The general objective of teaching different types of polygons in grade 5 math is to help students understand and identify various polygons, their properties, and how to classify them based on their attributes. This includes:

1. Recognizing and naming polygons: Students should be able to identify and name different polygons, such as triangles, quadrilaterals, pentagons, hexagons, etc.

2. Understanding polygon properties: Students should learn about the defining characteristics of polygons, such as the number of sides, angles, and vertices they have. They should also understand that the sum of the interior angles of any polygon is always equal to a specific value.

3. Classifying polygons: Students should be able to classify polygons based on their properties. For example, they should understand that all squares are also rectangles, but not all rectangles are squares.

4. Identifying regular and irregular polygons: Students should learn to differentiate between regular polygons (all sides and angles are equal) and irregular polygons (sides and angles are not equal).

5. Exploring the relationships between polygons: Students should understand how polygons can be related to each other, such as how a square is a special type of rectangle or how a triangle is a special type of polygon.

By achieving these objectives, students will develop a solid foundation in geometry and be able to apply their knowledge to solve problems involving polygons.