Poteau High School

OKLAHOMA

Priority Academic Student Skills

MATHEMATIC CONTENT STANDARDS

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GEOMETRY

  

The following skills are required of all students completing Geometry.  Major Concepts should be taught in depth using a variety of methods and applications (concrete to the abstract).  Maintenance Concepts have been taught previously and are a necessary foundation for this course.  The major concepts are considered minimal exit skills and districts are strongly encouraged to exceed these skills when building a Geometry curriculum.  Visual and physical models, calculators, and other technologies are recommended when appropriate and can enhance both instruction and assessment.

  MAJOR CONCEPTS                                                     MAINTENANCE CONCEPTS

Logical Reasoning                                                            Ratios, Proportions

Properties                                                                           Perimeter, Area, Surface Area, Volume

Coordinate Geometry                                                        Equations

Angles and Triangles                                                         Formulas

 

Standard I:                 Logical Reasoning The student will use deductive and inductive reasoning to solve problems.

1.                 Properties and Relationships of Figures

                        a.                  Identify the relationships of parallel lines with a transversal.  

b.                  Identify relationships between pairs of angles (e.g., adjacent, complementary, vertical).  

2.                 Determine and use the relationships of congruency and similarity to determine, unknown values. 

3.                 Use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, follow logical arguments, judge the validity of arguments and construct simple valid arguments.  

Standard 2:          Properties of 2- and 3-Dimensional Figures The student will use the   properties and formulas of geometric figures to solve problems.  

1.                 Polygons  

a.                  Identify and describe polygons (i.e., convex, concave, regular)  

b.                  Apply the interior and exterior angle sum of convex polygons to solve problems.  

c.                  Develop and apply the properties of quadrilaterals to solve problem (e.g., rectangles, parallelograms, rhombi, trapezoids, kites). 

2.                 Draw and analyze 2- and 3-dimensional figures.  

3.                 Use properties of 2- and 3-dimensional figures to determine unknown values (e.g., given the perimeter/circumference, find the area).  

4.                 Compute length, perimeter or circumference, area, volume, and surface area of geometric figures with missing information and correctly identify the appropriate unit of measure of each.  

5.                 *Use geometric tools (e.g., protractor, compass, straight edge) to construct a variety of figures. 

6.                 Find angle measures and arc measures related to circles. 

7.                 Chords, Secants and Tangents  

a.                  Identify and describe the relationship between two chords that intersect in the interior of a circle. 

b.                  Identify and describe the relationship between two secants that intersect in the exterior of a circle. 

c.                  Identify and describe the relationship between a secant and a tangent that intersect in the exterior of a circle. 

Standard 3:                Coordinate Geometry The student will solve problems with geometric figures in the coordinate plane.  

1.                 Use transformations (reflections, rotation, translation) within coordinate geometry (e.g., reflect points across the y-axis). 

2.                 Use coordinate geometry to find the distance between two points; the midpoint of a segment; and to calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.  

3.                 Given a set of points determine the type of figure based on its properties (e.g., parallelogram, isosceles triangle, regular octagon).  

Standard 4:                Angles, Triangles and Similar Polygons The student will use the properties of angles, right triangles and similar polygons to solve problems.  

1.                 Solve problems using properties of angles (e.g., interior, exterior, complementary, vertical, angle sums, 30-60-90). 

2.                 Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles.  

3.                 Apply the 45-45-90 and 30-60-90 right triangle relationships to solve problems.  

4.                 Express the trigonometric functions as ratios and derive the relationship between sine, cosine, and tangent ratios, and use to solve real-world problems.  

5.                 Similar Polygons 

a.                  Use similar figures to construct ratios and solve for a missing side.  

b.                  Use ratios of similar figures to find linear distance, perimeter, area, and volume.

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* Standards and objectives must be assessed by the local school district.  All other skills may be assessed by the Oklahoma School Testing Program (OSTP).

 

 


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