*The curriculum framework offers an explanation of the specific STRAND and detailed*

*expectations of the material*

*that should be covered by the teacher and learned by*

*the students (according to the Virginia Department of*

*Education Standards of Learning).*

K.11 The student will

a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and

b) compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).

UNDERSTANDING THE STANDARD

· An important part of the geometry strand in grades K through 2 is the naming and describing of figures. Children move from their own vocabulary and begin to incorporate conventional terminology as the teacher uses geometric terms.

· A plane geometric figure is any plane, closed figure. Circles and polygons are examples of plane geometric figures.

· Presentation of triangles, rectangles, and squares should be made in a variety of spatial orientations so that students do not develop the common misconception that triangles, rectangles, and squares must have one side parallel to the bottom of the page on which they are printed.

· The van Hiele theory of geometric understanding describes how students learn geometry and provides a framework for structuring student experiences that should lead to conceptual growth and understanding.

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**Level 0: Pre-recognition.**Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided polygons.

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**Level 1: Visualization.**Geometric figures are recognized as entities, without any awareness of parts of figures or relationships between components of a figure. Students should recognize and name figures and distinguish a given figure from others that look somewhat the same (e.g., “I know it’s a rectangle because it looks like a door, and I know that a door is a rectangle.”)

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**Level 2: Analysis.**Properties are perceived, but are isolated and unrelated. Students should recognize and name properties of geometric figures (e.g., “I know it’s a rectangle because it is closed; it has four sides and four right angles.”).

· A polygon is a geometric figure that

– has sides that are line segments;

– is simple (its sides do not cross);

– is closed; and

– is two-dimensional (lies in a plane).

· A triangle is a polygon with three angles and three sides. Children should be shown different types of triangles such as equilateral, isosceles, scalene, right, acute, and obtuse; however, they are not expected to name the various types.

· A quadrilateral is a polygon with four sides.

· A rectangle is a quadrilateral with four right angles.

· A square is a rectangle with all four sides of equal length.

· A circle is a closed curve with all points in one plane and the same distance from a fixed point (the center).

· Early experiences with comparing and sorting figures assist students in analyzing the characteristics of plane geometric figures.

· Attribute blocks, relational attribute blocks, and tangrams are among the manipulatives that are particularly appropriate for sorting and comparing size.

– Clay, straws, and paper and scissors are several manipulatives that are appropriate for constructing geometric figures.

K.12 The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.

UNDERSTANDING THE STANDARD

· Representations of circles, squares, rectangles, and triangles can be found in the students’ environment at school and at home. Students should have opportunities to identify/classify things in their environment by the type of figures those things represent.

· Children are often confused when a figure such as a square is rotated: they frequently refer to the rotated square as a diamond. Clarification needs to be ongoing — i.e., a square is a square regardless of its location in space; there is no such geometric figure as a diamond.