Where's the Math?
Geometry
Instructional programs from prekindergarten through grade 12 should enable all students to--
analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; apply transformations and use symmetry to analyze mathematical situations; use visualization, spatial reasoning, and geometric modeling to solve problems. Geometry and spatial sense are fundamental components of mathematics learning. They offer ways to interpret and reflect on our physical environment and can serve as tools for the study of other topics in mathematics and science.
Principles and Standards calls for geometry to be learned using concrete models, drawings, and dynamic software. With appropriate activities and tools and with teacher support, students can make and explore conjectures about geometry and reason carefully about geometric ideas.
Geometry Standard
Instructional programs from prekindergarten through grade 12
should enable all students to—
Apply transformations and use symmetry to analyze mathematical situations
Pre-K–2 Expectations:
In prekindergarten through grade 2 all students should–
• recognize and apply slides, flips, and turns;
• recognize and create shapes that have symmetry.
Grades 3–5 Expectations:
In grades 3–5 all students should–
• predict and describe the results of sliding, flipping, and turning two-dimensional shapes;
• describe a motion or a series of motions that will show that two shapes are congruent;
• identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs.
Grades 6–8 Expectations:
In grades 6–8 all students should–
• describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling;
• examine the congruence, similarity, and line or rotational symmetry of objects using transformations.
Grades 9–12 Expectations:
In grades 9–12 all students should–
• understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices;
• use various representations to help understand the effects of simple transformations and their compositions.
