The Geometry of Learning Unit Presentation By Dawn Brander

Unit Summary Grab your straightedge and compass and let’s begin to explore the world of Mathematics as viewed by the Greeks. We will construct simple geometric figures. The idea is to understand the construction of any figure so you can logically prove some of the great theories, like the Pythagoras Theorem in the same way that Euclid did in 300 BC.

Target Standards Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. Students write geometric proofs, including proofs by contradiction. Students prove basic theorems involving congruence and similarity. Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.

My Unit Vision Develop the ability to think logically Provide my students’ tools in understanding and eventually enumerating logical sequences Understand the concept of theories and proofs Know how to prove theories Enhance my students’ deductive reasoning

Essential Questions How can we prove or disprove a theory? What is logic? Unit Questions What skills/knowledge/tools do I have that can help me write proofs? How does logic apply to proofs? If I learn the proofs for one geometric figure, how can I apply it to others?

Content Questions Enumerate the different theorems used to prove congruence. Enumerate the steps to a proof. Define your logic or give reasons for actions. How do you disprove a statement? Prove the Pythagoras Theorem. Can you construct a square with the same area as a lune (crescent moon)?

Assessment to Gauge Student Needs Initial Assessment: Vocabulary of words used. Where do they see theory and logic in their lives? Continuing Assessment: Progress in writing logical if...then sentences Adapting their thought processes beyond initial concepts

Project Summary & Clarification of Project-Based Approach Our projects will consist of geometric constructions from parallel lines to equilateral triangles then eventually to lunes, squares and rectangles of equal areas. Along the way we will be learning how to prove that the shapes we’ve created are congruent. This activity-based learning will provide greater access to the subject at hand by: Offering greater retention Encouraging individualized thought process Enhancing understanding of the subject Developing critical thinking and verbalization Applying logical thought to other subjects and even day-to-day decisions

Food for Thought