Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

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.

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.

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.

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.

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.

The student will apply the formula for the area of regular polygons to solve problems.

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.

Given problem situations involving similar figures, the student will use ratios to solve the problems.

Students will explore volume conjectures and solve problems by applying  the volume formulas to composite figures.

Students will distinguish between undefined terms, definitions, postulates, conjectures, and theorems and investigate patterns to make conjectures about geometric relationships.

Given statements about a geometric relationship, the student will use counter examples to disprove statements that are false.

Students will practice identifying the converse, inverse, and contrapositive of conditional statements.

Given statements about a geometric relationship, the student will distinguish between the undefined terms, definitions, postulates, conjectures, and theorems to prove the statements are true.

Given examples of mathematics in the real world, the student will use properties of transformations and their composites to describe and perform transformations of figures in a plane.

The student will investigate patterns to make conjectures.

Given numerical and/or geometric patterns that represent geometric properties of polygons, the student will develop algebraic expressions that represent the geometric properties.

Given numerical and/or geometric patterns that represent geometric properties of angle relationships in polygons, the student will investigate patterns to make conjectures about interior and exterior angles of polygons.

The student will distinguish the difference between undefined terms, definitions, postulates, conjectures, and theorems.

Given a conditional statement, the student will determine its validity and the validity of the converse, inverse and contrapositive.