Geometry helps people describe the world around them through the study of geometric shapes, structures, and their characteristics and relationships. Through the study of geometry, students will learn about shapes and dimensions around them and how to analyze spatial relationships in everyday life. Spatial visualization—building and manipulating mental representations of two-and three-dimensional objects and perceiving an object from different perspectives—is an important aspect of geometric thinking. An understanding of the attributes and relationships of geometric objects can be applied to diverse contexts.
In the third grade, students begin a study of the area for a particular region that can be covered by a certain quantity of same-sized units of area. They also study perimeter. Through the study of perimeter, students not only can practice measuring in various units, but in adding and subtracting those units. Just as area connects to multiplication and division, perimeter connects to addition and subtraction. Letting students measure items in the classroom or around the school, sketch the item and label the measurements they made, and then solve problems involving those measurements is one way students can experience and gain a richer understanding of these geometric concepts. The use of geoboards is a way students can compare and contrast areas and perimeters.
Students begin to develop an initial understanding of a family of shapes, such as quadrilaterals. They apply their prior knowledge as well as new knowledge of the attributes that certain shapes possess. This will help students develop precision in describing the properties of geometric objects. They can articulate reasons and informal arguments about how certain shapes are related.