Making Big Plans

Contributor: Jamie Hagler. Lesson ID: 13841

Plan on completing this lesson to learn how to create and use scale drawings!

categories

Algebra I

subject
Math
learning style
Visual
personality style
Golden Retriever
Grade Level
High School (9-12)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

Audio:
  • How do you know if your house was burgled by Smurfs?

Look for blueprints!

Smurf blue prints

Image [cropped and shoe prints added] by Edouard Jausions, via Pixabay, was released into the public domain.

All kidding aside, we will be talking about scale drawings, and blueprints are the perfect scale drawing!

blueprint

First, let's talk about scale.

Scale is the ratio between corresponding measurements of a blueprint and the actual object.

In the example below, the blueprint is 1 inch by 3 inches, while the actual object is 4 inches by 12 inches:

example 1

In this example, the scale would be 1:4. This means that for every 1 unit on the blueprint, there are 4 units on the actual object.

This could possibly mean that 1 unit (maybe an inch) on the blueprint could represent 4 inches (or even 4 feet!) on the actual object.

Let's do a basic scale problem:

Jim made a blueprint of the White House. Jim's blueprint used a scale in which 1 inch represents 6 feet. The White House has an actual length of 168 feet.

  • What is the length in inches of Jim's blueprint?

We can solve this by setting up a proportion!

We will put the inches on the top of each fraction and feet on the bottom. We then cross-multiply and divide:

  inches = inches
  feet feet

 

  1 = x
  6 168

 

  168 = 6x
  6 6

 

  28 = x

 

Therefore, 28 inches is the length in inches of Jim's blueprint

  • Not too bad, huh?

Here's another one:

Lisa Ann drew the following blueprint of her store:

store blueprint

  • If 1 inch = 4 feet, what is the area of the store?

This one is a little different and involves one more step, but we've got this!

  • First, what would the dimensions of the store be?

We can set up proportions like before. However, this time we need to determine two different answers: the length and width in feet of the store.

  inches = inches   inches = inches
  feet feet   feet = feet

 

  1 = 5   1 = 9
  4 x   4 = x

 

  20 = x   36 = x

 

We can see the dimensions of the store would be 20 feet by 36 feet:

store blueprint

  • The question asked for the area of the store, so are we finished?

Nope! One more step!

  • How do we find area of a rectangle?

The formula is A = lw, so we will multiply the length and width. This will give us 20 x 36, which is 720.

Therefore, the area of the store is 720 square feet!

Now that you have a handle on using and describing scale drawings, let's move on to the Got It? section.

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