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Scale Drawings: Learn with Examples

Discover how to solve problems related to scale drawings with practical examples and step-by-step explanations in this interactive lesson.

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Scale Drawings: Learn with Examples

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  1. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 6-4d Objective Solve problems involving scale drawings

  4. Example 6-4d Vocabulary Scale drawing A representation of an object that is too large or too small to be drawn or built at actual size

  5. Example 6-4d Vocabulary Scale model A representation of an object that is too large or too small to be drawn or built at actual size

  6. Example 6-4d Vocabulary Scale A ratio of a given length on a drawing or model to its corresponding actual length

  7. Lesson 6 Contents Example 1Find a Missing Measurement Example 2Find the Scale Factor Example 3Find the Scale Example 4Construct a Scale Model

  8. map distance actual distance Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. Bingston Alanton Find the actual distance X Define the variable X = actual distance Using the scale given, write a ratio 1/4

  9. map distance map distance actual distance actual distance Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. X Write the second ratio with data given in problem Keep units of measure the same on each line X = actual distance 1/4

  10. map distance map distance actual distance actual distance Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. X Write a proportion with the 2 ratios Solve with cross multiplication of the numbers 1x = 1x = 5(1.5) 1/4

  11. Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. X 1x = 5(1.5) x x = x = 7.5 x = 7.5 miles Use Identify Property to multiply 1  x Answer: x = 7.5 miles Bring down = Multiply 5  1.5 Add dimensional analysis 1/4

  12. Example 6-1c MAPS The distance from Springfield to Capital City is 1.4 inches on the map. Find the actual distance. Answer: x = 9.8 miles 1/4

  13. Example 6-2a Find the scale factor for the map. Write a ratio with the scale For a scale factor, must have the same units Since inch is a smaller unit than mile, convert 5 miles to inches 2/4

  14. Example 6-2a Find the scale factor for the map. Since we know how many inches in a foot, Write the ratio and multiply by a conversion ratios of inches in a foot 1 foot  12 in Remember to put inches in the denominator so they can be cancelled out Cancel out same units 2/4

  15. Example 6-2a Find the scale factor for the map. Multiply the numerators 1 foot  Bring down unit of measure of foot 12 in 1 1 foot Multiply the denominators 60 60 mi Bring down unit of measure of mi 2/4

  16. Example 6-2a Find the scale factor for the map. 1 foot 1 mile 3  60 mi 5280 feet Since we know how many feet in a mile, Use the ratio and multiply by a conversion ratios of feet in a mile Remember to put feet in the denominator so they can be cancelled out 2/4

  17. Example 6-2a Find the scale factor for the map. 1 foot 1 mile 3  60 mi 5280 feet Cancel out same units of foot 1 3 316,800 Cancel out same units of mile Multiply numerator Answer: The scale factor = Multiply denominator 2/4

  18. Answer: Example 6-2c Find the scale factor for the map. 2/4

  19. Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? Write a ratio of the wall to the scale drawing Actual room 15 feet Scale drawing 6 inches Write a ratio for the scale Actual room x feet The scale will always be 1 unit for whatever the drawing is using Scale drawing 1 inch Since the actual distance is unknown define a variable 3/4

  20. Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? Write a proportion using the 2 ratios Actual room 15 feet Scale drawing 6 inches Cross multiply the numbers Actual room x feet Scale drawing 1 inch 15 feet x feet = 6 inches 1 inch 6x = 6x = 15(1) 3/4

  21. Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? Actual room x feet Bring down the 6x = 1 inch Scale drawing Multiply 15  1 x feet 15 feet = Ask “what is being done to the variable”? 6 inches 1 inch 6x = 15(1) The variable is being multiplied by 6 6x = 6x = 15 Do the inverse on each side of the equal sign 3/4

  22. Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? Actual room x feet Bring down the 6x = 15 1 inch Scale drawing Using the fraction bar, divide both sides by 6 6x = 15 6 6 Combine “like” terms Bring down = 1  x 1  x = 1  x = 2.5 Combine “like” terms x x = 2.5 Use Identity Property to multiply 1  x Bring down = 2.5 3/4

  23. Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? Actual room x feet Write the scale of the drawing 1 inch Scale drawing Substitute the value of x 6x = 15 Bring down the 1 inch 6 6 Can also be written: 1  x = 2.5 x = 2.5 Answer: 2.5 feet or 1 inch = 2.5 feet 1 inch 2.5 feet = 1 inch 3/4

  24. Example 6-3c SCALE DRAWINGS The length of a garage is 24 feet. On a scale drawing the length of the garage is 10 inches. What is the scale of the drawing? Answer: 1 inch = 2.4 feet 3/4

  25. Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? What is the length of the statue’s index finger on the model Using the scale given, write a ratio 1 inch model height 2.5 feet actual height Write the second ratio with data given in problem x inches model height actual height 8 feet Define variable x inches 1 inch = Write a proportion using the 2 ratios 2.5 feet 8 feet 4/4

  26. Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? Cross multiply the numbers 1 inch x inches = 2.5 feet 8 feet Bring down 2.5x = Multiply 1  8 2.5x 2.5x = 1(8) Ask “what is being done to the variable?” 2.5x = 2.5x = 8 The variable is being multiplied by 2.5 4/4

  27. Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? Do the inverse on each side of the equal sign 2.5x = 8 2.5x = 8 Bring down the 2.5x = 8 2.5 2.5 Using the fraction bar, divide both sides by 2.5 1  x 1  x = 3.2 1  x = Combine “like” terms Bring down = Combine “like” terms 4/4

  28. Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? Use the Identify Property to multiply 1  x 2.5x = 8 2.5x = 8 Bring down = 3.2 2.5 2.5 Add dimensional analysis 1  x 1  x = 3.2 1  x = x = x = 3.2 inches x = 3.2 Answer: x = 3.2 inches 4/4

  29. Example 6-4d * STATUE Marnie created a model of her town’s statue of Jebediah Springfield. Her model was 6 inches high. The actual statue is 27 feet tall. What is the length of the statue’s mustache on the model, which is 3 feet long on the actual statue. Use the scale 1 inch = 1.25 feet Answer: x = 2.4 inches 4/4

  30. End of Lesson 6 Assignment

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