Concepts for Geometry and Spatial Relationships

Spatial Relationships

Facts, Concepts, and Generalizations
Symmetry 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 16-28

Spatial 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 constructions

Two dimensional

Facts, Concepts, and Generalizations
Identify 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


Volume is the amount of space an object occupies.
Conservation of volume

Space Figures
Activity 16-23  
Size and Shape framework of geometry in elementary school. Activity 16-26  

Dr. Robert Sweetland's Notes ©