### DOE Archives

#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.7:
All Students Will Develop Spatial Sense And An Ability To Use Geometric Properties And Relationships To Solve Problems In Mathematics And In Everyday Life

Descriptive Statement: Spatial sense is an intuitive feel for shape and space. It involves the concepts of traditional geometry, including an ability to recognize, visualize, represent, and transform geometric shapes. It also involves other, less formal ways of looking at two- and three-dimensional space, such as paper-folding, transformations, tessellations, and projections. Geometry is all around us in art, nature, and the things we make. Students of geometry can apply their spatial sense and knowledge of the properties of shapes and space to the real world.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Explore spatial relationships such as the direction, orientation, and perspectives of objects in space, their relative shapes and sizes, and the relations between objects and their shadows or projections. 2 Explore relationships among shapes, such as congruence, symmetry, similarity, and self-similarity. 3 Explore properties of three- and two-dimensional shapes using concrete objects, drawings, and computer graphics. 4 Use properties of three- and two-dimensional shapes to identify, classify, and describe shapes. 5 Investigate and predict the results of combining, subdividing, and changing shapes. 6 Use tessellations to explore properties of geometric shapes and their relationships to the concepts of area and perimeter. 7 Explore geometric transformations such as rotations (turns), reflections (flips), and translations (slides). 8 Develop the concepts of coordinates and paths, using maps, tables, and grids. 9 Understand the variety of ways in which geometric shapes and objects can be measured. 10 Investigate the occurrence of geometry in nature, art, and other areas.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, students:

 11 Relate two-dimensional and three-dimensional geometry using shadows, perspectives, projections and maps. 12 Understand and apply the concepts of symmetry, similarity and congruence. 13 Identify, describe, compare, and classify plane and solid geometric figures. 14 Understand the properties of lines and planes, including parallel and perpendicular lines and planes, and intersecting lines and planes and their angles of incidence. 15 Explore the relationships among geometric transformations (translations, reflections, rotations, and dilations), tessellations (tilings), and congruence and similarity. 16 Develop, understand, and apply a variety of strategies for determining perimeter, area, surface area, angle measure, and volume. 17 Understand and apply the Pythagorean Theorem. 18 Explore patterns produced by processes of geometric change, relating iteration, approximation, and fractals. 19 Investigate, explore, and describe geometry in nature and real-world applications, using models, manipulatives, and appropriate technology.

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicators 16 and 19 above, by the end of Grade 12, students:

 20 Understand and apply properties involving angles, parallel lines, and perpendicular lines. 21 Analyze properties of three-dimensional shapes by constructing models and by drawing and interpreting two-dimensional representations of them. 22 Use transformations, coordinates, and vectors to solve problems in Euclidean geometry. 23 Use basic trigonometric ratios to solve problems involving indirect measurement. 24 Solve real-world and mathematical problems using geometric models. 25 Use inductive and deductive reasoning to solve problems and to present reasonable explanations of and justifications for the solutions. 26 Analyze patterns produced by processes of geometric change, and express them in terms of iteration, approximation, limits, self-similarity, and fractals. 27 Explore applications of other geometries in real-world contexts.

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