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Understanding Ratios and Scale Drawings Lesson

Learn about ratios and proportions in scale drawings, scale factors, and how to use them in scale models. Practice converting measurements and solve problems applying scale factors.

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Understanding Ratios and Scale Drawings Lesson

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 1 15 1 12 Warm Up Write each fraction in the simplest form. 4 48 9 135 2. 1. Convert the following measurements. 3. 192 inches = feet 16 4. 18.5 feet = inches 222 5. 324 inches = feet 27

  3. Problem of the Day A toy model of a 200 foot dinosaur is 3 in. long. How many times as long as the model is the dinosaur? 800

  4. What are blueprints? • What make maps and blueprints useful?

  5. Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

  6. Vocabulary scale drawing scale factor scale model scale

  7. 1 87 1 87 A scale drawingis a proportional two-dimensional drawing of an object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. For example, if a drawing of a building has a scale factor of , this means that each dimension of the drawing is of the corresponding dimension of the actual building.

  8. A scale model is a proportional three- dimensional model of an object. A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.

  9. Room Blueprint Length (in.)‏ 144 18 Width (in.)‏ 108 13.5 18 144 Caution! 1 8 A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. The scale factor is . Additional Example 1: Finding a Scale Factor Identify the scale factor. blueprint length room length Write a ratio using one of the dimensions. = 1 8 = Simplify.

  10. Model Aircraft Blueprint Length (in.)‏ 12 2 Wing span (in.)‏ 18 3 1 6 1 4 The scale factor is . This is reasonable because of the length of the model is 3 in. The length of the blueprint is 2, which is less. is less than . 1 6 1 4 Check It Out: Example 1 Identify the scale factor. blueprint length aircraft length 2 12 Write a ratio using one of the dimensions. = 1 6 = Simplify.

  11. Additional Example 2: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 = Think: 36 l 5 1 Write a proportion to find the length l. = 5l = 36 Find the cross products. l= 7.2 Divide.

  12. Additional Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 = Think: 20.5 w Write a proportion to find the width w. 5 1 = 5w = 20.5 Find the cross products. w= 4.1 Divide. The photo is 7.2 in. long and 4.1 in. wide.

  13. l 45 1.5 1 = Check It Out: Example 2 Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Think: Write a proportion to find the length l. Find the cross products. l = 45 · 1.5 l= 67.5 Multiply.

  14. Check It Out: Example 2 Continued Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Think: Write a proportion to find the width w. w 24 1.5 1 = w = 24 · 1.5 Find the cross products. w= 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.

  15. Additional Example 3: Measurement Application On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? Let d be the actual distance between the cities. 1.5 60 7.5 d = Write a proportion. 1.5 · d = 60 · 7.5 Find the cross products. 1.5d = 450 Multiply. 450 1.5 1.5d 1.5 = Divide both sides by 1.5. d = 300 The distance between the cities is 300 miles.

  16. Check It Out: Example 3 On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers? Let d be the actual distance between the cities. 1 50 7 d = Write a proportion. Find the cross products. 1 · d = 50 · 7 1d = 350 Multiply. d = 350 The distance between the cities is 350 kilometers.

  17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  18. Statue of Liberty Model Height (in.)‏ 1,824 8 1 228 On a scale drawing, a kitchen wall is 6 inches long. The scale factor is . What is the length of the actual wall? 1 24 Lesson Quiz: Part I Identify the scale factor. 1. 2. 144 inches, or 12 feet

  19. Lesson Quiz: Part II 3. On a road map, the distance from Green Bay to Chicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km

  20. Lesson Quiz for Student Response Systems 1. Identify the scale factor. A. C. 10 B.D. 20 1 20 1 10

  21. Lesson Quiz for Student Response Systems 2. On a scale drawing, the height of a building is 60 inches. The scale factor is . What is the height of the actual building? A. 240 in., or 20 ft B. 300 in., or 25 ft C. 600 in., or 50 ft D. 900 in., or 75 ft 1 15

  22. Lesson Quiz for Student Response Systems 3. On a road map, the distance from Washington, DC to New York is 15 cm. What is the actual distance between the cities if the map scale is 3 cm = 50 mi? A. 150 mi B. 200 mi C. 250 mi D. 300 mi

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