Learning and Teaching Geometry: Help for Parents

Learning and Teaching Geometry at Home

Geometric Concepts in Elementary Grades

Concepts presented in one grade are often repeated in more detail in later grades. To help you become familiar with what your child learns about geometry in grade school, a few basic concepts are listed here, along with some of the learning objectives and exercises associated with each.

Shapes

Create, compare and analyze shapes

Every time new shapes are learned, they're analyzed in terms of their size, numbers of sides and angles, kinds of angles, similarities and differences. Shapes are also joined to create new shapes, or composite shapes.

Names of shapes

Beginning with circles, squares and rectangles, students learn about more shapes until they can identify those that have up to 12 sides. Naming both 2-D and 3-D shapes begins in kindergarten.

Partitioning shapes

Shapes are divided into equal parts that are referred to as halves, thirds and quarters. This is a precursor to learning fractions.

Classifying shapes by their properties

Shapes are classified by the number of sides and angles, as well as the kinds of angles at times. Terms such as point, line, line segment and ray are intermingled with discussions of shape classifications. The broadest classifications are 2-D and 3-D shapes.

Using nets to learn about 3-D shapes

This may involve cutting out a 2-D shape and bending it to make a 3-D shape, such as a box.

Perimeters and areas

Perimeter of flat shapes

Perimeters are calculated by measuring the length of all the straight lines around the edge of a shape and adding the measurements.

Area of plane and solid shapes

The area of flat, or plane, geometric shapes are figured using unit cubes; this work gets translated to formulas for area. This exercise helps children learn in later lessons how to calculate the surface area and volume of solid (3-D) shapes.

Graphs

Coordinate graphs

The horizontal and vertical lines (axes) in a graph, with their intersections, are used to place given points using two numbers (coordinates) - one for each line. Real-life problems are described and sometimes solved using graphs.

At-Home Geometry

Geometry can be a lot of fun because shapes are such hands-on entities. Below are a few methods for teaching geometry at home. Choose the one that will appeal to your child's interests. For instance, if your child enjoys reading, try introducing the lesson with a book.

Books

Many kids love to be read to. It's also an enjoyable way for parents to surreptitiously review old, almost forgotten geometry concepts. If your child is just beginning to learn shapes, use books like When a Line Bends . . . A Shape Begins, by Rhonda Gowler Green, which presents 2-D shapes. To introduce 3-D shapes to your child, you could use a book such as Captain Invincible and the Space Shapes by Stuart J. Murphy.

Spaghetti and Meatballs for All! by Marilyn Burns introduces perimeters and area. Another approach to finding perimeters and areas of rectangles - including squares - is to look at the archaeological site of an old city in Mexico with the book Teotihuacan: Designing an Ancient Mexican City - Calculating Perimeters and Areas of Squares and Rectangles by Lynn George.

Even graphs have books to introduce them, some of which may foster a trip to the zoo. Examples of these books are Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda and Giraffe Graphs by Melissa Stewart.

Games

Most kids who play Battleship may not realize they're engaging with geometry because of the use of graph coordinates. For puzzles, use tangrams - you can even make them at home. There are a number of sites that give you a printable sheet that you can then cut into the shapes. Use challenges to make the puzzle more fun. Challenges may include:

1. Without using triangle shapes, make a square.
2. Without using the square, make a trapezoid.
3. Use all of the pieces to make a rectangle (not a square).
4. Find as many ways as possible to make a rectangle.
5. Find as many ways as possible to form a square with the tangram pieces.

You can find geometry game books for a variety of printable games. One example is 25 Super Cool Math Board Games: Easy-to-Play Reproducible Games that Teach Essential Math Skills by Lorraine Hopping Egan.

Music

Songs can introduce a concept, but they're most helpful in aiding retention of something your child has already learned. Some you'll need to purchase on CD or MP3 downloads, others can be found on YouTube.com. Most are very rhythmic and many include movements, which can make learning the concepts more fun.

Kids often like to make up their own songs. For instance, using a tune like Here We Go 'Round the Mulberry Bush, they might make up a song like:

Here we go 'round a 4-sided shape,
A 4-sided shape,
A 4-sided shape.
Here we go 'round a 4-sided shape,
A qua-dri-la-ter-al.

Field Trips

Field trips can be taken to teach or reinforce geometry concepts. A field trip around the block to discover different shapes can be very productive. Finding the perimeter and area of some of those shapes could add to the fun. Alternatively, if there's an art center or museum in your area, take a field trip there with your child to find pictures or artifacts that demonstrate a variety of geometric concepts.