For young children, geometry is really housed in a larger concept that we call “spatial thinking.”  This includes mathematical skills such as categorizing shapes and objects, measurement, perspective, mental transformation of shapes (being able to turn a shape upside down), scaling, proportion,and location. This list is in no way complete, as there are many more ways that spatial thinking can be taught and learned in the early years.

An examination of the physical environment is one sure-fire way to get kids talking about geometry.  Using examples from the area around you and them, try to look for shapes, edges, lengths, and areas.

Copying shapes using manipulatives such as tangrams is another way to explore geometry.  We are going to look broadly at tangrams another day, but for now, take a look at these two sets of tangrams and consider how children can explore them.

• CCSS.Math.Content.K.G.B.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).
• CCSS.Math.Content.K.G.B.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
• CCSS.Math.Content.K.G.B.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

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This half of the Geometry Standard is quite complex and subsumes many aspects of the previous standards.  Take for instance the phrase, “number of sides and vertices/corners”.  This requires that the child can count the sides or vertices, using one-to-one correspondence, understands the attributes and the vocabulary of “sides” and “vertices”, and then is able to compare all of those aspects of a shape to another.

Of course, if we are talking about triangles or squares, this isn’t very complex.  But when we are talking about solid shapes (3 dimensional) and then moving them in space to present different orientations, the ability to meet this standard is much more difficult.

Breaking this standard down into smaller parts will make the most sense for teaching.  First, children need to have exposure to 2 and 3 dimensional shapes and solids.  Next they need repeated opportunities to use the associated vocabulary to describe their attributes.  Then they need to see several examples of shapes and solids using manipulatives and real-world objects.

Another way to introduce these concepts is by using the second substandard above to support the first substandard above.   When children are afforded opportunities to build and create shapes and solids in many sizes, using a variety of materials, they will experience them on a sensory level as well.

The third substandard above may come easily to some children and may be much more difficult for others.  Children who are naturally drawn to puzzles and tangrams and who can easily manipulate shapes so that an “upside down triangle” is still a triangle will probably be able to put 2 triangles together to create a square.  Other children’s spatial skills may not be as developed, so working with these manipulatives will be important, but may be frustrating. Take a look at this post about Tangrams to see how this type of manipulative can provide a foundation for shape building.

• Two large right triangles

• One medium-sized right triangle

• Two small right triangles

• One small square

• One parallelogram

According to Gwen Dewar, PhD. in Parenting Science (2009)

Arranged correctly, the shapes can be fitted together as a large square, rectangle, or triangle. They can also be arranged in a variety of complex shapes, including fanciful ones (like the rabbit illustrated here).

There are many ways to play with tangrams. The simplest way is to let kids create their own complex shapes. But traditionally, tangrams are treated as puzzles. The player is shown a target shape (in outline, or silhouette only) and then asked to recreate that shape using the seven pieces.

As noted below, tangrams can also be used to teach kids to measure area without formulas—an approach that should help kids develop an intuitive sense of geometry.

The National Council of Teachers of Mathematics also says of that while children play with Tangrams, they;

• develop positive feelings about geometry

• classify shapes

• develop an intuitive feeling for shapes and geometric    relationships

• develop spatial rotation skills

• develop precise vocabulary for manipulating shapes (e.g., “flip,” “rotate”)

• learn the meaning of “congruent”

 

Try and get a set of these wonderful manipulatives for your center or classroom.  This website has sets of them for larger groups of children.