*Contributor: Marlene Vogel. Lesson ID: 10755*

Ever have a model railroad or race car set? Did it look like the original but smaller? How did they figure that out? Find out by working with problems and designing and building your own scale model!

categories

subject

Math

learning style

Visual

personality style

Lion, Beaver

Grade Level

Middle School (6-8)

Lesson Type

Dig Deeper

**Challenge!**

Oregon is approximately 400 miles from east to west and 300 miles north to south. What is the largest scale that can be used to fit a map of Oregon on a sheet of 8-½ in x 11 in paper, if:

- The 11 in side runs north-south?
- The 8-½ in side runs north-south?

Your teacher can access the *Oregon Answer Key* found in the **Downloadable Resources** in the right-hand sidebar to check your answers.

Early map makers found that one difficulty in drawing a scale model of the earth was *distortion*.

Merriam-Webster online dictionary defines "distortion" as "the act of . . . making inaccurate."

An object that is *distorted* is either twisted out of shape or is made inaccurately. For the early map makers, this meant that the parts of the world drawn on the maps were drawn inaccurately. Now, for those who make maps today, and for the rest of us working with scale models, distortion can be prevented by choosing a good scale.

Below is an example of how to use a good scale to make an accurate scale model of an object (A scale model can be a drawing or an actual model, like a globe or a model car.):

Tim is making a scale drawing of a locomotive on an 8-½ in. x 11 in. sheet of paper. The paper is positioned as 11 inches long and 8-½ inches tall (the paper is being held portrait or "hot dog" style). The actual locomotive is 12 feet tall and 22 feet long from cab to caboose. What scale should he use if he wants the drawing to be as large as possible?

- The first step is to understand what the problem is saying and asking for. You can do this by listing the important information from the problem.

- The height of the locomotive is 12 feet (this is from the rails to the roof).
- The length of the locomotive is 22 feet (this is from the cab to the caboose).
- The paper that Tim is going to draw the scale model of the locomotive on is 11 inches long and 8-½ inches tall.

- Tim now knows that the picture he draws of the locomotive can only be 11 inches long. In order to figure out the scale he should use to draw the length of the locomotive, he will have to use a formula. The formula he will use is below:

Scale Length |

Actual Length |

- Now Tim will substitute the numerical values for the words in the formula. See below:

11 in |

22 ft |

- Tim replaced the words Scale Length with the numerical value of 11 as he knows that the scale length of the model can only be 11 inches long. He replaced the words Actual Length with the numerical value of 22 because he knows that the actual length of the locomotive is 22 feet.
- Tim looks at the fraction and realizes that he can simplify it to:

1 in |

2 ft |

This tells Tim that for every 2 feet of the real locomotive, he needs to draw 1 inch on the paper. That way, he will be able to draw the entire length of the actual locomotive on the piece of paper.

- Help Tim by figuring out the other dimension. Using the formula from above, determine the scale for the height of the locomotive. Remember, the height of the paper is 8-½ inches, and the height of the locomotive is 12 feet.

- You should have calculated that the scale for the height of the drawing should be 1 inch : 2 feet. This means that the height of the drawing will be 6 in., which fits easily on the paper!

Great job!

Move on to the *Got It?* section where you will have more opportunities to practice this new skill and make sure you understand it!

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