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 (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. | Understands that geometric shapes are useful for representing and describing real world situations |
| | | | | Knowledge/skill statements |
| | | | | | 1. | Understands that geometric shapes are useful in representing the world |
| | | | 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 |
