Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.




This is not a one time teachable objective. This objective is basically telling us that when you introduce new vocabulary to class, define it precisely. This objective would often work in conjunction with the other objectives throughout the year.


One thing that is specific to now, at the beginning of the year is the discussion of undefined terms. Students need to understand the difference between a definition and a representation.






(1) The student will be able to define any geometric term using words, diagrams and notation.


(2) The student will be able to explain what the undefined terms are and why they are undefined.






Euclidean geometry is created from three essential building blocks: the Point, the Line and the Plane. From these three terms all other geometrical objects and relationships are formed and created. They are known as the undefined terms because it is impossible to define all words and phrases in terms of simpler words and phrases, some words must be left undefined. While we may lack a definition for these three words, we do assign generally accepted representations.






Working without a textbook I found that the notation that usually was strong with my students (in previous years) began to be very weak. I hadn't realized how powerful the textbook had been to reinforce the written form of geometry. In class I spoke the language, gave the written notes and reinforced the notation but it didn't seem to stick like in previous years.  My advice to you is to provide examples and notes full geometric notation as often as possible.




Students come to geometry with a variety of informal definitions. When introducing new, more formal, definitions we should help students make connections to them by bridging their past knowledge to the current relationships.



Students will continue to define geometric concepts throughout the entire course. These formal definitions will helps us in many places such as proof where we need students to connect concepts and express them in a clear way.





MY REFLECTIONS (over line l)

When I first interpreted this objective I saw it as a standalone item. I began my year having students learn many new definitions. We played matching games, we designed a vocabulary list, and we connected a visual and a verbal context to the terms - this is a great thing to do but it wasn't needed. I found myself reintroducing all of these terms as they came up throughout the year. The problem was that it was out of context and some of the terms I was defining weren't showing up till late in the year and they had forgotten the material by then anyways. So learn from me.... This is not a standalone objective, it is meant to tell you and me that vocabulary is a very very important part of geometry and that when you introduce terms, they need to be well defined!!! As the year progresses you might even add to certain definitions to give it more power.