Learning About the World

Mathematics


Geometry and Spatial Reasoning -- Geometry and Spatial Sense

Goal 1: Children increasingly recognize two- and three-dimensional objects and use spatial reasoning.

By the end of each age group or grade level, most children will have met prior age group or grade level standards in this domain.

Infants Through Older Toddlers

Infants

(0-12 Months)

  1. Explore objects of different shapes using different senses
  2. Continue to look for an object when it is completely hidden
  3. Attend to how objects move in space by tracking objects with their eyes and head
  4. Explore relationships between objects through different actions (e.g., banging, rubbing, tapping together)
  5. Put objects into other objects (e.g., rattle into bowl)

Young Toddlers

(9-18 Months)

  1. Experiment with body’s relationship to objects (e.g. move body to see the front of doll)
  2. Manipulate objects of different sizes and shapes and how they fit together (e.g., nesting cups, or any object perceived to fit in container or tube)
  3. Explore space with entire body (e.g., crawl under table, climb into a box)
  4. Complete simple knob non-connecting puzzles by turning shapes and fitting shape into place using trial and error
  5. Follow simple directions related to position (e.g., in, on, up) with modeling and assistance

Older Toddlers

(18-36 Months)

  1. Follow simple directions related to position (e.g., in, on, up) and proximity (e.g., next to, between)
  2. Match basic two-dimensional shapes of same size
  3. Create pictures using simple shapes (e.g., using pattern blocks or parquetry blocks)
  4. Put together and take apart shapes to form new shapes
  5. Build simple three-dimensional structures (e.g., stacking blocks)
  6. Complete 9-12 piece non-connecting puzzles by matching pictures or shapes
Younger Preschoolers Through Kindergartners

Younger Preschoolers

(36-48 months)

  1. Name common two-dimensional shapes (e.g. square, rectangle, circle, triangle) regardless of orientation
  2. Use position words such as behind, in, on accurately
  3. Use two- and three-dimensional shapes to create pictures and structures
  4. Complete a 5-7 piece connecting puzzle by looking at the picture and/or shapes

Older Preschoolers

(48-60 months)

  1. Name common two- and three-dimensional shapes, and their parts and attributes (e.g., “A triangle has 3 points.”)
  2. Combine (i.e., compose) and separate (i.e., decompose) shapes to make other shapes.
  3. Use terms such as on top of, beside, in front, etc. to communicate ideas about the relative position of objects
  4. Follow simple directions related to relative position (beside, between, next to, etc.)
  5. Complete a 9-12 piece jigsaw puzzle by looking at the picture and/or shapes

Kindergartners

  1. No standards in this age group for this Element.
First Graders Through Third Graders

First Graders

  1. No standards in this age group for this Element.

Second Graders

  1. No standards in this age group for this Element.

Third Graders

  1. No standards in this age group for this Element.

Vermont Agency of Education
Secretary Daniel M. French
219 North Main Street, Suite 402
Barre, VT 05641

Web and Document Accessibility Policy​
Public Records Requests

(802) 479-1030 | aoe.edinfo@vermont.gov
Staff Directory | Division Phone Numbers