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Dec 7, 2023 · Level 3: Deduction (Formal deduction) Students at the formal deductive level think about relationships between properties of shapes and also understand relationships between axioms, definitions, theorems, corollaries, and postulates. They understand how to do a formal proof and understand why it is needed. Level 4: Rigor.
three-dimensional figures provides opportunities for students to learn about the geometric properties of three-dimensional figures and about the geometric rela-tionships between three-dimensional figures and their two-dimensional faces. The discussion of each big idea in this section includes:
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The objects of thought here are the properties of shapes. Students begin “if-then” thinking; for example, “If it’s a rectangle, then it has all right angles.” Students can begin to think about the minimum information necessary to define figures; for example, a quadrilateral with four congruent sides and one right angle must be a square.
Use geometry software to explore triangles, parallel and perpendicular lines, angles, quadrilaterals, and circles. When students can drag vertices and display measures, they can really begin to grasp how the properties of each figure work. Understanding: The student can identify figures, or components of figures.
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Spatial sense is an intuitive feel for shape and space. Itinvolves the concepts of traditional geometry, including an ability torecognize, visualize, represent, and transform geometric shapes. Italso involves other, less formal ways of looking at two- andthree-dimensional space, such as paper-folding, transformations,tessellations, and projections....
Geometry is the study of spatial relationships. It is connected toevery strand in the mathematics curriculum and to a multitude ofsituations in real life. Geometric figures and relationships haveplayed an important role in society's sense of what isaesthetically pleasing. From the Greek discovery and architecturaluse of the golden ratio to M. C. Es...
Traditionally, elementary school geometry instruction has focusedon the categorization of shapes; at the secondary level, it has beentaught as the prime example of a formal deductive system. While theseperspectives of the content are important, they are also limiting. Inorder to develop spatial sense, students should be exposed to abroader range of...
ing geometric figures. The experiences and explorations can take place at different levels of sophistication: from shapes and their appearances to properties of shapes to relationships among properties. The spirit of informal geometry is one of exploration, almost always in a hands-on, engaging activity. Spatial Sense
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What are the properties of geometric figures?
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What are the properties of geometric objects at Level 3?
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The objects of thought at level 2 are the properties of shapes. Students develop relationships between and among properties. Shapes can be classified using minimal characteristics; e.g., "Rectangles are parallelograms with a right angle." Students at level 2 will be able to follow an informal deductive argument about shapes and their properties.
