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Scale Model Builder

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About This MicroSim

A scale of 1:k means that every length on the model is the real length divided by \(k\). Areas and volumes do not shrink by the same factor:

Measurement Divide the original by
Length \(k\)
Area \(k^2\)
Volume \(k^3\)

The left panel shows the real object as a box with its dimensions in meters, beside a person 1.7 m tall. The right panel shows the model with its dimensions in centimeters, beside a 30 cm ruler. The three panels below work out one length, the floor area, and the volume.

At 1:20 a classroom that is 10 m long becomes a model 50 cm long, but its volume is divided by 8,000. This is why a model needs far less material than its size suggests.

Each object is drawn as the box that encloses it. The scale slider steps through scales in common use, including 1:12 for dollhouses, 1:50 for architectural models, and 1:87 for HO model trains.

How to Use

  1. Choose a real object from the Object menu.
  2. Drag Scale from 1:5 to 1:100 and watch the model shrink beside the ruler.
  3. Compare the three panels: which measurement shrinks fastest?
  4. Find a scale at which the model of the house would fit on a desk.

Iframe Embed Code

<iframe src="main.html"
        height="582"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

9-12 (High School Geometry)

Duration

15-20 minutes

Prerequisites

Ratios and proportions, unit conversion between meters and centimeters, and area and volume of a rectangular prism.

Bloom's Taxonomy Level

Apply (L3)

Learning Objective

Students will be able to apply a scale factor to find the dimensions of a scale model and analyze how the scale affects length, area, and volume.

Activities

  1. Convert (5 min): Students choose an object and a scale, compute the three model dimensions by hand, and check them against the model panel.
  2. Compare (5 min): Students record the divisors for length, area, and volume at 1:10 and 1:20 and explain why doubling k multiplies them by 2, 4, and 8.
  3. Design (5 min): Students choose a scale so that a model of the classroom fits on a 60 cm by 60 cm board, and estimate the cardboard needed for the floor.

Assessment

A model car is 18 cm long and the real car is 4.5 m long. Students find the scale, then determine how many times greater the real car's volume is than the model's.

References

  1. Wikipedia. Scale model.
  2. Wikipedia. Square-cube law.
  3. Common Core State Standards Initiative. High School Geometry: Modeling with Geometry (HSG-MG.A.3).