Standard 7: Geometry from a Synthetic Perspective

In grades 9-12, the mathematics curriculum should include the continued study of geometry of two and three dimensions so that students can:

• Interpret and draw three-dimensional objects

Benchmarks 9C (The Mathematical World: Shapes)
Grades 3-5, page 223
Many objects can be described in terms of simple plane figures and solids. Shapes can be compared in terms of concepts such as parallel and perpendicular, congruence, similarity, and symmetry. Symmetry can be found by reflection, turns, or slides.
 

• Represent problem situations with geometric models and apply properties of figures

Benchmarks 9C (The Mathematical World: Shapes)
Grades 9-12, page 225
Different ways to map a curved surface (like the earth’s) onto a flat surface have different advantages.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 9-12, page 297
Make and interpret scale drawings.

Benchmarks 9C page 225 (The Mathematical World: Shapes)
Grades 9-112
Distances and angles that are inconvenient to measure directly can be found from measurable distances and angles using scale drawings or formulas.
 

• Classify figures in terms of congruence and similarity and apply these relationships

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 9-12, page 297
Describe spatial relationships in geometric terms such as perpendicular, parallel, tangent, similar, congruent, and symmetrical.
 

• Deduce properties of, and relationships between, figures from given assumptions

Benchmarks 9C (The Mathematical World: Shapes)
Grades 9-12, page 225
There are formulas for calculating the surface areas and volumes of regular shapes.

When the linear size of a shape changes by some factor, its area and volume change disproportionately: area in proportion to the square of the factor, and volume in proportion to its cube. Properties of an object that depend on its area or volume also change disproportionately.