Honors Geometry Unit 4 Scale

HonorsGeometry

Unit 4	Segments and Angles
Priority Standards:	30, 31
Supporting Standards:	3, 29, 33
Level 4	I can...   Construct formal arguments and justifications using segment and angle relationships.   Solve multi-step problems involving bisectors, vertical angles, or algebraic expressions.   Use precise geometric vocabulary and notation in explanations.
Level 3.5
Level 3	I can...   Identify and apply relationships among a variety of angles.   Use segment and angle addition postulates to solve problems.   Apply theorems about angles formed by parallel/perpendicular lines and transversals to solve problems.   Solve for unknown angle or segment measures using diagrams and equations.
Level 2.5
Level 2	I can...   Recognize and label points, lines, segments, and angles with guidance.   Identify basic relationships (e.g., vertical angles, midpoint) with some support.   Use formulas or properties when steps are scaffolded.
Level 1.5
Level 1	I can...   Recognize segments and angles but struggles to describe relationships.   Receive assistance to set up or solve basic geometric problems.   Misuse or confuse geometric terms or symbols.

Priority

Knowledge

Students know:

• Undefined notions of point, line, distance along a line, and distance around a circular arc.
• Properties of a mathematical definition, i.e., the smallest amount of information and properties that are enough to determine the concept. (Note: May not include all information related to the concept.)
• Requirements for a mathematical proof.
• Techniques for presenting a proof of geometric theorems.

---

Skills

Students are able to:

• Use known and developed definitions and logical connections to develop new definitions.
• Communicate logical reasoning in a systematic way to present a mathematical proof of geometric theorems.
• Generate a conjecture about geometric relationships that call for proof.

---

Understanding

Students understand that:

• Geometric definitions are developed from a few undefined notions by a logical sequence of connections that lead to a precise definition.
• A precise definition should allow for the inclusion of all examples of the concept, and require the exclusion of all non-examples.
• Proof is necessary to establish that a conjecture about a relationship in mathematics is always true, and may also provide insight into the mathematics being addressed.

Supporting

Knowledge

Students know:

• Substitution, elimination, and graphing methods to solve simultaneous linear equations.
• Use technology and other tools to discover patterns and relationships in figures.
• Use patterns. relationships and properties to construct figures.

---

Skills

Students are able to:

• Find the coordinates of the vertices of a polygon given a set of lines and their equations by setting their function rules equal and solving or by using their graph.
• Use properties to create methods for constructing different objects and prove that the constructions are accurate.

---

Understanding

Students understand that:

• Given the equations to a set of lines you can find the coordinates of the vertices of a polygon by setting their function rules equal and solving or by using their graph.
• Many of the constructions build on the relationships among the objects and are justified by the properties used during the construction.
• Technology can be used as a means to explain the properties and definitions by developing procedures to carry out the construction.