Eighth Grade, Ninth Grade, Tenth Grade
Middle School, Upper School
Core Connections Geometry is the second course in a five-year sequence of college preparatory mathematics courses that starts with Algebra I and continues through Calculus. It aims to formalize and extend the geometry that students have learned in previous courses. It does this by focusing on establishing triangle congruence criteria using rigid motions and formal constructions and building a formal understanding of similarity based on dilations and proportional reasoning. It also helps students develop the concepts of formal proof, explore the properties of two- and three-dimensional objects, work within the rectangular coordinate system to verify geometric relationships and prove basic theorems about circles. Students also use the language of set theory to compute and interpret probabilities for compound events.
On a daily basis, students in Core Connections Geometry use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas.
The course is well balanced between procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and transference). The lessons in the course meet all of the content standards, including the “plus” standards, of Appendix A of the Common Core State Standards for Mathematics. The course embeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.
Key concepts addressed in this course are:
Geometric transformations (reflection, rotation, translation, dilation) and symmetry.
Relationships between figures (such as similarity and congruence) in terms of rigid motions and similarity transformations.
Properties of plane figures.
Proofs of geometric theorems (investigating patterns to make conjectures, and formally proving them).
Using coordinates to prove geometric theorems.
Modeling with geometry.
Measurements of plane figures (such as area, perimeter, and angle measure).
Theorems about circles, including arc lengths and areas of sectors.
Measurements of three-dimensional solids (such as volume and surface area).
Tools for analyzing and measuring right triangles, general triangles, and complex shapes (such as the Pythagorean Theorem, trigonometric ratios, and the Laws of Sines and Cosines).
Geometric constructions (with compass and straightedge).
Using algebra to formulate and solve equations arising from geometric situations.
Probability (independence and conditional probability, compound events, expected value, and permutations and combinations).