Elementary Math Lessons: Triangles and Other Basic Shapes

What Elementary Children Learn about Basic Shapes

Shapes Learned in Elementary School

As early as kindergarten, children learn to recognize 2-dimensional shapes, such as triangles, squares, rectangles, circles and hexagons. Students are also introduced to 3-dimensional shapes, including cubes, spheres, cones and cylinders, in early elementary school.

Elementary students learn to divide shapes into equal parts, such as halves and fourths, and compare the different parts. For instance, if you divide a triangle in half horizontally, the top and bottom would not look the same; however, if you divide it in half vertically, the left and right sides would look the same. Eventually, students learn to identify this line as the line of symmetry.

Plane and Solid Shapes

Students recognize that closed, 2-dimensional shapes fall into the classification of plane geometry. All 2-dimensional shapes are called polygons. Solid geometry covers 3-dimensional shapes. The categories for shapes are based on the number of sides and angles they have.

Quadrilaterals have four sides and four angles. This category includes:

• Squares
• Rectangles
• Trapezoids
• Parallelograms
• Rhombuses

Triangles have three sides and three angles. This category includes:

• Right triangle
• Acute triangle
• Obtuse triangle

Shapes with more than four sides include the following:

• Pentagon
• Hexagon
• Octagon

Perimeter and Area

In the elementary grades, students learn to find the perimeter of a polygon by adding up its sides. When given the perimeter and all sides but one, students can determine the length of the missing side. They will also be able to draw two rectangles that have the same perimeter but different areas, or conversely, two rectangles with the same area but different perimeters.

Third graders discover how to figure the area of a rectangle by deconstructing it into smaller, equal rectangles and counting them. They are then shown that multiplying the number of units in a row by the number of units in a column gives the same number as the area.

By the end of fifth grade, student have learned the formula for the area of a rectangle, A = l x w. They also know how to figure the volume of right rectangular prisms using the formulas V = l * w * h and V = b * h.