Mechanical and electronic tools are used to perform constructions of common geometric shapes and patterns, and to develop the idea of geometric similarity, which can be integrated with the ideas of ratio and proportion. Students' use of formal reasoning and proof should increase as they progress through school. Students can apply methods developed in the geometric context to make sense of fractions and variables, construct graphs and other representations of data, and to make and interpret maps, blueprints, and schematic drawings. In high school, students use formal reasoning to justify conclusions about geometry. They should recognize the logical structure of the system of geometric axioms, become increasingly proficient in proving theorems within the axiomatic system, and use axioms and theorems to verify conjectures generated through their own work or by their peers.
Students learn to apply coordinate geometry to the solution of problems.
They extend their experience with transformational geometry to a variety of congruence and similarity transformations and their composition. Measurement, like no other aspect of science, is responsible for the historical development of mathematics. It is one topic that naturally lends itself to connections within mathematics and across other disciplines, including the social, physical, and biological sciences. Teaching measurement is best accomplished through direct applications or by being embedded within other mathematical topics. A measurable attribute of an object is a characteristic that is most readily quantified and compared.