Standard+1

**Standard 1** ** Teachers know the subjects they are teaching. ** // The teacher understands the central concepts, tools of inquiry, and structures of the disciplines she or he teaches and can create learning experiences that make these aspects of subject matter meaningful for pupils //.


 * Evidence:** Geometer’s Sketchpad Lesson on Composite Reflections

Lesson plan for teachers:

Instructions for students:


 * Rationale:** When reading the description of Standard 1, the words “tools of inquiry” stuck out to me. To me, inquiry is a way for students to investigate a particular mathematical concept to gain knowledge and insight. Geometer’s Sketchpad is a program that I use to allow students a chance to make observations, conjectures, and conclusions about what we are studying. In this lesson, students are building on their prior knowledge of single reflections and their properties. Students will be able to see how the properties of reflections stay consistent even as the shapes and lines can change. I have created some of these lessons to align with the common core standards that understanding transformations can help in students’ understanding of congruency. Because of this, I have rearranged the curriculum so that the unit on transformations is done before congruency. I found when I did this last year; students were much better at identifying the congruency statements and were able to see connections with congruent figures.

Doing a lesson on Geometer’s Sketchpad changes the way I teach. I am able to facilitate their learning with a more one-on-one approach as questions arise. It also gives students more responsibility and ownership in their own learning.


 * KSD:**
 * 1.K.1 The teacher understands the major concepts, assumptions, debates, processes of inquiry, and ways of knowing that are central to the discipline(s) s/he teaches.**

The major concept addressed in this lesson is that all congruent figures can be found by doing a composite of reflections. This is vital to understanding and performing proofs of congruency later on.


 * 1.S.4 The teacher engages students in generating knowledge and testing hypotheses according to the methods of inquiry and standards of evidence used in the discipline.**

This lesson allows students to generate ideas and come up with their own conclusions. The questioning process allows them to lay a foundation for future use with congruent figures.


 * 1.D.3 The teacher has enthusiasm for the discipline(s) s/he teaches and sees connections to everyday life.**

The students were able to see an application for reflections in their previous lesson involving miniature golf.