SF - Scale Drawings and Scale Models Lesson

Scale Drawings and Scale Models

In earlier lessons, you learned about proportions and how to set them up and solve them. In this lesson, you will learn to use scale drawings and scale models to solve problems. A scale drawing shows an object with its measurements in proportion to the actual measurements of the object. They are similar (proportional) to the actual object. The scale is a ratio that compares the measurement used in a scale drawing with the actual measurements. Scales do not have to be in the same units. The scale factor is the constant of proportionality. When the units are the same, scale factor tells you how many times larger or smaller the actual object is compared to the measurements in the drawings or models.

Scale drawings are typically used when objects are too small or too large to be drawn to their actual size. Maps, house plans, biology cell drawings are examples of items that use scale drawings. When using a model, scale factor is always the ratio of the model's dimensions to the actual object's dimensions.

Investigate

The Statue of Liberty is 1824 inches tall. Jamie bought a model in the souvenir shop that was 8 inches tall. How can we find out what scale factor was used to build the model?

Strategy

We know that the measurements of the statue and the model are proportional, so we can start by writing this as a proportion: .

Solution

We simplify the fraction by dividing 8 into both the numerator and the denominator to get $\frac{1}{228}$. This means that the statue is 228 times taller than the model, or we reduced the size of the statue by 228 to get the model.

A map is a type of scale drawing. You can use the scale on a map to find real-world distances, or you can use the scale to make an accurate map.

Investigate

What is the actual distance between the pond and the cabins?

Strategy

Write the scale as a ratio: $\frac{5\:in}{30\:yd}$

Next, write a proportion and let x represent the actual distance. $\frac{5\:in}{30\:yd}=\frac{scale\:drawing\:distance}{actual\:distance}=\frac{5}{30}=\frac{8}{x}$

Solve the proportion:

 $\frac{5}{30}=\frac{8}{x}\\ 5x=240\\ x=48$

Solution

The actual distance between the cabins and the pond is 48 yards.

Scale Drawings are often used to build houses.

Investigate

Patty's father made her a dollhouse which was designed after the blueprint of their home. The blueprint is 20 inches wide by 42 inches long. The scale factor is $\frac{3}{1}$. Find the size of the dollhouse.

Strategy

Think: $\frac{Dollhouse}{Blueprint}$

Let's start with the width (w) and write a proportion

$\frac{3}{1}=\frac{w}{20}\\ w=60$

Let the length be represented by l. Write a proportion.

$\frac{3}{1}=\frac{l}{42}\\ l=126$

Solution

The dollhouse will be 60 inches wide and 126 inches long.

Take a look at the video to see a step by step example of how to solve a scale drawing problem. 

Now you try a few word problems using scale factor to solve problems involving maps and models. If you need to see another example, watch this video to see a word problem worked out for you. 

Scale Drawing Practice

Scale Drawings and Scale Models Homework

Now that you have spent some time learning strategies for solving problems involving scale factor, you are ready to complete your Scale Factor: Scale Drawings and Scale Models Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key. Links to an external site.

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