### Lesson Unit

### Lesson Plans

- Derivation of Mid-Point (docx)

### Lesson Seeds

- Expressing Geometric Properties with Equations (docx)
- Using Coordinates to Prove a Shape is a Parallelogram (docx)

##### Unit Overview

Building on their work with the Pythagorean Theorem in 8th grade to find distances, students use a Cartesian coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in Algebra 1.

**Essential Questions:**

- How is visualization essential to the study of geometry?
- How does adding coordinates to a geometric figure aid in the visualization of that figure and of the relationships of its parts?
- How does geometry explain or describe the structure of our world?
- How does adding coordinates to a geometric figure more concretely tie the figure to its referent in the real world?
- How can reasoning be used to establish or refute conjectures?
- How does manipulating coordinates algebraically provide a valid form of proof?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

##### Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.