This chapter brings together three approaches to ideas of measurement and scale. First students focus on scale drawing, learning the powerful mathematical ideas of proportional reasoning and invariant ratios.
Students then develop the concept of similarity and ways of establishing similarity.
The chapter ends by introducing fundamental concepts of trigonometry as ways of relating invariant ratios to angles. Applications including indirect measurement, design, construction, and art are provided throughout. Students begin by reading read maps and blueprints and using the provided scales to calculate distances and lengths. They examine enlargements and reductions of a horse skeleton picture some accurate and some not to formulate their own tests for deciding what makes a good scaled copy. The section ends with students' applying their tests to triangles and polygons.