Geometry for Beginners: A Parent's Guide to Beginning Geometry

Beginning Geometry, Grades K-2

Parents as Teachers

Parents - even those who don't homeschool their children - already teach many geometric concepts at home. For example, when you teach your child the name of a 3-sided figure (triangle), you wear the hat of a geometry teacher. Here are some other concepts you may find yourself teaching your child while wearing that hat.

Kindergarten

In kindergarten, children learn to identify, describe and compare a variety of shapes. Some shapes are considered part of plane geometry (2-dimensional or 'flat' figures), including circles, squares, rectangles and triangles. In the field of solid geometry (3-dimensional figures) kindergarteners learn about cubes, spheres, cylinders and cones. Kindergartners also learn to:

1. Describe the position of these shapes in relation to other shapes and objects, using prepositions, like beside, next to, behind, in front of, above and below.
2. Compare shapes by how many sides and corners they have. It's likely that the terms vertex and vertices will be used as an alternative to corner and corners.
3. Draw shapes on paper and build them from clay or sticks.

First Grade

First graders continue to talk about definitions of shapes in terms of the number of sides and vertices, being closed (no space between any two sides). They also learn that color, size and relation to other shapes or objects make no difference to the shape's definition. They'll begin to use the word prism. The shape trapezoid is introduced to describe a 4-sided shape with two parallel sides and two non-parallel sides.

Right-circular cones and cylinders are discussed. First graders can have fun making composite shapes using the shapes they've learned. Circles and rectangles can be divided into two and four equal parts, introducing the new jargon of halves, fourths and quarters.

Second Grade

In second grade, several new terms or shapes are learned:

• Shapes with four sides are also called quadrilaterals.
• Pentagons have five sides.
• Six-sided shapes are called hexagons.

Second graders also learn to divide squares and rectangles into smaller, but equal, squares in rows and columns. Counting the number of squares inside these quadrilaterals will be their first introduction to the area of a square or rectangle.

Circles and rectangles are divided into three equal parts. The term thirds will be added to their vocabulary of halves and quarters. They'll describe a whole as two halves, four fourths or three thirds.

In second grade, kids find out that you can divide rectangles into equal parts that have different shapes. For example, they can divide a rectangle into two halves, and then divide one of the halves into two equal parts with a horizontal line and the other half into equal parts with a vertical line).