Using Logical Reasoning to Prove Conjectures about Circles
Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.
Creating Nets for Three-Dimensional Figures
Given nets for three-dimensional figures, the student will apply the formulas for the total and lateral surface area of three-dimensional figures to solve problems using appropriate units of measure.
Drawing Conclusions about Three-Dimensional Figures from Nets
Given a net for a three-dimensional figure, the student will make conjectures and draw conclusions about the three-dimensional figure formed by the given net.
Generalizing Geometric Properties of Ratios in Similar Figures
Students will investigate patterns to make conjectures about geometric relationships and apply the definition of similarity, in terms of a dilation, to identify similar figures and their proportional sides and congruent corresponding angles.
Determining Area: Sectors of Circles
Students will use proportional reasoning to develop formulas to determine the area of sectors of circles. Students will then solve problems involving the area of sectors of circles.
Making Conjectures About Circles and Segments
Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties and relationships among the resulting segments.
Determining Area: Regular Polygons and Circles
The student will apply the formula for the area of regular polygons to solve problems.
Making Conjectures About Circles and Angles
Given examples of circles and the lines that intersect them, the student will use explorations and concrete models to formulate and test conjectures about the properties of and relationships among the resulting angles.
Solving Problems With Similar Figures
Given problem situations involving similar figures, the student will use ratios to solve the problems.
Introducing Conic Sections
Given a verbal description or a pictorial representation, the student will describe a conic section as the intersection of a cone and a plane.
Graphing Conic Sections: Ellipses
Given an equation, the student will use parameter changes to graph an ellipse and to identify the changes in the graph of an ellipse.
Graphing Conic Sections: Hyperbolas
Given an equation, the student will use parameter changes to graph a hyperbola and to identify the changes in the graph of a hyperbola.
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 and Verifying Conjectures about Lines
Students will investigate patterns and make conjectures about geometric relationships.
Making and Verifying Conjectures about Polygons
Students will investigate patterns and make conjectures about geometric relationships, including interior angles of polygons.
Making and Verifying Conjectures About Circles
Given information about the relationship(s) witnin one circle or a set of circles, the student will explore special segments and angles of circles.
Writing the Converse, Inverse, and Contrapositive
Given a conditional statement, the student will write its converse, inverse, and contrapositive.
Making and Verifying Conjectures about Three-Dimensional Figures
Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.