Calculating with Scales

Contributor: Elephango Editors. Lesson ID: 10776

Calculating with scales does not involve fish, unless you are trying to draw a six-foot sturgeon on a piece of notebook paper! Practice with easy online problems to learn this important math skill!

categories

Pre-Algebra, Ratios, Rates, Percentages, and Proportions

subject
Math
learning style
Visual
personality style
Lion, Otter
Grade Level
Middle School (6-8)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

Audio:

Lee drew a picture of his car for a comic book he is making. He wants his comic book to be accurate so that the car is the right size when it is next to people in the story.

In order to accomplish that, Lee decided on a scale for his drawings. Lee wants to use the scale of 1 inch to 4 feet.

comic book

  • What is scale?

Scale is a math concept you see and use all the time, probably without even knowing it!

Scale refers to when the actual size of something is enlarged or reduced by a specific amount, or scale.

For example, maps are scale drawings of actual places and distances. Blueprints are scale drawings of buildings. Toys and model cars or airplanes are scale figures of actual objects.

  • Can you think of any other examples?

Even though the size changes from the actual to the scale, the proportions of the object stay the same.

For example, if you are making a scale drawing of a giraffe, the drawing will obviously be smaller than the actual size of a giraffe. However, the proportions will stay the same. You will still draw a tall and skinny giraffe, not a short and wide giraffe.

giraffe scale

Let's look at the scale from the beginning of the lesson:

Lee wants to use the scale of 1 inch to 4 feet.

This means every 1 inch of Lee's drawing represents 4 feet of the actual size of the car.

This scale can be written as a ratio:

1:4

Scale size: actual size

The scale can also be written as a fractional proportion:

  1
  4

 

  scale size
  actual size

 

When calculating with scale, we use two fractional proportions.

On the left, we write the scale given in the story problem. Remember, Lee is using a scale of 1 inch to 4 feet:

scale

On the right, we fill in the other information we know. We also identify the unknown information we need to solve for, labeling it as X.

In this story, we know Lee's car is actually 15 feet long. We need to figure out how long Lee will make the scale drawing.

scale

Now, all you have to do is cross multiply to solve for X:

cross multiply

x = 3.75 which you can now plug back into the fractional proportion:

scale

The actual size of Lee's car is 15 feet, and the scale drawing size of Lee's car should be 3.75 inches!

Lee's car

Before you move on to practice, watch this short video to learn more about scale!

Grade 7 Math 8.1A, Dimensions, Area, and Scale Drawings (New version) from JoAnn's School:

Click NEXT to visit the Got It? section to practice using scale!

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