give an example of an object that measures Compare measurements within and between measurement systems. Convert measurements within and between measurement systems. Use measures expressed as rates to solve problems. a. 1 millimeter b. 1 milliliter c. 1 gram d. 15 centimeters e. 2 liter f. 1 kilogram 2. Give an example of an object that measures a. 1 inch b. 3 fluid ounces c. 4 ounces d. 1 foot e. 1 cup f. 1 pound GEO5 SP1
5.1 Conversions CONVERSION STATEMENTS Length Volume Weight 1 foot = 12 inches 1 yard = 3 feet 1 mile = 5,280 feet 1 kilometer = 1,000 meters 1 meter = 100 centimeter 1 centimeter 0.4 inches 1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 4 cups 1 gallon = 4 quarts 1 pound = 16 ounces 1 ton = 2,000 pounds 1 kilogram = 1,000 grams 1 meter 39 inches 1 kilometer 0.6 mile Area 1 acre = 43,560 square feet Write abbreviations for each unit. 1 liter 1.06 quarts 1 kilogram 2.2 pounds Unit Abbreviation Unit Abbreviation 1. inches 8. cups 2. meters 9. quarts 3. miles 10. liters 4. kilometers 11. fluid ounces 5. feet 12. pints 6. foot 13. ounces 7. centimeters 14. pounds 15. Use abbreviations to write 6 cubic feet in two different ways (hint: use exponents). 16. Use abbreviations to write five feet six inches in two different ways (hint: use hatch marks). GEO5 SP2
5.1 Conversions CONVERSION RATES A conversion statement can be written as a conversion rate. For example, since the statement 12 inches equals 1 foot provides the same information as 12 inches per 1 foot, it can be written as: 12 inches = 1 foot or 12 inches 1 foot or 1 foot 12 inches Write each conversion statement as two different conversion rates. 1. 1 lb = 16 oz 2. 0.4 in = 1 cm 3. 1,000 m = 1 km 4. 1 acre = 43,560 ft 2 5. 1 mile = 5,280 ft 6. 1 gallon = 4 quarts When no direct conversion statement is given, you can convert in steps by creating a chain of measurement units that link the known unit of measure to the unknown one. Example: To write a chain of measurement units to convert from meters to feet, first convert meters to inches, then convert inches to feet. meters (m) inches (in) feet (ft) Write a chain of measurement units that can be used to convert from the first unit to the second unit. Be sure you know a conversion statement for each link. 7. From yards to meters 8. From yards to miles 9. From liters to cups 10. From tons to ounces GEO5 SP3
5.1 Conversions MULTIPLYING RATES TO MAKE CONVERSIONS You can use conversion statements, written as rates that are equal to 1, to make new conversion statements. Example: How many grams equal one ounce? Step 1: Make a chain of measurement units that link the unit you know to the unit you want to find. Be sure you know a conversion statement for each link. Step 2: Step 3: ounce (oz) pounds (lb) kilograms (kg) grams (g) Begin with the unit that you know. Multiply by conversion rates, in order of the links. Select rates that allow you to cancel units along the way. End with the unit that you want to find. 1 oz 1 lb 16 oz 1 kg 2.2 lb 1,000 g 28. 4 g 1 kg Write a new conversion statement: 1 ounce 28.4 grams This process of making conversions by multiplying a known unit of measure by conversion rates to get a new unit of measure is called dimensional analysis. Use dimensional analysis to find each conversion. 1. How many yards equal one mile? a. Make a chain of measurement units. mi b. Multiply by rates. 2. How many centimeters equal one inch? a. Make a chain of measurement units. b. Multiply by rates. c. Write a new conversion statement. 1 mile = yards c. Write a new conversion statement. 1 inch = centimeters GEO5 SP4
5.1 Conversions MULTIPLYING RATES TO MAKE CONVERSIONS (continued) Use dimensional analysis to find each conversion. 3. How many fluid ounces equal one gallon? 4. How many feet equal one meter? a. Make a chain of measurement units. a. Make a chain of measurement units. b. Multiply by rates. c. Write a new conversion statement. b. Multiply by rates. c. Write a new conversion statement. 5. How many ounces equal one kilogram? 6. How many kilograms equal one pound? a. Make a chain of measurement units. a. Make a chain of measurement units. b. Multiply by rates. b. Multiply by rates. c. Write a new conversion statement. c. Write a new conversion statement. GEO5 SP5
5.1 Conversions LENGTH DISTANCE RACES Conversion Tool Kit Write some conversions statements for length. Add other statements as needed. 1 yard = feet. 1 kilometer = meters. 1 foot = inches. 1 mile = feet. 1 kilometer mile(s). 1 mile = yards. 1. The most famous long distance race is the marathon, which is approximately 26.2 miles. Convert this distance to kilometers and to meters. 2. Another popular long distance race is the 5K (or 5 kilometers). Convert this distance to miles. 3. A middle distance track event is the 800 meters race. Convert this distance to yards. 4. One of the short distance races in track is the 100-meter dash. Convert this distance to feet. GEO5 SP6
5.1 Conversions AREA HOW BIG IS AN ACRE? Here is a scale drawing of a football field. It is 100 yards long plus two 10-yard end zones. It is 160 feet wide. 1. What are the dimensions of the football field in feet? Do not include the endzones. ENDZONE 10 20 30 40 50 40 30 20 10 ENDZONE 2. What is the area of the football field in square feet? Do not include the endzones. 3. An acre is 43,560 2 ft. Shade a portion of the football field that represents about one acre. One acre is an area that is about of a football field. 4. A mile is 5,280 feet. How many square feet are in one square mile? Write this in numbers and words. 5. How many acres are in one square mile? 10 20 30 40 50 40 30 20 10 6. In October 2007, four major fires in San Diego, California burned nearly 300,000 acres of land. About how many square miles of land were burned? GEO5 SP7
5.1 Conversions VOLUME PRICES OF LIQUIDS In 2008, gasoline prices reached nearly $5.00 per gallon. Let s explore and see how the cost of gasoline compares to other liquid products. Conversion Tool Kit Write some conversions statements for volume. Add other statements as needed. 1 gallon = quarts 1 cup = fluid ounces 1 quart = cups 1 liter quart(s) 1 pint = cups For each liquid product, determine the price per gallon for the given quantities at prices found in a grocery store in 2008. 1. Item: orange drink 2. Item: milk Price: $1.70 for 1 liter Price: $2.20 for 1 quart Think: liter quart gallon $1. 70 1 liter 1 liter 1.06 qt 4 qt $6.42 1 gal 1 gal Lemonade is $6.42 per gallon. 3. Item: bottled water Price: $3.60 for 2.5 gallons 4. Item: cottage cheese Price: $1.50 for 2 cups 5. Item: mustard Price: $4.00 for 4 fluid ounces 6. Item: shampoo Price: $9.00 for 15 fluid ounces GEO5 SP8
5.1 Conversions WEIGHT BANANA CONSUMPTION The average person in the United States eats about 25 pounds of bananas per year. By contrast, the average person in Uganda eats about 500 pounds of the bananas annually. The average banana (without the skin) weighs about 5 ounces. Conversion Tool Kit Write some conversions statements. Add other statements as needed 1 banana ounces 1 pound = ounces 1 year = months 1 year = weeks 1 year = days Determine the number of bananas that an average person in each country consumes. Number of Uganda United States Bananas 1. Per year 2. Per month 3. Per week 4. Per day GEO5 SP9
5.1 Conversions DIGITAL MEMORY In the world of computers, cameras, and MP3s, digital memory is measured in bytes. 1. Write fractions that behave as 1 for each digital storage measurement. 1 kilobyte (KB) 1000 bytes. 1 megabyte (MB) 1000 kilobytes 1000 bytes 1 KB = 1 KB 1000 bytes 1 gigabyte (GB) 1000 megabytes A terabyte (TB) 1000 gigabytes 2. How many bytes are in a gigabyte? Write this number in scientific notation. Write this number in words. 3. How many bytes are in a terabyte? Write this number in scientific notation. Write this number in words. GEO5 SP10
5.1 Conversions DIGITAL MEMORY (continued) 4. An MP3 music file is typically about 4 megabytes. How many music files can be stored on an MP3 player that has 8 gigabytes of digital memory? 5. Arturo s workstation computer had 500 gigabytes hard drive. His new workstation has a 1 terabyte hard drive. Which workstation holds more data? By how much? 6. Helen has a 4 gigabyte memory stick for her camera. According to the manufacturer, the memory stick will hold 1595 pictures. About how many megabytes are required for each picture? GEO5 SP11
5.1 Conversions COMPARING MEASUREMENTS Use the symbols <, =, or > to compare the values of these quantities. Make calculations if needed. Within measurement systems 1. 14 feet 140 inches 2. 1 mile 5,300 feet 3. 2 yards 2 feet 4. 400 yards 1 4 mile 5. 32 fluid ounces 1 quart 6. 4 gallons 16 quarts 7. 32 ounces 1 pound 8. 4 tons 8,500 pounds Between measurement systems 9. 4 liter 1 gallon 10. 2 liters 8 cups 11. 1 meter 1 yard 12. 800 yards 1 kilometer 13. 5 pounds 10 kilograms 14. 1 ton 1,000 kilograms 15. 100 centimeters 3 feet 16. 10 centimeters 6 inches Do not write in this area GEO5 SP12
5.2 Scale Drawings SCALE DRAWINGS Ready (Summary) We will use ratio strips and scale rulers to construct and read drawings made to scale. Set (Goals) Construct and read drawings made to scale. Go (Warmup) A scale factor is a positive factor by which the linear measurements of an object are multiplied in order to create a proportional enlargement or reduction of the object. Scale drawings are used to represet real objects such as a room or a garden. You will use Ratio Strip 1 below to interpret scale drawings where 2 cm = 9 ft. 1. Complete the sequence of numbers on each edge of the strip. 2. Cut out the ratio strip along the solid lines. 3. A scale drawing of a room is created so that 2 centimeters represents 9 feet. If the scale width of the room measures 8 centimeters, what is the actual width of the room? 8 cm 2 cm 4 cm 8 cm 10 cm 1 9 ft 27 ft 2 cm = 9 ft 63 ft GEO5 SP13
5.2 Scale Drawings USING A RATIO STRIP The ratio strip you used on the previous page converts a scale of 2 centimeters on the drawing to 9 feet of an actual object. Here is a scale drawing of a garden that was created using a 2 cm = 9 ft scale. 1. Use Ratio Strip 1 to determine the actual dimensions and area of the garden. Scale Dimensions Scale Area Actual Dimensions Actual Area Length Width 2. What is the ratio of the scale length to the actual length? 3. What is the ratio of the scale area to the actual area (in simplified form)? 4. How does the ratio of the lengths compare to the ratio of the areas? Do not write in this area GEO5 SP14
5.2 Scale Drawings A FLOOR PLAN Architects often use scale drawings to represent actual building floor plans. Use Ratio Strip 1 to measure some scale rooms and determine their actual dimensions. BEDROOM 1 CLOSET 1. Bath 2. Bedroom 2 3. Laundry Scale: 2 cm = 9 ft Room Scale Length Scale Width Actual Length Actual Width 4. Dining Room 3 cm cm cm ft ft 5. Bedroom 1 18 ft 13.5 ft 6. Living Room BATH LIVING ROOM BEDROOM 2 7. If the scale length and width of the dining room were increased by 2 cm each, what would be the new actual dimensions? LAUNDRY DINING ROOM KITCHEN Do not write in this area GEO5 SP15
5.2 Scale Drawings THE MUSEUM Here is a scale drawing of a museum floor plan. 1. The actual width of the Photography Room is 22.5 feet. Find the scale of this drawing using inches, rounding all measurements to the nearest 0.25. Then, create Ratio Strip 2 based on your scale. Cafe Entrance Painting Video Photography 2. Use two different ways to determine how much wider the Painting Room is compared to the Sculpture Room. 3. Determine the actual dimensions of the museum building. 4. Determine the actual area of the museum. Music Sculpture Gift Shop 2 in = ft GEO5 SP16
5.2 Scale Drawings SPORTS FIELDS Here are actual dimensions of various sports fields. Use the actual measures of each field and a ratio of 3 cm = 20 ft to determine the scale dimensions. Ratio Strip 3 is provided below to help you make conversions. Sport Field Actual Length Actual Width Scale Length Scale Width 1. Soccer Field 340 ft 200 ft 2. Volleyball Court 60 ft 30 ft 3. Football Field 360 ft 160 ft 4. Roller Rink 70 ft 150 ft 5. Bowling Lane 60 ft 3 ft 6. Why is it not possible to use Ratio Strip 3 as a ruler? cm 7. EXTRA CREDIT: Choose a field, and create a scale drawing of it on a sheet of paper using the scale 3 cm = 20 ft. Research the lengths and locations of some of the inside dimensions of the field, and include them in your scale drawing. 3cm 3 3 cm = 20 ft GEO5 SP17
5.2 Scale Drawings This page is left intentionally blank. GEO5 SP18
5.3 Vocabulary, Skill Builders, and Review FOCUS ON VOCABULARY (GEO5) Find the words in the word search puzzle. Then, choose five words and write their definitions or give examples. E N R T R T I S E E R O R T T I I E R S A O L L O E A A R R I N E C T O N A R R E L U R O I T A R R I L N O I L O A N I E E N E E O C A R N A N E C E T A W I O D R A A A I R W R I R S C A L E D R A W I N G S R N R T W P T D A N C E A E T A R T I N U A R P A N V R T I O N C T L W A O G N U N D C A A U R T G A E O U E E R L A I A N L G T C U T N I R R G E N I E R Word Bank scale drawing conversion rate ratio rate unit price unit rate ratio ruler GEO5 SP19
5.3 Vocabulary, Skill Builders, and Review SKILL BUILDER 1 The table to the right shows the number of boys and girls in two different classes. Boys Girls Class A 18 16 Class B 22 14 Show each ratio in three different ways. Ex: 1. 2. 3. Number of boys in class A to the number of boys in class B. Number of girls in class A to the number of girls in class B. Number of students in class A to the number of students in class B. Number of students in class B to the number of girls in class A. 18 to 22 18 : 22 to : to : to : For each statement, write a ratio as a fraction in simplest form. 4. In one class, there were 8 girls for every 10 boys. 5. In one school, 4 out of 10 students lived within 5 miles of the school For each statement, write a fraction to express each unit rate. 6. You read 12 books in 3 months. What is the rate per month? 18 22 7. You grew 3 inches in 11 weeks. What is the rate per week? 8. You earn $50 in 2 hours. What is the rate per hour? 9. You use 42 gallons of water in 7 minutes. What is the rate per minute? GEO5 SP20
5.3 Vocabulary, Skill Builders, and Review SKILL BUILDER 2 Find the missing number in each proportion. 1. 4 n = 5 35 2. 16 4 = 3. n 9 n 3 = 12 4 Solve each proportion. 4. 3 7 = 6 x 5. 4 x = 6 9 Write a proportion for each problem. Then solve each proportion. 7. If 5 pencils cost $0.45, then what is the cost of 4 pencils? 6. x 16 = 18 24 8. If 18 copies cost $1.08, how many copies can be made for $2.40? GEO5 SP21
5.3 Vocabulary, Skill Builders, and Review SKILL BUILDER 3 Draw a picture, write an appropriate formula, and substitute to solve each problem. 1. A rectangular garden has a width of 22 meters and an area of 264 square meters. What is the length of the garden? 2. The area of a trapezoid is 269.5 square centimeters and the measures of its bases are 14 cm and 24.5 cm. What is the height of the trapezoid? a. Sketch the figure: a. Sketch the figure: b. Write an appropriate formula: b. Write an appropriate formula: c. Substitute and solve: c. Substitute and solve: d. Answer the question: d. Answer the question: GEO5 SP22
5.3 Vocabulary, Skill Builders, and Review SKILL BUILDER 4 Draw a picture, use the formula, and substitute to solve each problem. 1. The length of a rectangular prism is 3.6 in. The width is one inch more than the length. The height is 2 more inches more than the length. Sketch the prism. Length: L = Find the surface area. Formula: S = 2( Lw + wh + Lh ) Substitute: Answer: Width: w = Height: h = Find the volume. Formula: V = Lwh Substitute: Answer: 2. The diameter of a cylinder is 200 cm. The height is half the radius. Sketch the cylinder. Diameter: d = Find the surface area. Radius: r = Height: h = Find the volume. 2 Formula: S =2πr + 2π rh Substitute: Formula: V Substitute: = π 2 r h Answer: Answer: GEO5 SP23
5.3 Vocabulary, Skill Builders, and Review TEST PREPARATION (GEO5) Show your work on a separate sheet of paper and choose the best answer. 1. How many centimeters are in one yard? A. 90 cm B. 14.4 cm C. 1.6 cm D. 1 36 cm 2. How many cups are in 4 gallons? A. 64 cups B. 16 cups C. 8 cups D. 4 cups 3. How many feet are in 200 meters? A. 6,500 ft B. 650 ft C. 65 ft D. 6.5 ft 4. Orange juice costs $4 for one quart. What is the price per gallon? A. $16 B. $10 C. $2.50 D. $1 5. A scale drawing of a school was created using a 1.5 cm = 10 ft scale conversion. What is the actual distance for 6 cm on the scale drawing? A. 0.15 ft B. 15 feet C. 9 feet D. 40 feet 6. A scale drawing has a scale of 1 inch = 10 feet. What is the length on the scale drawing 2 for an actual length of 40 ft? A. 20 in B. 5 in C. 4 in D. 2 in GEO5 SP24
5.3 Vocabulary, Skill Builders, and Review KNOWLEDGE CHECK (GEO5) Show your work on a separate sheet of paper and write your answers on this page. 5.1 Conversions Use dimensional analysis to each conversion. 1. How many pints are in one gallon? 2. How many centimeters are in 5 yards? 3. If peanut butter costs $3.50 for 8 fluid ounces, how much will it cost per quart? 5.2 Scale Drawings 4. The actual length of a room is 16 ft. The scale drawing of a blueprint is 1 in = 1 ft. Find the 2 room s length in the blueprint. The scale drawing on a map is 2 cm = 15 km. Find the actual distance for each map distance. 5. 6 cm 6. 10 mm GEO5 SP25
Home-School Connection (GEO5) Here are some questions to review with your young mathematician. Compare the values of the quantities. Make calculations if needed. Use <, =, or >. 1. 6 cups 1 liter 2. If apples cost $1.50 per pound, what is the price per ounce? 3. The scale drawing on a map is 3 cm = 14 km. Find the actual distance for 15 cm on the map distance. Parent (or Guardian) signature NS 6.2.3 AF 7.1.2 Selected California Mathematics Content Standards Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations 2 Use correct order of operations to evaluate algebraic expressions such as 3(2x + 5). FIRST PRINTING DO NOT DUPLICATE 2009 GEO5 SP26