Young children should start to become familar with the concept of shapes and the idea that almost everything can be made with a series of shapes. For example, a house might be a rectangle, with another rectangle for a door, squares for windows and a triangle for a roof. Initially, they’ll start with basic shapes, like circle, square, and triangle, then move on to more complex shapes, like rhombus and trapezoid. Encourage students to recognize shapes in their world by going on a “shape walk” or graphing the number of items of each shape you can find in the classroom.
An important concept in geometry is that some shapes can be broken down into smaller shapes. When looking at a parallelogram, for example, you can draw two straight lines to make a rectangle and two right-angled parallelograms. Tangram puzzles can be a big help with this concept, as the children can play with shapes, moving them around to create different images. You can also give a child a paper shape and have her cut out other shapes from the first.
Teach children that, when two lines meet, they form an angle. Though young children may not be ready to actually measure the degree of angle, you can teach the difference between obtuse, acute and right angles. Point out how various shapes contain these types of angles -- a rectangle has four right angles and a parallelogram has two acute angles and two obtuse angles. Older students might be able to cut the points off of the triangles and glue them next to each other, showing that all three angles of a triangle add up to 180 degrees.
Finding the area of shapes is a more advanced geometric technique, but you don’t have to start out with the formulas. Have students make shapes on graphing paper, filling in the small squares. To find the area, they only have to count the number of squares they’ve colored. The answer will be in “square units.” Students will then understand what area truly means before memorizing formulas. It may also be easier for them to see how a complex shape might really just be a combination of other shapes.