Thematic+Unit

**// Greek Mathematics //**//(Thematic Unit)// **// (The study of Geometry and formal proofs, Number theory, and Applied mathematics) //** (Inquiry Lesson) ** How do I relate? ** // A look at geometric shapes and their properties // 1. Help students to find relationships between triangles, rectangles, parallel lines, perpendicular lines, and other polygons. Inductive reasoning skills will be further developed creating a greater distinction between inductive and deductive reasoning. This is an inquiry based model that would be considered free inquiry. Conjectures made and relationships thought need not be right or wrong. Students will be able to establish connections in a plane based geometric setting. This will help students foreshadow to a high level the upcoming plane based geometric arguments and theorems. Thus the transition from inductive reasoning to deductive reasoning will follow with greater ease.
 * __Thematic Unit Lesson Plan:__**
 * Lesson Objectives: (Classroom Standards) **
 * Objectives: (State Standards) **
 * 1) __ G.1.B __
 * 2) Use inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counterexample.
 * 3) __ G.7.G __
 * 4) Synthesize information to draw conclusions and evaluate the arguments and conclusions of others.
 * Foreshadowed Objectives: (State Standards) **
 * 1) G.3.B
 * 2) Determine and prove triangle congruence, triangle similarity, and other properties of triangles.
 * 3) G.3.C
 * 4) Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems.
 * Introduction/Investigation: **
 * 1) Students can work independently or in a small group.
 * 2) Explain that students are to use the shapes to make any conjectures that seem to make sense.
 * 3) Students can use graph paper to check for parallel lines perpendicular lines and find any relationships between the objects.
 * 4) Example: Take the parallelogram and check for // sides.
 * 5) Students should write down any relationships they see and any conjectures that they have.
 * Teacher/Student Roles: **
 * 1) Teacher:
 * 2) Limited Guided instruction. This is Free Inquiry
 * 3) Student:
 * 4) Make conjectures and look for relationships
 * 5) Explore conjectures and relationships of other students
 * Rationale: **

**__Thematic Unit Overview:__** My thematic unit is called **//Greek Mathematics//** //(The study of Geometry and formal proofs, Number theory, and Applied mathematics)//. Thus the unit will be broken into three sections: 1.) The study of Geometry and formal proofs, 2.) Number theory, and 3.) Applied mathematics. The investigations will center around mathematical concepts however there will be some brief discussion of the Greek mathematicians along the way. Our first section will be the geometry and proof section. This inquiry lesson will be the first investigation of this section. We will start by using inductive reasoning and then move toward proving conjectures using deductive reasoning. The Greek mathematicians are famous for their development in this area of mathematics and thus quite appropriate. For instance Euclid and his book the elements. Although we will not go this deep into the geometry the name Euclid is synonymous with plane geometry. Further investigations will be more formal throughout the rest of the geometry section using a constructivist learning model. Number theory will be the second section of this unit. To start this section students will do another inquiry based investigation relating to number theory exposing them to the basic ideas behind number theory. Here we will be using elementary and algebraic number theory that can be attributed to many Greek mathematicians such as Plato and Ptolemy. The subsequent investigations will be more formal but constructivist in nature. The third section of this unit will be the study of applied mathematics. Again this section will start with an inquiry based investigation. The following lessons here will also be more formal although constructivists in nature with a minimum of traditional direct instruction. Archimedes and Pythagoras, two Greek mathematicians that are famous in this area of mathematics will be discussed. Students will use prior knowledge along with new concepts to develop critical thinking skills in the area of applied mathematics. Here mathematics may cross over to other domains such as astronomy or science. This section will complete the unit on Greek Mathematics.