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Creating Nets for ThreeDimensional Figures
Given nets for threedimensional figures, the student will apply the formulas for the total and lateral surface area of threedimensional figures to solve problems using appropriate units of measure.
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.
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.
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 ThreeDimensional 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.