In the fourth grade, students' concept of a line goes beyond "something straight you draw with a ruler" to include the idea that lines extend forever in either direction. Fourth grade geometry includes introduction of parallel lines, intersecting lines, line segments, and points on a line. Students also learn that intersecting lines form angles, and different types of angles have different properties. Students can experiment with drawing lines that intersect at different angles to cement their understanding of these concepts.
Introducing students to different two- and three-dimensional shapes is a great way to begin teaching them the vocabulary of geometry, including terms like vertex, face, base and edge. Studying polygons can help students identify the prefixes tri-, quad-, pent-, hex- and oct- in both mathematical and non-mathematical contexts. Students can look for polygons and shapes in their environment, and they can draw and sculpt shapes to create a tactile connection to the properties they are studying.
By drawing, building and manipulating geometric shapes, students will be able to better understand the ideas of symmetry and congruence. They will start to realize that a shape flipped upside down and rotated 90 degrees is still the same shape, even though it looks different. By strengthening students' abilities to think in this way, teachers can prepare them for more advanced geometry instruction to come.
Geometry is a hands-on subject, and use of math manipulatives and hands-on activities can be enormously helpful. Translucent geometric tiles are very useful for overhead demonstrations, especially when discussing rotation and symmetry. Compasses are effective as tools for studying circles and angles. Students can use tangrams and pattern blocks for physical creation and manipulation of polygons, and they can explore polygons and learn about area and perimeter with geoboards.