1. Lesson 4

1.3. Lesson 4 Summary

Mathematics 20-2 M6 Lesson 4

Module 6: Proportional Reasoning

 
Lesson 4 Summary
 

In this lesson you investigated how diagrams and models can be used to represent 2-D shapes and 3-D objects. These diagrams allow sculptors and designers to produce an accurate representation of what their designs would look like on larger-than-life canvases, like a mountain, or smaller canvases, such as a coffee mug.

 

Scale models are proportional representations of 3-D objects. Scale diagrams are proportional representations of 2-D shapes. Designers use scale to produce accurate and proportional representations of objects and shapes. By relating the diagram or model’s measurement to the actual measurement, the scale factor can be determined.

 

This is an illustration of the formulas for calculating the scale factor of 2-D shapes and 3-D objects. The scale factor for 2-D shapes can be calculated by dividing the diagram measurement by the actual measurement. The scale factor for 3-D objects is calculated by dividing the linear measurement of the scale model by the corresponding linear measurement of the object.

 

A scale factor of greater than 1 will result in an enlargement, while a scale factor between 0 and 1 results in a reduction. A scale factor of exactly 1 represents a full scale (1:1) model, which means that the dimensions stay the same.

 

In order for a diagram to be proportional to the original, all items on the diagram have to be drawn to the same scale. Likewise, in order for a model to be proportional to the original shape, all linear measurements need to be related by the same scale factor.

 

In Lesson 5 you will use scale diagrams and models to determine unknown dimensions.