Samantha and I took a little bit of time to get acquainted. I looked at her book and the previous session summaries to gain a better idea of where to start with her. We defined polygons, and named several different types of polygons. We discussed the different types of quadrilaterals. Samantha made the statement "If you cut a rectangle in half, you will get 2 squares." I had her draw a 5" x 3" rectangle, and then draw a line to divide it into 2 even shapes. She measured and discovered that the 2 new shapes were in fact NOT squares. She conjectured that a rectangle with one side twice the length of the other side can be divided into 2 squares.
We also looked at triangles. I taught her the Triangle Congruency Theorem, including ASA, SSS, and SAS. She used them to decide if two triangles were congruent to each other. We talked about the angles in a triangle adding to 180 degrees, and the Exterior Angle Theorem, which states that the remote interior angles of a triangle add up to the measure of the exterior angle. We started using these theorems to find missing angles and variables.
Samantha has a good grasp on her basic Algebra skills, and was interested in the material. She appreciated that I wrote notes and examples on paper for her. We started a notebook for her to keep notes and assignments in order.