Get Ready for the Lesson

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1 Lesson 6 8 Scale Drawings Get Ready for the Lesson Let 1 unit on the grid paper represent 2 feet. How many feet are the bleachers? doors? Title Page Get Ready Quick Review Solve each proportion. 5 7 = a p = Vocabulary: Scale Drawings and Scale Models: used to represent objects that are too large or too small to be drawn or built at actual size. (A map is an example of a scale drawing.) Scale: gives the ratio that compares the measurements of the drawing or model to the measurements of the real object. These measurements are proportional. Find the LCM for the set of numbers. 3, 15, 20 Quick Review Vocabulary! Example 1: Use a Map Scale What is the actual distance between Hagerstown and Annapolis? On the map of Arkansas shown, find the actual distance between Clarksville and Little Rock. Use a ruler to measure. Step 1: Use a cm ruler to find the map distance between the two cities. (The map distance is about 4 cm.) Step 2: Write and solve a proportion using the scale. Let d represent the actual distance between the cities. 1

2 A blueprint is another example of a scale drawing.! Example 2: Use a Blueprint Scale On the blueprint of the deck, each square has a side length of 1/2 inch. What is the actual width of the deck? The deck on the blueprint is 2 inches wide. Write and solve a proportion using the scale. Let w represent the actual width of the deck. The actual width of the deck is 16 feet. blueprints On the blueprint of the living room, each square has a side length of 1/4 inch. What are the actual dimensions of the living room? 12 feet by 10.5 feet! Example 3: Use a Scale Model A graphic artist is creating an advertisement for a new cell phone. If she uses a scale of 5 inches = 1 inch, what is the length of the cell phone on the advertisement? Write a proportion using the scale. Let a represent the length of the advertisement cell phone. The length on the ad is 20 inches long. A scooter is 3.5 feet long. Find the length of a scale model of the scooter if the scale is 1 inch = 3/4 feet. 4 2/3 inches 2

3 Remember? In Lesson 6 4, you used ratios to convert units. You can use a similar method to simplify a scale. Scale factors can be used to calculate actual distances from the distances shown in a scale drawing or map. If, for example, a drawing has a scale factor of 1/96, then something that measures 1 inch in the drawing will actually measure 96 inches, or 8 feet. Since scale factors don't include units, the units used in the drawing MUST also be used in the calculation of actual distances. Vocabulary: Scale Factor: A scale written as a ratio without units in simplest form Reminder! Example 4: Find a Scale Factor Find the scale factor of a model sailboat if the scale is 1 inch = 6 feet. 1 inch 6 feet = 1 inch inches The scale factor is 1/72. What is the scale factor of a model car if the scale is 1 inch = 2 feet? 1/24 Word Problem Practice Check your Understanding Find the scale factor of each scale drawing or model. An engineer makes a model of the bridge using a scale of 1 inch = 3 yards. 1/48 2/3 a) What is he length of the model? 16 2/3 in. Find the length of each model. Then, find the scale factor. b) What is the height of the model? 1 1/3 in. 12 cm 1/300 6 in. 1/720 Word Problem Practice Check Your Understanding 3

4 Check your Understanding Compare and contrast the terms scale and scale factor. Include an example in your comparison. A scale drawing of a doctor's office is shown: The scale is the ratio comparing the measurements, including the units, on the model to the measurements on the actual figure. Once the units have been converted to the same unit, the scale factor is this ratio written without units as a fraction in simplest form. For example, if the scale of the model to the actual figure is 1 in. = 4.5 feet, then the scale factor would be 1/4.5 x 12 or 1/54. What are the actual dimensions of the doctor's office? A) 24 ft by 48 ft C) 40 ft by 60 ft B) 30 ft by 52 ft D) 37.5 ft by 65 ft Check Your Understanding A certain map has a scale of 1/4 in. = 30 miles. How many miles are represented by 4 inches on this map? A) 480 miles C) 120 miles B) 30 miles D) 16 miles Angel drew a map of his school. He used a scale of 1 inch : 50 feet. What distance on the map should represent the 625 feet between the cafeteria and the science lab? A) 8 in. C) 12.5 in. B) 10.5 in. D) 15 in. CHALLENGE of the DAY Nic constructed three models, A, B, and C, of the same figure, with scales of 0.5 cm = 1 mm, 1.5 mm = 4cm, and 0.25 cm = 2.5 mm, respectively. a) Which model is larger than the actual figure? b) Which model is smaller than the actual figure? c) Which model is the same size as the actual figure? CHALLENGE of the DAY At Molly's family reunion, 4/5 of the people are 18 years old or older. Half of the remaining people are under 12 years old. If 20 children are under 12 years old, how many people are at the reunion? (Draw a diagram.) Challenge Challenge 4

5 Complete Lesson 6-8 "Practice" wks. Homework 5