Concepts for Geometry and Spatial Relationships
Spatial Relationships
Facts, Concepts, and Generalizations Activities Assessment
EvaluationSymmetry is an identical relationship on two sides of a line drawn through a figure A 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 position is 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 system Activity 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 tessellate the 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 line has different properties (line, line segments, ray) Circle has different properties (circle, circumference, diameter, radius, sector, chord, area, and infinite lines of symmetry) Perimeter is the distance around a shape Area is a measure of the surface space Pi is the relationship between the diameter of a circle and its circumference Parallel two lines that lie in a plane are parallel or intersect. Angle - Lines that intersect create angles. Perpendicular create Right Angles - 90 degree angles. Activity 16-22 Polygon is a plane figure. Most simple closed figure whose sides are line segments, can be convex or non convex. Activity 16-6 Regular polygons have angles and sides all of equal measure. Three dimensional
Facts, Concepts, and Generalizations Activities Assessment
EvaluationVolume
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Volume is the amount of space an object occupies.
Conservation of volume Space FiguresActivity 16-23 Size and Shape framework of geometry in elementary school. Activity 16-26 Dr. Robert Sweetland's Notes ©