1. Pre-Algebra 7-8 Scale Models 7-8 Scale Models Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Pre-Algebra 7-8 Scale Models Warm Up The scale of a drawing is 4 in. = 12 ft. Find each actual measurement. 1. 6 in.2. 2.5 in. The scale of a map is 1 in. = 3.5 mi. Find each length on the map. 3. 21 mi4. 1.75 mi 18 ft7.5 ft 6 in. Pre-Algebra 7-8 Scale Models 0.5 in.

3. Pre-Algebra 7-8 Scale Models Problem of the Day There is a 2.5-mile racetrack at the Indianapolis Motor Speedway. If a drawing of the racetrack has a scale of 1:1760, what is the length of the track on the drawing? 7.5 ft

4. Pre-Algebra 7-8 Scale Models Learn to make comparisons between and find dimensions of scale models and actual objects.

5. Pre-Algebra 7-8 Scale Models Vocabulary scale model

6. Pre-Algebra 7-8 Scale Models Very large and very small objects are often modeled. A scale model is a three-dimensional model that accurately represents a solid object. The scale model is mathematically similar to the solid object. A scale gives the ratio of the dimensions of the model to the actual dimensions.

7. Pre-Algebra 7-8 Scale Models Tell whether each scale reduces, enlarges, or preserves the size of the actual object. A. 1 in:1 yd Additional Example 1A: Analyzing and Classifying Scale Factors 1 in. 1 yd = 1 in. 36 in. = Convert: 1 yd = 36 in. Simplify. The scale reduces the size of the actual object by a factor of. 1 36 1

8. Pre-Algebra 7-8 Scale Models Tell whether each scale reduces, enlarges, or preserves the size of the actual object. B. 1 m:10 cm Additional Example 1B: Analyzing and Classifying Scale Factors = 100 cm 10 cm = 10 Convert: 1 m = 100 cm. Simplify. The scale enlarges the size of the actual object 10 times. 1 m 10 cm

9. Pre-Algebra 7-8 Scale Models Tell whether each scale reduces, enlarges, or preserves the size of the actual object. A. 1 in:1 ft Try This: Example 1A 1 in. 1 ft = 1 in. 12 in. = Convert: 1 ft = 12 in. Simplify. The scale reduces the size of the actual object by a factor of. 1 12 1

10. Pre-Algebra 7-8 Scale Models Tell whether each scale reduces, enlarges, or preserves the size of the actual object. B. 12 in:1 ft Try This: Example 1B 12 in. 1 ft = = 1Convert: 12 in. = 1 ft. Simplify. The scale preserves the size of the actual object.

11. Pre-Algebra 7-8 Scale Models What scale factor relates a 12 in. scale model to a 6 ft. man? Additional Example 2: Finding Scale Factors 12 in 6 ft = 12 in. 72 in. = Write the scale factor as a ratio and simplify. 12 in:6 ft State the scale. 1 6 The scale factor is, or 1:6. 1 6

12. Pre-Algebra 7-8 Scale Models What scale factor relates a 12 in. scale model to a 4 ft. tree? Try This: Example 2 12 in 4 ft = 12 in. 48 in. = Write the scale factor as a ratio and simplify. 12 in:4 ft State the scale. 1 4 The scale factor is, or 1:4. 1 4

13. Pre-Algebra 7-8 Scale Models A model of a 32 ft tall house was made using the scale 3 in:2 ft. What is the height of the model? Additional Example 3: Finding Unknown Dimensions Given Scale Factors First find the scale factor. The scale factor for the model is. Now set up a proportion. 1 8 3 in. 2 ft = 3 in. 24 in. = 1 in. 8 in. = 1 8 384 = 8h Convert: 32 ft = 384 in. Cross multiply. 48 = h The height of the model is 48 in. Solve for the height. 1 8 = h in. 384 in.

14. Pre-Algebra 7-8 Scale Models A model of 24 ft tall bridge was made using the scale 4 in:2 ft. What is the height of the model? Try This: Example 3 First find the scale factor. The scale factor for the model is. Now set up a proportion. 1 6 4 in. 2 ft = 4 in. 24 in. = 1 in. 6 in. = 1 6 288 = 6h Convert: 24 ft = 288 in. Cross multiply. 48 = h The height of the model is 48 in. Solve for the height. 1 6 = h in. 288 in.

15. Pre-Algebra 7-8 Scale Models 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. Additional Example 4: Life Science Application The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain. 5 cm 0.0000001 mm 50 mm 0.0000001 mm == 500,000,000

16. Pre-Algebra 7-8 Scale Models Additional Example 4 Continued 500,000,000 1 20 cm x cm =Set up a proportion. 500,000,000x = 1(20) x = 0.00000004 The length of the DNA chain is 4  10 -8 cm. Cross multiply. Solve for the length.

17. Pre-Algebra 7-8 Scale Models 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. Try This: Example 4 The scale factor for the model is 2,000. This means the actual object is 2 thousand times larger than the model. 2 cm 0.01 mm 20 mm 0.01 mm == 2,000

18. Pre-Algebra 7-8 Scale Models Try This: Example 4 Continued 2,000 1 30 cm x cm =Set up a proportion. 2,000x = 1(30) x = 0.015 The length of the actual object is 0.015 cm. Cross multiply. Solve for the length.

19. Pre-Algebra 7-8 Scale Models Lesson Quiz: Part 1 Tell whether each scale reduces, enlarges, or preserves the size of the actual object. 1. 75 ft:40 in 2. 1 mi:1760 yd 3. 400 m:1 km 4. What scale factor was used to build a 5 in. model of a 60 ft statue? preserves enlarges 1:144 reduces

20. Pre-Algebra 7-8 Scale Models Lesson Quiz: Part 2 5. To create a model of the Eustachian tube of the human ear, an audiologist used the scale 1.5 cm = 0.6 mm. If the diameter of the Eustachian tube is 1.8 mm, what is the diameter of the model? 4.5 cm