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.
Making and Verifying Conjectures about Three-Dimensional Figures
Students will explore volume conjectures and solve problems by applying the volume formulas to composite figures.
Constructing and Justifying Statements about Geometric Figures
Students will distinguish between undefined terms, definitions, postulates, conjectures, and theorems and investigate patterns to make conjectures about geometric relationships.
Using Counter Examples to Disprove Statements That Are False
Given statements about a geometric relationship, the student will use counter examples to disprove statements that are false.
Using Inductive Reasoning to Formulate Conjectures
Students will practice identifying the converse, inverse, and contrapositive of conditional statements.
Using Logical Reasoning to Prove Statements are True
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.
Using Properties of Transformations
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.
Developing Algebraic Expressions to Represent Geometric Properties
The student will investigate patterns to make conjectures.
Developing Algebraic Expressions to Represent Geometric Properties of Polygons
Given numerical and/or geometric patterns that represent geometric properties of polygons, the student will develop algebraic expressions that represent the geometric properties.
Developing Algebraic Expressions to Represent Geometric Properties of Angle Relationships in Polygons
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.
Applying Pythagorean Triples to Solve Problems
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.
Introduction to Coordinate Geometry
The students will use multiple representations of undefined terms on a coordinate plane to solve problems.
Coordinate Geometry: Parallel and Perpendicular Lines
Given characteristics of two lines, such as slopes and equations, the student will determine whether the lines are parallel, perpendicular, or neither.
Coordinate Geometry: Special Segments
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.
Coordinate Geometry: Length and Distance
Given coordinates of points, the student will use the distance formula to solve problems involving length and distance.
Coordinate Geometry: Slope
Given coordinate points, the student will use slope formulas to solve problems.
Describing and Drawing Cross Sections
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.
Determining Area: Composite Figures
Given information about composite fiugres, the student will determine the area of composite 2-dimensional figures comprised of a combination of triangles and parallelograms using appropriate units of measure.
Determining Arc Length
Given a problem situation involving sectors of circles, the student will use proportional reasoning to solve the problem.
Using The Pythagorean Theorem
The student will use triangle relationships to prove the Pythagorean Theorem and solve problems.