Matemáticas, lógica y resolución de problemas en la escuela secundaria: transformaciones rígidas y congruencia

This is the first course in a series of small group classes for middle school math. These classes are a hybrid of individualized learning and traditional classes. Each section has no more than five learners which provides a foundation for strong relationships, social-emotional learning, and truly individualized instruction. 
This series is based on an accelerated math curriculum that covers three years of content, aligned to Common Core Math Standards, over the course of two school years. It is perfect for students beginning middle school and students who need to catch up. The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs. This process prepares students well who may seek advanced mathematics in high-school or beyond. Students will complete a math notebook In the style of a main lesson book to help with recall and long-term retention.
In this unit, students will learn to understand types of transformation including reflection, rotation, and translation and be able to recognize determining factors of each transformation. They will learn to differentiate rigid transformations.
 Students will learn to identity corresponding sides and angles and recognize the preservation of information throughout transformations. Students will use these to generate and draw images on and off the coordinate plane. Students will reason with congruence and justify claims. They will investigate the qualities of side lengths and angle measurements which create unique and multiple triangles or which can not create a triangle.  Students will study and apply angle relationships including the terms complementary, supplementary, vertical and unique. 

Week 1: We will begin with a pre-unit readiness check to refresh pre-requisite skills and introduce key ideas of the unit. Then we will practice describing ways figures can move in the plane and justify relationships between angles and rays. We will introduce vocabulary including translations, rotations, and reflection. We will focus on what happens to the coordinates of points as we transform figures. 
Week 2: We will transform polygons based on the coordinates of their vertices and rotate figures in a plane. We will compare measurements before and after translations, rotations, and reflections. We will transform parallel lines and discuss vertical angles. We will find missing side lengths and angle measures using the properties of rigid transformation. 
Week 3: We will begin with a mid-unit check in to gauge understanding and secure new skills. We will introduce the ideas of congruence and reason with figures. We will begin working with alternate interior angles, complementary, and supplementary. We will also work with transversals.  We will use our new found angle skills to explore triangles. 
Week 4: We will continue working with triangle proofs relating to angles and sides. We will explain the relationship between lines and triangles. We will use a compass to build shapes and justify ideas about sets of lines and angles which can not construct specific shapes. We will work on identifying triangles based on congruence theories. We will rotate and tessellate shapes on plane to create art. We will finish with a end-of-unit check in.