November+-+December

Geometry

 * 2.15 The student will **
 *  a) draw a line of symmetry in a figure; and **
 *  b) identify and create figures with at least one line of symmetry. **

 (Background Information for Instructor Use Only)
 * UNDERSTANDING THE STANDARD **
 * A figure is symmetric along a line when one-half of the figure is the mirror image of the other half.
 * A line of symmetry divides a symmetrical figure, object, or arrangement of objects into two parts that are congruent if one part is reflected over the line of symmetry.
 * Children learn about symmetry through hands-on experiences with geometric figures and the creation of geometric pictures and patterns.
 * Guided explorations of the study of symmetry by using mirrors, miras, paper folding, and pattern blocks will enhance students’ understanding of the attributes of symmetrical figures.
 * While investigating symmetry, children move figures, such as pattern blocks, intuitively, thereby exploring transformations of those figures. A transformation is the movement of a figure — either a translation, rotation, or reflection. A translation is the result of sliding a figure in any direction; rotation is the result of turning a figure around a point or a vertex; and reflection is the result of flipping a figure over a line.

ESSENTIAL UNDERSTANDINGS
All students should · Develop strategies to determine whether or not a figure has at least one line of symmetry. · Develop strategies to create figures with at least one line of symmetry. · Understand that some figures may have more than one line of symmetry.

<span style="font-family: Verdana,Geneva,sans-serif;"> ESSENTIAL KNOWLEDGE AND SKILLS
<span style="font-family: Verdana,Geneva,sans-serif;">The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to <span style="font-family: Verdana,Geneva,sans-serif;">· Identify figures with at least one line of symmetry, using various concrete materials. <span style="font-family: Verdana,Geneva,sans-serif;">· Draw a line of symmetry — horizontal, vertical, and diagonal — in a figure. <span style="font-family: Verdana,Geneva,sans-serif;">· Create figures with at least one line of symmetry using various concrete materials.

<span style="font-family: Verdana,Geneva,sans-serif;"> (Background Information for Instructor Use Only) · 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. – **Level 0: Pre-recognition.** Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided polygons. – **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.”). – **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, and opposite sides are parallel.”). · An important part of geometry is naming and describing figures in two-dimensions (plane figures) and three-dimensions (solid figures). · A vertex is a point where two or more line segments, lines, or rays meet to form an angle. · An angle is two rays that share an endpoint. · Plane figures are two-dimensional figures formed by lines that are curved, straight, or a combination of both. They have angles and sides. · The identification of plane and solid figures is accomplished by working with and handling objects. · Tracing faces of solid figures is valuable to understanding the set of plane figures related to the solid figure (e.g., cube and rectangular prism). · A circle is a closed curve in a plane with all its points the same distance from the center. · A sphere is a solid figure with all of its points the same distance from its center. · A square is a rectangle with four sides of equal length. · A rectangular prism is a solid in which all six faces are rectangles. A rectangular prism has 8 vertices and 12 edges. · A cube is a solid figure with six congruent, square faces. All edges are the same length. A cube has 8 vertices and 12 edges. It is a rectangular prism. · A rectangle is a plane figure with four right angles. A square is a rectangle. · The edge is the line segment where two faces of a solid figure intersect. · A face is a polygon that serves as one side of a solid figure (e.g., a square is a face of a cube). · A base is a special face of a solid figure. The relationship between plane and solid geometric figures, such as the square and the cube or the rectangle and the rectangular prism helps build the foundation for future geometric study of faces, edges, angles, and vertices.
 * <span style="font-family: Verdana,Geneva,sans-serif;">2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism). **
 * <span style="font-family: Verdana,Geneva,sans-serif;">UNDERSTANDING THE STANDARD **