OUR+LESSON

= = = Current Lesson Plan: = = = = = _____________________________________________________________________________________________________ =OLD (VERRRRRY BARE) LESSON PLAN:=

Mathematics Lesson Plan for grade 11. For the lesson on July 10 At PCMI, Working Group: Lesson Study Instructor: Stacey Lesson plan developed by: Working Group: Lesson Study

=**1.** **Title of the Lesson: Mathematical Reasoning **= = = 2. Goals (Objectives) of the Lesson: Use inductive and deductive reasoning to develop mathematical arguments. Draw and evaluate the validity of conclusions from given information.

b. Students will be able to defend a conjecture about the number of regular tilings.
=**3.** ** Relationship of the Lesson to the Standards **= This section typically describes how this lesson fits between the standards (local, state, NCTM) from prior grades and the standards for this or later grades. It is usually done graphically, like this:

Related prior learning methods --> THIS LESSON -- > Related Post pearning standards

=**4.** **Unit Plan**= //Shows how this lesson fits into a larger unit. Briefly describes lessons before and after this lesson.// =**5.** **Instruction of the Lesson**= //This section typically discusses:// //(a) what the students need to learn according to standards or the curriculum;// //(b) what the students have learned so far, from observations;// //(c) the major focus or theme of this lesson; the differences and similarities between deduction and induction // //(d) how we will accomplish the above objective.//using tesselations and properties of regular tesselations to have the students use inductive reasoning to form a conjecture and then deductive reasoning to justify/disprove their conjectures.

=**6.** **Plan of the Lesson**= Teacher’s Questions and Expected Student Reactions || Teacher’s Support || Points of Evaluation ||
 * Steps, Learning Activities
 * // This column shows the major events and flow of the lesson. // || // This column shows additional moves, questions, or statements that the teacher may need to make to help students. // || // This column identifies what the teacher should look for to determine whether to proceed, and what observers should look for to determine the effectiveness of the lesson. // ||
 * ** 1. **** Introduction ** || || ||
 * ** 2. **** Posing the Problem ** || || ||
 * ** 3. **** Anticipated Student Responses ** || ||  ||
 * ** 4. Comparing and Discussing **

Student descriptions of their experiences with the "playing" (investigative/inductive) and "proving" (deductive) portions of the lesson are posted on board, in columns or Venn diagram-like areas.

Additional vignettes are provided, and students sort vignettes by whether they are more like the "playing" or "proving" thought processes, and why.

We give students the vocabulary -- "inductive" and "deductive" to name those thought processes, and we explain their roles in geometry and mathematics in general. || || || > Deduction is ... || || ||
 * ** 5. Summing Up **
 * Induction is ...
 * Remember we used the tiles not to do a tessellation but to think about the types of thinking and reasoning we used.
 * In deduction the conditions are very important. How about if I changed the conditions so the polygon is not regular? How about if we have no vertices?

=**7.** **Evaluation**=

This section often includes questions that the planning team hopes to explore through this lesson and the post-lesson discussion.