Analyze, compare, create, and compose shapes.
- 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?”
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.