California Early Math Project 2019

Geometry

A critical area of instruction in kindergarten is for students to describe shapes and space. Students develop geometric concepts and spatial reasoning from experience with the shapes of objects and the relative positions of objects.

Students use positional words to describe objects in the environment (K.G.1). Examples of positional words include in and out, inside and outside, down and up, above and below, over and under, before and after, top and bottom, front and back, right and left, on and off, begin and end, and near and far.

 

Students develop spatial sense by connecting geometric shapes to their everyday lives. Students need opportunities to identify and name two- and three-dimensional shapes in and outside of the classroom and describe relative positions by answering questions such as these:

  • Which way is the cafeteria? (The cafeteria is to the right.)

  • Which shape is near the rectangle? (The circle is near the rectangle.)

  • Where is the green ball? (The green ball is on top of the cupboard.)

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Example Exercise

 

What types of shapes do you see on the floor of the basketball court? (I see a rectangle and a circle on the basketball court.)

Kindergarten students connect their work with identifying and classifying simple shapes to help them compare shapes and manipulate two or more shapes to create a new shape. This understanding also builds foundations for students to “reason with shapes and their attributes” in grade one.

 

Students describe similarities and differences between and among shapes using informal language.

 

These experiences help young students begin to understand how three-dimensional shapes are composed of two-dimensional shapes—for example:

  • The base and the top of a cylinder is a circle.

  • The face of a cube is a square.

  • A circle is formed in the shadow of a sphere.

 

In early explorations of geometric properties, students discover how categories of shapes are subsumed within other categories. Puzzles provide opportunities for students to apply spatial relationships and develop problem-solving skills in an entertaining and meaningful way. Pattern blocks and tangrams are often utilized when students work with two-dimensional shapes.