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

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

Scale Drawings and Scale Models Course 2 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

Scale Drawings and Scale Models 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.

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

Scale Models and Scale Drawings 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 gauge model train is . 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

Scale Models and Scale Drawings 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.

Additional Example 1: Finding a Scale Factor Course 2 5-9 Scale Drawings and Scale Models Additional Example 1: Finding a Scale Factor Identify the scale factor. Room Blueprint Length (in.) 144 18 Width (in.) 108 13.5 blueprint length room length 18 144 Write a ratio using one of the dimensions. = 1 8 = Simplify. A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions. Caution! 1 8 The scale factor is .

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

Additional Example 2: Using Scale Factors to Find Unknown Lengths 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. 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.

Additional Example 2 Continued Course 2 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 . Find the size of the photograph. 5 1 poster photo 5 1 Think: = 20.5 w 5 1 Write a proportion to find the width w. = 5w = 20.5 Find the cross products. w = 4.1 Divide. The photo is 7.2 in. long and 4.1 in. wide.

Scale Drawings and Scale Models 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 factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 Think: = l 45 = 1.5 1 Write a proportion to find the length l. Find the cross products. l = 45 · 1.5 l = 67.5 Multiply.

Check It Out: 2 Continued Course 2 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 factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 Think: = w 24 1.5 1 Write a proportion to find the width w. = w = 24 · 1.5 Find the cross products. w = 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.

Additional Example 3: Measurement Application 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 60 7.5 d = Write a proportion. 1.5 · d = 60 · 7.5 Find the cross products. 1.5d = 450 Multiply. 1.5d 1.5 450 1.5 = Divide both sides by 1.5. d = 300 The distance between the cities is 300 miles.

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

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

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