Concepts for Geometry and Spatial Relationships

Spatial Relationships

Facts, Concepts, and Generalizations Activities Assessment

EvaluationSymmetryis an identical relationship on two sides of a line drawn through a figureA figure has line symmetry if it can be flipped about a line so that the resulting figure coincides with the original one. Activity 16-12 Turning Symmetry:rotate an object about its center to obtain a figure that coincides with the original one.Activity 16-31 Patterns can be described mathematically Activity 16-12 Relationships can be a pattern Relative positionis used to locate objects in space (directions). Use vocabulary involving important prepositions-in, on, under, inside, between, upon, from, outside, above, and so on.Activity 16-4 Spatial relationships and geometric patterns can be found in our everyday world Spatial references use vertical and horizontal references Coordinate systemActivity 16-21

Activity 16-28Spatial representations can be created with models, diagrams, ... (geoboards, visual representation).

Cross Sections:students need hands on activities to determine cross sections (clay models p. 433)Activity 16-32 To tessellatethe plane we must find plane figures that will fit together to fill the plane, leaving no spaces.Congruence -two figures have the same shape and size.Activity 16-19 Ruler and compass constructionsTwo dimensional

Facts, Concepts, and Generalizations Activities Assessment

EvaluationIdentify circle, square, triangle, rectangle visually A linehas different properties (line, line segments, ray)Circlehas different properties (circle, circumference, diameter, radius, sector, chord, area, and infinite lines of symmetry)Perimeteris the distance around a shapeAreais a measure of the surface spacePiis the relationship between the diameter of a circle and its circumferenceParalleltwolines that lie in a plane are parallel or intersect. Angle -Linesthat intersect create angles.PerpendicularcreateRight Angles- 90 degree angles.Activity 16-22 Polygonis a plane figure. Most simple closed figure whose sides are line segments, can be convex or non convex.Activity 16-6 Regular polygonshave angles and sides all of equal measure.Three dimensional

Facts, Concepts, and Generalizations Activities Assessment

Evaluation

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Volume is the amount of space an object occupies.

Conservation of volumeSpace FiguresActivity 16-23 Size and Shapeframework of geometry in elementary school.Activity 16-26 Dr. Robert Sweetland's Notes ©