Learning About the World

Mathematics


Geometry and Spatial Reasoning -- Geometry

Goal 1: Children count in sequence and by multiples, represent numerals, connect counting to cardinality, and compare quantities.

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. No standards in this age group for this Element.

Young Toddlers

(9-18 Months)

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

Older Toddlers

(18-36 Months)

  1. No standards in this age group for this Element.
Younger Preschoolers Through Kindergartners

Younger Preschoolers

(36-48 months)

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

Older Preschoolers

(48-60 months)

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

Kindergartners

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

  1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
  2. Correctly name shapes regardless of their orientations or overall size.
  3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

Analyze, compare, create, and compose shapes.

  1. 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).
  2. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
  3. Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”
First Graders Through Third Graders

First Graders

Reason with shapes and their attributes.

  1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
  2. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
  3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Second Graders

Reason with shapes and their attributes.

  1. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
  2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
  3. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Third Graders

Reason with shapes and their attributes.

  1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
  2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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

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