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Topic: Shapes and figures 

Mathematics

 Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry
  Level Pre-K (Grade Pre-K)
   Benchmark 1.Knows basic geometric language for naming shapes (e.g., circle, triangle, square, rectangle)
    Knowledge/skill statements
     1.Understands the term "circle"
     2.Understands the term "triangle"
     3.Understands the term "square"
     4.Understands the term "rectangle"
     5.Identifies a circle
     6.Identifies a triangle
     7.Identifies a square
     8.Identifies a rectangle
   Benchmark 3.Knows that geometric shapes can be put together or taken apart to form other shapes
    Knowledge/skill statements
     1.Knows that geometric shapes can be put together to form other shapes
     2.Knows that geometric shapes can be taken apart to form other shapes
   Benchmark 5.Sorts and groups objects by attributes (e.g., shape, size, color)
    Knowledge/skill statements
     1.Sorts objects by different attributes
     2.Groups objects by different attributes
     3.Sorts objects by shape
     4.Sorts objects by size
     5.Sorts objects by color
     6.Groups objects by shape
     7.Groups objects by size
     8.Groups objects by color
     9.Understands that objects can be sorted by their attributes
     10.Understands that objects can be grouped by their attributes
  Level I (Grade K-2)
   Benchmark 1.Understands basic properties of simple geometric shapes (e.g., number of sides, corners, square corners) and similarities and differences between simple geometric shapes
    Knowledge/skill statements
     1. Understands the concept of sides
     2.Understands the concept of a triangle
     3.Understands the concept of a square
     4.Understands the differences between basic shapes
     5.Understands the concept of a circle
     6.Understands the concept of corners
     7.Understands the concept of square corners
     8.Understands the concept of a rectangle
     9.Understands the similarities among basic shapes
   Benchmark 3.Uses the names of simple geometric shapes (e.g., circles, squares, triangles) to represent and describe real world situations
    Knowledge/skill statements
     1.Understands that geometric shapes are useful in representing the world
     2.Uses circles to represent real world situations
     3.Uses squares to represent real world situations
     4.Uses triangles to represent real world situations
     5.Uses circles to describe real world situations
     6.Uses squares to describe real world situations
     7.Uses triangles to describe real world situations
   Benchmark 4.Understands that patterns can be made by putting different shapes together or taking them apart
    Knowledge/skill statements
     1.Understands that patterns can be made by putting shapes together
     2.Understands that patterns can be made by taking shapes apart
  Level II (Grade 3-5)
   Benchmark 1.Knows basic geometric language for describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere)
    Knowledge/skill statements
     1.Understands the concept of a trapezoid
     2.Understands the concept of a parallelogram
     3.Understands the concept of a sphere
     4.Understands the concept of a cube
   Benchmark 2.Understands basic properties of figures (e.g., two- or three-dimensionality, symmetry, number of faces, type of angle)
    Knowledge/skill statements
     1.Understands the concept of two-dimensionality
     2.Understands the concept of three-dimensionality
     3.Understands the concept of symmetry
     4.Understand the defining number of faces for a three-dimensional object
     5.Understands that objects have a defining number and types of angles
   Benchmark 3.Predicts and verifies the effects of combining, subdividing, and changing basic shapes
    Knowledge/skill statements
     1.Predicts the effects of subdividing shapes
     2.Predicts the effects of changing shapes
     3.Predicts the effects of combining shapes
     4.Verifies the effects of subdividing shapes
     5.Verifies the effects of changing shapes
     6.Verifies the effects of combining shapes
   Benchmark 4.Understands that shapes can be congruent or similar
    Knowledge/skill statements
     1.Understands the concept of similar shapes
     2.Understands the concept of congruent shapes
  Level III (Grade 6-8)
   Benchmark 1.Uses geometric methods (i.e., an unmarked straightedge and a compass using an algorithm) to complete basic geometric constructions (e.g., perpendicular bisector of a line segment, angle bisector)
    Knowledge/skill statements
     1.Uses a straight edge and compass to construct angle bisectors
     2.Uses a straight edge and compass to construct perpendicular bisectors
     3. Understands the concept of geometric constructions
     4.Understands the concept of an angle bisector
     5.Understands the concept of a perpendicular bisector
   Benchmark 2.Understands the defining properties of three-dimensional figures (e.g., a cube has edges with equal lengths, faces with equal areas and congruent shapes, right angle corners)
    Knowledge/skill statements
     1.Understands the concept of a three-dimensional figure
     2.Understands the properties of three-dimensional figures
     3.Understands that the properties of a cube include faces that are congruent, faces that have equal areas, edges with equal lengths, and right angle corners
  Level IV (Grade 9-12)
   Benchmark 3.Uses synthetic (i.e., pictorial) representations and analytic (i.e., coordinate) methods to solve problems involving symmetry and transformations of figures (e.g., problems involving distance, midpoint, and slope; determination of symmetry with respect to a point or line)
    Knowledge/skill statements
     1.Uses synthetic geometric models to solve slope problems
     2.Uses synthetic geometric models to solve line symmetry problems
     3.Uses synthetic geometric models to solve point symmetry problems
     4.Uses synthetic geometric models to solve distance problems
     5.Uses synthetic geometric models to solve midpoint problems
     6.Understands the concept of a synthetic model (i.e., a pictorial representation)
     7.Uses analytic methods to solve slope problems
     8.Uses analytic methods to solve line symmetry problems
     9.Uses analytic methods to solve point symmetry problems
     10.Uses analytic methods to solve distance problems
     11.Uses analytic methods to solve midpoint problems
   Benchmark 5.Uses geometric constructions (e.g., the parallel to a line through a given point not on the line, line segment congruent to a given line segment) to complete simple proofs, to model, and to solve mathematical and real-world problems
    Knowledge/skill statements
     1. Constructs a line segment congruent to a line segment
     2.Understands the basic concept of a geometric construction
     3.Constructs a line through a given point not on the line
     4.Uses a line segment congruent to given line segment in proofs
     5.Uses geometric constructions to complete simple proofs
     6.Determines whether a problem can be modeled by geometric constructions
     7.Determines whether a problem can be solved by using geometric constructions
   Benchmark 10.Uses inductive and deductive reasoning to make observations about and to verify properties of and relationships among figures (e.g., the relationship among interior angles of parallel lines cut by a transversal)
    Knowledge/skill statements
     1.Makes deductions about the relationships among geometric figures
     2.Makes inductions about the relationships among geometric figures
     3.Understands the concept of a transversal
     4.Makes deductions about the properties of figures
     5.Makes inductions about the properties of figures
   Benchmark 11.Uses properties of and relationships among figures to solve mathematical and real-world problems (e.g., uses the property that the sum of the angles in a quadrilateral is equal to 360 degrees to square up the frame for a building; uses understanding of arc, chord, tangents, and properties of circles to determine the radius given a circular edge of a circle without the center)
    Knowledge/skill statements
     1.Determines whether a problem can be solved by making use of the relationships among angles
     2.Understands the concept of a chord
     3.Determines whether a problem can be solved by using chords
     4.Understands the concept of an arc
     5.Determines whether a problem can be solved by using arcs
     6.Understands the concept of a tangent to a circle
     7.Determines whether a problem can be solved by using tangents to a circle
     8.Determines whether a problem can be solved by using radii
     9.Determines whether a problem can be solved by making use of the properties of figures
     10.Determines whether a problem can be solved by making use of relationships among figures
     11.Understands the properties of circles

Engineering Education

 Standard 12.  Understands the techniques, tools, and technologies related to the production of technical drawings
  Level IV (Grade 9-12)
   Benchmark 8.Knows procedures for creating geometric constructions (e.g., arcs, angles, bisecting lines, perpendicular and parallel lines, geometric shapes)
    Knowledge/skill statements
     1.Knows procedures for creating geometric constructions such as arcs
     5.Knows procedures for creating geometric constructions such as geometric shapes