Using The Pythagorean Theorem
The student will use triangle relationships to prove the Pythagorean Theorem and solve problems.
Applying Geometric Probability
The student will find the area of polygons and circles. Then, the student will use probability to solve real-world problems.
Determining the Surface Area of Cones and Cylinders
Given a problem involving cones or cylinders, the student will find the surface area using appropriate units of measure.
Determining the Volume of Cones and Cylinders
Given a problem involving cones or cylinders, the student will find the volume using appropriate units of measure.
Determining the Surface Area and Volume of Spheres
Given a problem involving spheres, the student will find the surface area and volume.
Determining the Surface Area and Volume of Composite Figures
Given a problem involving composite figures made from prisms, pyramids, spheres, cones, and/or cylinders, the student will find the surface area and volume of the composite figure.
Making Conjectures about Parallel and Perpendicular Lines
The student will verify theorems about angles formed by parallel lines cut by a transversal and apply these relationships to solve problems.
Making and Verifying Conjectures About Triangles
Given examples of triangles and their component parts, the student will use explorations and concrete models to verify and apply the Triangle Inequality theorem and find the sum of interior angles.
Determining the Surface Area of Prisms and Pyramids
Given a problem involving prisms or pyramids, the student will find the surface area using appropriate units of measure.
Determining the Volume of Prisms and Pyramids
Given a problem involving prisms or pyramids, the student will find the volume using appropriate units of measure.
Making Conjectures About Congruence Transformations
Given geometric figures on the coordinate plane, the student will apply the definition of congruence, in terms of rigid transformations, to identify congruent figures. The student will also identify and distinguish between reflectional and rotational symmetry in a plane figure.
Making Conjectures About Quadrilaterals
Given examples of quadrilaterals and their component parts, the student will use explorations and concrete models to prove a quadrilateral is a parallelogram, rectangle, square, or rhombus using opposite sides, opposite angles, or diagonals.
Connecting Postulates, Definitions, and Theorems
The student will distinguish the difference between undefined terms, definitions, postulates, conjectures, and theorems.
Determining the Validity of Conditional Statements
Given a conditional statement, the student will determine its validity and the validity of the converse, inverse and contrapositive.
Making and Verifying Conjectures about Angles
Given the relationship(s) among a set of angles, the student investigates the patterns and makes conjectures about the geometric relationships, including angles formed by parallel lines cut by a transversal.
Making Conjectures About Other Polygons
Given information about the properties of polygons, students will verify theorems about the relationships, including the sum of interior angles, and apply these relationships to solve problems.
Investigating and Applying Dimension Changes: Area
The student will describe the effects of changing one or more dimensions on the area of a figure.
Applying Triangle Congruence Relationships
Given congruent triangles, the student will justify and apply triangle congruence relationships.
Making Conjectures About Similar Figures
Given problem situations involving similar figures, the student will use and extend similarity properties and transformations to explore and justify conjectures about the given figures.
Developing Algebraic Expressions to Represent Properties of Angles in Circles
Given numerical and/or geometric patterns that represent angle relationships in circles, the student will investigate inscribed angle relationships.