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5-8 Scale Drawings and Scale Models

5-8 Scale Drawings and Scale Models. I can use ratios and proportions in scale drawings and models. Now set up the left side of the page & complete: Page number Lesson title Learning goal What I know :. Vocabulary. Scale factor The ratio used to enlarge or reduce similar figures

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5-8 Scale Drawings and Scale Models

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  1. 5-8 Scale Drawings and Scale Models I can use ratios and proportions in scale drawings and models. Now set up the left side of the page & complete: Page number Lesson title Learning goal What I know:

  2. Vocabulary • Scale factor • The ratio used to enlarge or reduce similar figures • Example: the scale factor for our problem of the month drawing is • Scale drawing • A drawing that uses a scale to make an object smaller than or larger than the real object • Scale model • A proportional three-dimensional model of an object • Scale • The ratio between two sets of measurements • Example: 1cm : 5 mi

  3. 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 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. Visualize the vocabulary

  4. Visualize the Vocabulary 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 drawingis a proportional two-dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

  5. 13.5 108 18 144 1 8 The scale factor is . Example 1: Finding a Scale Factor Identify the scale factor. You can use the lengths or widths to find the scale factor. 1 8 blueprint length room length = = Write a ratio. Then simplify. 1 8 blueprint width room width = = Write a ratio. Then simplify.

  6. 1 6 The scale factor is . YOUR TURN! WHITE BOARD PRACTICE Identify the scale factor. blueprint length aircraft length 2 12 1 6 = Write a ratio. Then simplify. = blueprint wing span aircraft wing span 3 18 1 6 = Write a ratio. Then simplify. =

  7. 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 original photograph to the nearest tenth of an inch. 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.

  8. 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.

  9. l 45 1.5 1 = YOUR TURN! WHITE BOARD PRACTICE 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.

  10. YOUR TURN! WHITE BOARD PRACTICE 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.

  11. Example 3: Measurement Application On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities? 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 product. 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.

  12. YOUR TURN! WHITE BOARD PRACTICE On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities? 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.

  13. 5-8 Left side time! What I learned: write 1-2 sentences about what you learned. Proof: Critical thinking. A countertop is 18 ft. long. How long is it on a scale drawing with the scale 1 in.= 3 yd.? Reflection:Write about it. A scale for a scale drawing is 10 cm = 1 mm. Which will be larger, the actual object or the scale drawing? EXPLAIN

  14. 5-8 TICKET OUT THE DOOR 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?

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