Third-graders learn types of polygons and their characteristics to identify them. Triangles studies include equilateral, with equal angle and side measurements; isosceles, having two equal sides and angles; scalene, which has no sides or angles that measure equally; right triangle, containing one right angle; an acute triangle with all three angles measuring less than 90 degrees; and an obtuse triangle, which contains one angle larger than 90 degrees.
Four-sided polygons, or quadrilaterals, and their attributes include squares, rectangles, rhombuses, trapezoids and parallelograms, which contain at least one set of parallel sides. Larger polygons characterized by their number of sides and angles are infinite and include pentagons, hexagons, heptagons, octagons and decagons whose prefixes lead students to the shape of the polygon.
Introductory three-dimensional shapes are also studied in third-grade geometry to include cubes, spheres, pyramids, cylinders and cones. Manipulative examples may be helpful in describing three-dimensional shapes to young children.
Lines, line segments, rays and angles to include acute, right and obtuse are discussed and identified in elementary geometry. The use of these mathematical tools create polygons studied in other areas of third-grade geometry. Lines go on infinitely in both directions while line segments are a portion of a line ending with endpoints. Rays have one endpoint and travel on forever on the other end. Angles that are acute may be compared to "a cute" or small angle measuring less than 90 degrees while a right angle measures exactly 90 degrees. An obtuse angle is one measuring more than 90 degrees but less than 180 degrees, or a straight line.
The shapes of polygons may be learned in combination with properties such as symmetry, which displays an imaginary line dividing the same into equal parts that when folded on that line of symmetry would be exactly the same. Reflection is when a shape is flipped over an imaginary line outside the shape showing the exact opposite of the current orientation. Rotation is also touched upon in the third-grade, which spins the polygon on an imaginary center point within the surface of the two-dimensional shape. Third-graders learn the difference between similar -- polygons that are the same shape but not the same size -- and congruent, displaying exactly the same shape and size. Translation only moves the shape to another location but does not change any of its attributes.
The calculation of simple area and perimeter are used with the study of polygons. The students are introduced to formulas to calculate the area of a rectangle or square -- multiplying the length times the width -- while perimeter adds the four sides' lengths. Circles are a bit more complicated and involve "pi" which can be confusing to some third-grade students and may be used only for enrichment activities. The volume of a three-dimensional cube can be computed by multiplying length, width and height.
When learning about vertices, students often graph the shapes on a grid using both "x" and "y" axes. Coordinates may be used to graph the polygon as well as finding points on the grid paper. The use of line segments and their endpoints can be reinforced while graphing as well. Graphing at this stage of elementary school is very basic.