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.

This activity provides the opportunity to explore the validity of the converse, inverse, and contrapositive of statements. It also assists in recognizing the connections between biconditional statements and true conditional statements with a true converse.

This activity provides the opportunity to explore the difference between finding the probability of independent events and dependent events. It also addresses how to use a tree diagram when calculating conditional probabilities.

Given verbal and pictorial representations of problem situations, the student will apply patterns from right triangles whose sides are Pythagorean Triples to solve the problems.

The students will use multiple representations of undefined terms on a coordinate plane to solve problems.

Given characteristics of two lines, such as slopes and equations, the student will determine whether the lines are parallel, perpendicular, or neither.

The student will derive and use the slope and midpoint formulas to verify geometric relationship that include parallelism and perpendicularity of lines. Then, the student will determine an equation of a line parallel or perpendicular to a given line.

Given coordinates of points, the student will use the distance formula to solve problems involving length and distance.

Given coordinate points, the student will use slope formulas to solve problems.

Given a verbal and/or pictorial description of the intersection of a plane with various three-dimensional geometric figures, the student will describe and/or draw the intersection.