5 9 Scale Drawings and Scale Models Warm

5 -9 Scale Drawings and Scale Models Warm Up Problem of the Day Lesson Presentation Course 2

5 -9 Scale Drawings and Scale Models Warm Up Write each fraction in the simplest form. 4 1 1. 48 12 2. 9 135 1 15 Convert the following measurements. 3. 192 inches = 4. 18. 5 feet = 5. 324 inches = Course 2 feet 16 inches 222 feet 27

5 -9 Scale Drawings and Scale Models 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 Course 2

5 -9 Scale Drawings and Scale Models Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale. Course 2

5 -9 Scale Insert. Drawings Lesson Title and. Here Scale Models Vocabulary scale model scale factor scale drawing Course 2

5 -9 Scale Models and Scale Drawings This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO 1 gauge model train is 87. 1 This means that each dimension of the model is 87 of the corresponding dimension of the actual train. Course 2

5 -9 Scale Models and Scale Drawings 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. A scale drawing is a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent. Course 2

5 -9 Scale Drawings and Scale Models Additional Example 1: Finding a Scale Factor Identify the scale factor. Length (in. ) Width (in. ) blueprint length = 18 144 room length = 1 8 The scale factor is 1. 8 Course 2 Room 144 108 Blueprint 18 13. 5 Write a ratio using one of the dimensions. Simplify. Caution! A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.

5 -9 Scale Insert Drawings Lesson Title and. Here Scale Models Check It Out: Example 1 Identify the scale factor. Model Aircraft Blueprint Length (in. ) 12 2 Wing span (in. ) 18 3 blueprint length = 2 aircraft length 12 Write a ratio using one of the dimensions. = 1 Simplify. 6 1 1 The scale factor is 6. This is reasonable because 4 of the length of the model is 3 in. The length of the blueprint is 2, which is less. is 1 less than. 1 6 4 Course 2

5 -9 Scale Drawings and Scale Models 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. 5 The scale factor is. Find the size of the 1 photograph. poster = 5 Think: photo 1 36 = 5 l 1 5 l = 36 l = 7. 2 Course 2 Write a proportion to find the length l. Find the cross products. Divide.

5 -9 Scale Drawings and Scale Models 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 5. Find the size of the 1 photograph. Think: poster = 5 photo 1 20. 5 = 5 w 1 5 w = 20. 5 w = 4. 1 Write a proportion to find the width w. Find the cross products. Divide. The photo is 7. 2 in. long and 4. 1 in. wide. Course 2

5 -9 Scale Drawings and Scale Models 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 1. 5 factor is 1. Find the size of the dollhouse. Think: dollhouse = 1. 5 blueprint 1 l = 1. 5 45 1 Course 2 Write a proportion to find the length l. l = 45 · 1. 5 Find the cross products. l = 67. 5 Multiply.

5 -9 Scale Drawings and Scale Models Check It Out: 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 1. 5 factor is 1. Find the size of the dollhouse. Think: dollhouse = 1. 5 blueprint 1 w = 1. 5 24 1 Write a proportion to find the width w. w = 24 · 1. 5 Find the cross products. Multiply. w = 36 The dollhouse is 67. 5 inches long and 36 inches wide. Course 2

5 -9 Scale Drawings and Scale Models 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 = 7. 5 Write a proportion. 60 d 1. 5 · d = 60 · 7. 5 Find the cross products. 1. 5 d = 450 Multiply. 1. 5 d = 450 Divide both sides by 1. 5 d = 300 The distance between the cities is 300 miles. Course 2

5 -9 Scale Insert Drawings Lesson Title and. Here Scale Models 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=7 Write a proportion. 50 d 1 · d = 50 · 7 1 d = 350 Find the cross products. Multiply. d = 350 The distance between the cities is 350 kilometers. Course 2

5 -9 Scale Insert. Drawings Lesson Title and. Here Scale Models Lesson Quiz: Part I Identify the scale factor. 1. Height (in. ) Statue of Liberty Model 1, 824 8 1 228 2. On a scale drawing, a kitchen wall is 6 inches long. 1 The scale factor is. What is the length of the 24 actual wall? 144 inches, or 12 feet Course 2

5 -9 Scale Insert. Drawings Lesson Title and. Here Scale Models 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 Course 2