In kindergarten and first grade, educators introduce students to shape recognition. Students should learn about the basic shapes, including triangle, circle, square, rectangle, oval and diamond. They should be able to identify the shapes, draw them and distinguish one from one another. Teachers will use shape identification games, mnemonic devices and written activities in class lessons.
At the second- and third-grade levels, teachers introduce students to geometry as a mathematical concept. They begin by expanding the definition of a shape to include polygons, which are shapes with a certain number of sides. Students will learn about many-sided shapes, such as pentagons, heptagons and octagons. Students will also begin drawing lines and creating shapes with defined measurements using a ruler.
At these grade levels, teachers expound on the mathematical concepts in geometry. Students will begin learning about area, the quantity of space within an object, and perimeter, the sum of the length of all sides of an object. They will perform simple area and perimeter calculations for squares and circles. Students will also learn about three-dimensional shapes and volume, which is the amount of space within a three-dimensional shape. Teachers will expand the concept of polygons to include area and perimeter equations. Additionally, teachers will expand basic shapes to include types of triangles (such as acute and obtuse) and rectangles (rhombus and parallelograms).
For students who are learning at an advanced level, geometry education will include several higher-level concepts. Students will begin learning about symmetry and congruency in shapes. They will also learn the equations for area and volume of more advanced shapes, such as cylinders and trapezoids. Students may be introduced to the fundamentals of Euclidean geometry and trigonometry.