SWBAT explain key concepts of Euclidean Geometry

This is the first content lesson of the Geometry course. Students will explore the undefined notions of points, lines and planes through the context of the painting Composition 8 by Vasily Kandinsky.

10 minutes

At the beginning of the school year, I like to show my students Kandinsky's *Composition 8. *This activity exposes students to geometry in the real world. I project the painting of the board. Students look at the painting and write a list of all of the geometrical objects they can find in it. After about five minutes, we go over students’ lists. I call a few different students up to the board to point out what they have found.

15 minutes

In this section, students will create a graphic organizer to explain the “undefined terms.” We start off going over the concept of an undefined term. I like to use the following example: “Have you ever come across a word you didn’t know and looked up its meaning in the dictionary? However, in that definition, there was another word you didn’t know? When you looked up that one, the same thing happened. If you continued the process, eventually, you would get to a word that doesn’t have a specific definition, but can be understood in context, like the word, ‘the.’’ I use this example to help students relate to a word not having a definition. The three terms, point, line, and plane, are building blocks for understanding geometry and can be used to define other geometric terms (G.CO.1, MP6).

We then create a three-tab graphic organizer. On the first second and third tab, students draw a point, line and plane, respectively. We discuss the characteristics of a good representation of a point, line and plane. For example, a line has arrows on the end of it and a plane is usually represented by a parallelogram. Students write “Point,” “Line,” and “Plane” on the top inside section of each tab. On the bottom section, students write a description of each term. Students are usually able to come up with their own descriptions based on prior knowledge. We go over their descriptions and add anything they may have left out. This is a good time to talk about 0, 1, and 2 dimensions.

Students will refer back to this graphic organizer in later lessons.

15 minutes

In this part of the lesson, students will read a passage, “What is Geometry?” from the book, *Timed Reading in Mathematics: Book 3 *by Glencoe/McGraw-Hill.This passage gives a good introduction to Geometry. After they read, students answer reading comprehension questions. I suggest that students who have an Individualized Education Plan or are English Language Learners look at the questions before reading in order to give them a focus while they read. Since this is the first lesson in the year, it helps me to gather more information about my students’ abilities to decode information.

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When the students finish answering the questions, we go over them. I choose a student to read the question and their answer. Then we discuss the validity of their answers. Another way to go over the answers is to have the students write the letter of their answer on a mini-whiteboard. By using the whiteboards, I am able to see each of the students’ responses.

5 minutes

**Exit Ticket: **Students will complete an exit ticket. The question, “What is Euclidean Geometry?”, can be answered based on information from the reading.

Sample student responses are, "Euclidean Geometry is the geometry we study in school. Euclidean Geometry deals with points, lines and planes. Euclidean Geometry is the set of principles written by the Greek Mathematician Euclid.

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