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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 3. 4. 1. 10. 2. 1. 5. 4. Warm Up Evaluate the following for x = 16. 1. 3 x 2. x Evaluate the following for x = . 3. 10 x 4. x. 48. 12. 4. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 3 4 1 10 2 1 5 4 Warm Up Evaluate the following for x = 16. 1.3x2.x Evaluate the following for x = . 3. 10x4.x 48 12 4

  3. California Standards MG1.2 Construct and read drawings and models made to scale.

  4. Vocabulary scale drawing scale model scale scale factor

  5. A scale drawing is a two-dimensional drawing of an object that is proportional to the object. A scale model is a three-dimensional model that is proportional to the object. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

  6. 8 mm = x mm 1000 1 Write a proportion using the scale. Let x be the actual length of the amoeba. Additional Example 1: Finding Actual Measurements Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? 1000 x = 1  8 The cross products are equal. Solve the proportion. x = 0.008 The actual length of the amoeba is 0.008 mm.

  7. 1 mm = x mm 10,000 1 Write a proportion using the scale. Let x be the actual length of the fiber. Check It Out! Example 1 Under a 10,000:1 microscope view, a fiber appears to have length of 1 mm. What is its actual length? 10,000 x = 1  1 The cross products are equal. x = 0.0001 Solve the proportion. The actual length of the fiber is 0.0001 mm.

  8. 2 cm scale length . Set up proportion using 8 m actual length 1 cm x m Additional Example 2: Using Proportions to Find Unknown Scales A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? = 1  8 = x 2 Find the cross products. 8 = 2x 4 = x Divide both sides by 2. The scale is 1 cm:4 m.

  9. Reading Math The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.”

  10. 4 cm scale length . Set up proportion using 12 m actual length 1 cm x m Check It Out! Example 2 The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? = 1  12 = x 4 Find the cross products. 12 = 4x 3 = x Divide both sides by 4. The scale is 1 cm:3 m.

  11. The ratio of a length on a scale drawing or model to the corresponding length on the actual object is called the scale factor. When finding a scale factor, you must use the same measurement units. You can use a scale factor to find unknown dimensions.

  12. = = 1 2 in. 2 in. 1 in. 1 The scale factor for the model is . Now set up a proportion. 18 in. 18 18 3 ft 36 in. h in. = 324 in. 1 18 Additional Example 3: Using Scale Factors to Find Unknown Dimensions A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model? = Find the scale factor. Convert: 27 ft = 324 in. 324 = 18h Find the cross products. 18 = h Divide both sides by 18. The height of the model is 18 in.

  13. = = 1 4 in. 4 in. 1 in. 1 The scale factor for the model is . Now set up a proportion. 6 in. 6 6 2 ft 24 in. h in. = 288 in. 1 6 Check It Out! Example 3 A model of a 24 ft tall bridge was made using a scale of 4 in.:2 ft. What is the height of the model? = Find the scale factor. Convert: 24 ft = 288 in. 288 = 6h Find the cross products. 48 = h Divide both sides by 6. The height of the model is 48 in.

  14. = = 500,000,000 5 cm 50 mm 0.0000001 mm 0.0000001 mm Additional Example 4: Life Science Application A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Find the scale factor. The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.

  15. 500,000,000 20 cm 1 x cm Additional Example 4 Continued = Set up a proportion. 500,000,000x = 1(20) Find the cross products. Divide both sides by 500,000,000. x = 0.00000004 The length of the DNA chain is 4  10-8 cm.

  16. = = 2,000 2 cm 20 mm 0.01 mm 0.01 mm Check It Out! Example 4 A model was built using the scale 2 cm:0.01 mm. If the model is 30 cm long, what is the length of the actual object? Find the scale factor. The scale factor for the model is 2,000. This means the actual object is two thousand times larger than the model.

  17. 2,000 30 cm 1 x cm Check It Out! Example 4 Continued = Set up a proportion. 2,000x = 1(30) Find the cross products. Divide both sides by 2,000. x = 0.015 The length of the actual object is 1.5  10-2 cm.

  18. 1 4 Lesson Quiz 1. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be? 2. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? 5.5 in. 1 cm = 1.5 ft 72 in.

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